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ANSYS Mechanical APDL Feature Archive

Release 14.0ANSYS, Inc.November 2011Southpointe

275 Technology DriveCanonsburg, PA 15317 ANSYS, Inc. is

certified to ISO9001:2008.

[email protected]://www.ansys.com(T) 724-746-3304(F) 724-514-9494

Copyright and Trademark Information

© 2011 SAS IP, Inc. All rights reserved. Unauthorized use, distribution or duplication is prohibited.

ANSYS, ANSYS Workbench, Ansoft, AUTODYN, EKM, Engineering Knowledge Manager, CFX, FLUENT, HFSS and anyand all ANSYS, Inc. brand, product, service and feature names, logos and slogans are registered trademarks ortrademarks of ANSYS, Inc. or its subsidiaries in the United States or other countries. ICEM CFD is a trademark usedby ANSYS, Inc. under license. CFX is a trademark of Sony Corporation in Japan. All other brand, product, serviceand feature names or trademarks are the property of their respective owners.

Disclaimer Notice

THIS ANSYS SOFTWARE PRODUCT AND PROGRAM DOCUMENTATION INCLUDE TRADE SECRETS AND ARE CONFID-ENTIAL AND PROPRIETARY PRODUCTS OF ANSYS, INC., ITS SUBSIDIARIES, OR LICENSORS. The software productsand documentation are furnished by ANSYS, Inc., its subsidiaries, or affiliates under a software license agreementthat contains provisions concerning non-disclosure, copying, length and nature of use, compliance with exportinglaws, warranties, disclaimers, limitations of liability, and remedies, and other provisions. The software productsand documentation may be used, disclosed, transferred, or copied only in accordance with the terms and conditionsof that software license agreement.

ANSYS, Inc. is certified to ISO 9001:2008.

U.S. Government Rights

For U.S. Government users, except as specifically granted by the ANSYS, Inc. software license agreement, the use,duplication, or disclosure by the United States Government is subject to restrictions stated in the ANSYS, Inc.software license agreement and FAR 12.212 (for non-DOD licenses).

Third-Party Software

See the legal information in the product help files for the complete Legal Notice for ANSYS proprietary softwareand third-party software. If you are unable to access the Legal Notice, please contact ANSYS, Inc.

Published in the U.S.A.

Table of Contents

About This Archive .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viiI. Legacy Features . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

1. Piping Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31.1. What the Piping Commands Can Do for You .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31.2. Modeling Piping Systems with Piping Commands .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

1.2.1. Specify the Jobname and Title ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41.2.2. Set Up the Basic Piping Data .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41.2.3. Define the Piping System's Geometry .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

1.2.3.1. Review and Modify Your Piping Model ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51.3. Example Piping Model Input .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

2. Subroutines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92.1. Creep Subroutine UserCr .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92.2. Subroutine UserPL (Writing Your Own Plasticity Laws) ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102.3. Subroutine UserVisLaw (Defining Viscosity Laws) ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122.4. Subroutine usflex (Computes the flexibility factor for PIPE16 and PIPE18) ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

3. Restarting a Direct Coupled-Field Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153.1. Singleframe Restart ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

3.1.1. Singleframe Restart Requirements .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153.1.2. Singleframe Restart Procedure .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 173.1.3. Restarting a Nonlinear Analysis From an Incompatible Database .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

3.1.3.1. Re-establishing Boundary Conditions .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 194. Partial Solution Procedure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

4.1. Partial Inertia Relief Calculations .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 214.2. Comparison of Linear Perturbation and Partial Solution Procedures .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 224.3. Surface Solution .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

II. Legacy Commands . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25III. Legacy Elements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75

BEAM4: 3-D Elastic Beam ..... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77CONTAC12: 2-D Point-to-Point Contact ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91PIPE16: Elastic Straight Pipe .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99PIPE18: Elastic Curved Pipe .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109PLANE42: 2-D Structural Solid .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119SOLID45: 3-D Structural Solid .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127CONTAC52: 3-D Point-to-Point Contact ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135PIPE59: Immersed Pipe or Cable .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143SHELL63: Elastic Shell .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 161PLANE82: 2-D 8-Node Structural Solid .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 171SOLID92: 3-D 10-Node Tetrahedral Structural Solid .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 179SOLID95: 3-D 20-Node Structural Solid .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 185

IV. Legacy Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1931. Archived Theory Element Library . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 195

1.1. BEAM4 - 3-D Elastic Beam ..... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1951.1.1. Stiffness and Mass Matrices .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1951.1.2. Gyroscopic Damping Matrix ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1991.1.3. Pressure and Temperature Load Vector ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1991.1.4. Local to Global Conversion .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1991.1.5. Stress Calculations .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 201

1.2. CONTAC12 - 2-D Point-to-Point Contact ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2031.2.1. Element Matrices .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2031.2.2. Orientation of the Element .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 205

iiiRelease 14.0 - © SAS IP, Inc. All rights reserved. - Contains proprietary and confidential information

of ANSYS, Inc. and its subsidiaries and affiliates.

1.2.3. Rigid Coulomb Friction .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2051.3. PIPE16 - Elastic Straight Pipe .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 206

1.3.1. Assumptions and Restrictions .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2071.3.2. Stiffness Matrix ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2071.3.3. Mass Matrix ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2081.3.4. Gyroscopic Damping Matrix ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2081.3.5. Load Vector ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2091.3.6. Stress Calculation .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 212

1.4. PIPE18 - Elastic Curved Pipe .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2171.4.1. Other Applicable Sections .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2181.4.2. Stiffness Matrix ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2181.4.3. Mass Matrix ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2211.4.4. Load Vector ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2211.4.5. Stress Calculations .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 222

1.5. PLANE42 - 2-D Structural Solid .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2221.5.1. Other Applicable Sections .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 223

1.6. SOLID45 - 3-D Structural Solid .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2231.6.1. Other Applicable Sections .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 224

1.7. CONTAC52 - 3-D Point-to-Point Contact ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2241.7.1. Other Applicable Sections .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2251.7.2. Element Matrices .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2251.7.3. Orientation of Element .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 226

1.8. PIPE59 - Immersed Pipe or Cable .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2261.8.1. Overview of the Element .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2271.8.2. Location of the Element .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2271.8.3. Stiffness Matrix ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2281.8.4. Mass Matrix ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2291.8.5. Load Vector ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2291.8.6. Hydrostatic Effects ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2301.8.7. Hydrodynamic Effects ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2321.8.8. Stress Output .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 232

1.9. SHELL63 - Elastic Shell .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2341.9.1. Other Applicable Sections .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2351.9.2. Foundation Stiffness .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2351.9.3. In-Plane Rotational Stiffness .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2361.9.4. Warping .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2361.9.5. Options for Non-Uniform Material ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2371.9.6. Extrapolation of Results to the Nodes .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 239

1.10. PLANE82 - 2-D 8-Node Structural Solid .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2391.10.1. Other Applicable Sections .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2391.10.2. Assumptions and Restrictions .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 239

1.11. SOLID92 - 3-D 10-Node Tetrahedral Structural Solid .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2401.11.1. Other Applicable Sections .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 240

1.12. SOLID95 - 3-D 20-Node Structural Solid .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2411.12.1. Other Applicable Sections .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 241

2. Hydrodynamic Loads on Line Elements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2432.1. Wave Theory .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 243

List of Figures

1.1. Order of Degrees of Freedom ..... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 196

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1.2. Force-Deflection Relations for Standard Case .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2051.3. Force-Deflection Relations for Rigid Coulomb Option .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2061.4. Thermal and Pressure Effects ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2111.5. Elastic Pipe Direct Stress Output .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2131.6. Elastic Pipe Shear Stress Output .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2131.7. Stress Point Locations .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2161.8. Mohr Circles .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2161.9. Plane Element .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2182.1. Velocity Profiles for Wave-Current Interactions .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 247

List of Tables

3.1. Restart Information for Nonlinear Analyses .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 164.1. Linear Perturbation vs. Partial Solution Procedures .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 224.2. Output Available via ETABLE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 231.1. Stress Intensification Factors ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2132.1. Wave Theory Table .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 243

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About This Archive

The purpose of this archive is to provide a location for legacy feature, element, theory, and commanddocumentation.

The Mechanical APDL product continues to provide limited support for capabilities documented in thisarchive. In most cases, however, access via the graphical user interface (GUI) is no longer available.

As Mechanical APDL evolves and improves, be aware that ANSYS, Inc. may undocument and discontinuesupport for any legacy capability at a future release.

The following topics are available:

• Part I:Legacy Features (p. 1)

• Part II:Legacy Commands (p. 25)

• Part III:Legacy Elements (p. 75)

• Part IV:Legacy Theory (p. 193)

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Legacy Features

Following is the archived documentation for legacy Mechanical APDL features.

Chapter 1: Piping Models

The ANSYS Multiphysics, ANSYS Mechanical, ANSYS Structural, and ANSYS Professional products offera group of commands that enable you to model piping systems and their loads in terms of conventionalpiping input data, instead of in terms of standard ANSYS direct-generation modeling operations. Asyou input piping commands, the program internally converts your piping data to direct-generationmodel data, then stores the converted information in the database. Once this information is stored, youcan list it, display it, modify it, redefine it, etc., using any of the standard direct-generation commands.

The piping system modeling methods described here apply to straight-pipe PIPE16 and curved-pipePIPE18 elements. (Both elements are described in Part III: Legacy Elements.)

The following topics concerning piping models are available:1.1.What the Piping Commands Can Do for You1.2. Modeling Piping Systems with Piping Commands1.3. Example Piping Model Input

1.1. What the Piping Commands Can Do for You

Some special features of the piping module are:

• Creates a line model of a piping network using straight-pipe PIPE16 and curved-pipe PIPE18 ele-ments. (Both elements are described in Part III:Legacy Elements (p. 75).) Node and element geometryare defined in terms of incremental run lengths and bend radii, rather than in terms of absolutecoordinates.

• Automatically calculates tangency points for bends.

• Relates standard piping designations (such as nominal diameter and schedule) to geometric values.

• Assigns pipe specifications to element real constants.

• Calculates and assigns flexibility and stress intensification factors based on the pressures and thetemperatures specified in the pipe module before the creation of the piping elements as appropriatefor each element type. The flexibility factors are not be changed automatically if the pipe pressuresor temperatures are subsequently revised.

• Determines drag pressure loads from a pressure vs. height relationship.

1.2. Modeling Piping Systems with Piping Commands

Building a model with the piping commands consists of three primary tasks:1.2.1. Specify the Jobname and Title1.2.2. Set Up the Basic Piping Data1.2.3. Define the Piping System's Geometry

All piping commands referenced here are described in Part II:Legacy Commands (p. 25).

Other actions required for a piping system analysis include applying additional loads (D, F, etc.), obtainingthe solution, and reviewing the results. See the Basic Analysis Guide for more information.

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1.2.1. Specify the Jobname and Title

Perform these steps at the Begin level.

1. Specify the jobname you want to use for all files that are subsequently created by the analysis(/FILNAME).

2. Write an analysis file (/TITLE).

3. Issue a "reminder" to yourself about the system of units you intend to use (/UNITS).

This step does not convert data from one system of units to another.

1.2.2. Set Up the Basic Piping Data

Set up the basic piping data as follows:

1. Enter PREP7 (/PREP7).

2. Define the material properties for all materials referenced by the model (MP, MPTEMP, etc.).

3. Select a system of units, if other than consistent (PUNIT).

The PUNIT command determines how the program interprets the data input for the PDRAG,BRANCH, RUN, BEND, MITER, REDUCE, VALVE, BELLOW, FLANGE, PSPRNG, PGAP, /PSPEC,PINSUL, and PCORRO commands. The difference between PUNIT and the /UNITS commandis that PUNIT affects how the program behaves, whereas /UNITS does not.

4. Define the pipe specifications. These specifications are applied to the elements as they are gener-ated via the RUN command.

a. Define pipe material and dimensions (PSPEC).

b. Define the contained fluid density for a piping run (PFLUID).

c. Define the external insulation constants in a piping run (PINSUL).

d. Specify the allowable exterior corrosion thickness for a piping run (PCORRO).

5. Select the piping analysis standard (POPT).:

The program calculates and assigns flexibility and stress intensification factors for curvedpipe elements based on the pressures and the temperatures specified in the pipe modulebefore the creation of the piping elements as appropriate for each element type. The flexib-ility factors and stress intensification factors are not changed retroactively if the pipe pressuresor temperatures are subsequently revised.

6. Select the pipe loadings.

a. Define the pipe wall temperatures in a piping run (PTEMP).

b. Define the internal pressure for a piping run (PPRES).

c. Define the external fluid drag loading for a piping run (PDRAG).

1.2.3. Define the Piping System's Geometry

Define the basic skeleton layout of your piping model as follows.

1. Specify the starting point of your piping system (BRANCH).

2. Follow up with a series of RUN commands to define incremental "straight" runs of pipe.

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Pipe elements are generated "straight" in the active coordinate system. Each RUN commanduses length dimensions in the format specified by the PUNIT command to generate a nodeand a PIPE16 element (along with its real constants, material properties, and loads).

3. Insert bends and other components (tees, valves, reducers, flanges, bellows, and spring restraints)into the model at existing nodes that are shared by two or more existing pipe elements. Theprogram automatically updates your model's geometry to account for the inserted components.Inserted pipe components take their specifications and loadings from the adjacent straight pipes.

• To define a bend in a piping run, issue the BEND command.

• To define a mitered bend in a piping run, issue the MITER command.

• To define a tee in a piping run, issue the TEE command.

• To define a valve in a piping run, issue the VALVE command.

• To define a reducer in a piping run, issue the REDUCE command.

• To define a flange in a piping run, issue the FLANGE command.

• To define a bellows in a piping run, issue the BELLOW command.

• To define a spring constraint in a piping run, issue the PSPRNG command.

• To define a spring-gap constraint in a piping run, issue the PGAP command.

Another BRANCH command defines the junction point from which another run of pipe branches off ofthe previously defined run. Subsequent RUN commands define, in incremental fashion, another run of"straight" pipe elements, starting from the last junction point.

1.2.3.1. Review and Modify Your Piping Model

When you have completed piping data input, you can review the information that has been stored inthe database via standard listing and display commands (NLIST, NPLOT, ELIST, EPLOT, SFELIST,BFELIST, etc.).

If necessary, you can modify the data using standard procedures for revising your model and your loads.See "Loading" in the Basic Analysis Guide for details.

1.3. Example Piping Model Input

The following example input shows how to model this piping system:



Example Piping Model Input

End of first run

Start of second run

(second BRANCH)

Starting point (first BRANCH)

End of second run

MITER

Hangers (PSPRNG)BEND

TEE

Y

Z

X

!! Sample piping data input!/FILNAM,EXAMPLE/TITLE, EXAMPLE PIPING INPUT/UNITS,BIN ! A reminder that consistent units are U. S. Customary inches!/PREP7 ! Define material properties for pipe elementsMP,EX,1,30e6MP,PRXY,1,0.3MP,ALPX,1,8e-6 MP,DENS,1,.283 PUNIT,1 ! Units are read as ft+in+fraction and converted to ! decimal inchesPSPEC,1,8,STD ! 8" standard pipePOPT,B31.1 ! Piping analysis standard: ANSI B31.1PTEMP,200 ! Temperature = 200°PPRES,1000 ! Internal pressure = 1000 psiPDRAG,,,-.2 ! Drag = 0.2 psi in -Z direction at any height (Y)BRANCH,1,0+12,0+12 ! Start first pipe run at (12",12",0")RUN,,7+4 ! Run 7'-4" in +Y directionRUN,9+5+1/2 ! Run 9'-5 1/2" in +X directionRUN,,,-8+4 ! Run 8'-4" in -Z directionRUN,,8+4 ! Run 8'-4" in +Y direction/PNUM,NODE,1/VIEW,1,1,2,3 EPLOT ! Identify node number at which 2nd run startsBRANCH,4 ! Start second pipe run at node 4RUN,6+2+1/2 ! Run 6'-2 1/2" in +X directionTEE,4,WT ! Insert a tee at node 4/PNUM,DEFA/PNUM,ELEM,1EPLOT ! Identify element numbers for bend and miter insertsBEND,1,2,SR ! Insert a "short-radius" bend between elements 1 and 2MITER,2,3,LR,2 ! Insert a two-piece miter between elements 2 and 3/PNUM,DEFA/PNUM,NODE,1! Zoom in on miter bend to identify nodes for spring hangers/ZOOM, 1, 242.93 , 206.62 , -39.059 , 26.866 PSPRNG,14,TRAN,1e4,,0+12 ! Insert Y-direction spring at node 14PSPRNG,16,TRAN,1e4,,0+12 ! Insert Y-direction spring at node 16



! List and display interpreted input data/AUTO/PNUM,DEFA EPLOTNLISTELISTSFELISTBFELIST!

Although two hangers are provided, more restraints are needed before proceeding to the solution.



Example Piping Model Input


Chapter 2: Subroutines

2.1. Creep Subroutine UserCr

In contrast to the UserCreep subroutine, the UserCr subroutine requires that you specify the creepstrain tensor. A detailed explanation of this subroutine follows.

*deck,usercr USERSDISTRIB subroutine usercr (elem,intpt,mat,ncomp,kfirst,kfsteq,e,posn,d, x proptb,timval,timinc,tem,dtem,toffst,fluen,dfluen,epel,epcrp, x statev,usvr,delcr)cc *** primary function: allow users to write their own creep laws.c this logic is accessed with c6 = 100c *** secondary function: demonstrate the use of user-written creep lawscc *** Notice - This file contains ANSYS Confidential information ***ccc *** copyright(c) 2009 SAS IP, Inc. All rights reserved.c *** ansys, inc.cc input arguments:c variable (type,sze,intent) descriptioncc elem (int,sc,in) - element number (label)c intpt (int,sc,in) - element integration point numberc mat (int,sc,in) - material reference numberc ncomp (int,sc,in) - no. of stress/strain components (1,4 or 6)c 1 - xc 4 - x,y,z,xyc 6 - x,y,z,xy,yz,xzc kfirst (int,sc,in) - 1 if first time through, 0 otherwisec (useful for initializing state variablesc to a non-zero value)c kfsteq (int,sc,in) - 1 if first equilibrium iteration of ac substep, 0 otherwiseccc e (dp,sc,in) - elastic young'S MODULUSc posn (dp,sc,in) - poisson'S RATIOc d (dp,ar(ncomp,ncomp),in)- elastic stress-strain matrixc proptb (dp,ar(72),in) - material properties input on tb commandsc (do not use proptb(13), as it is used elsewhere)c timval (dp,sc,in) - current time valuec timinc (dp,sc,in) - time increment over this substepc tem (dp,sc,in) - temperature at the end of this substepc dtem (dp,sc,in) - temperature increment over this substepc toffst (dp,sc,in) - temperature offset from absolute zeroc fluen (dp,sc,in) - fluence at the end of this substepc dfluen (dp,sc,in) - fluence increment over this substepcc epel (dp,ar(ncomp),inout)- elastic strainc epcrp (dp,ar(ncomp),inout)- creep strain from previous substepc statev (dp,ar(ncomp*5+2),inout)- state variables from previous c (converged) substep. This variable is forc explicit creep only and refers to a c different internal variable than that c defined by TB,stat which is used by c implicit creep (usercreep) and usermat.c usvr (dp,ar(nuval,nintp),inout)- additional state variables from



c previous equilibrium iteration (savedc if the nsvr command is used)ccc output arguments:c variable (type,sze,intent) descriptioncc epel (dp,ar(ncomp),inout)- elastic strain adjusted for creep incrementc epcrp (dp,ar(ncomp),inout)- updated creep strainc statev (dp,ar(ncomp*5+2),inout)- updated state variablesc usvr (dp,ar(nuval,nintp),inout)- updated additional state variablesc delcr (dp,sc,out) - equivalent creep strain increment (usedc for creep ratio calculation)cc fortran parameters (to be defined by the user):c variable (type) descriptionc nuval (int) - number of additional state variables perc integration pointc nintp (int) - maximum number of integration points ofc an element to be used with this routinec (14 is the maximum)c note: nuval x nintp = nstv(on nsvr command); cannot exceed 840!cc internal variables:c variable (type,sze) descriptionc con (dp,sc) - temporary variablec del (dp,ar(6)) - creep strain incrementsc epet (dp,sc) - equivalent elastic strain (before creep)c ept (dp,ar(6)) - total strainc eptot (dp,sc) - equivalent total strain, elastic + creepc sigen (dp,sc) - equivalent stress (before creep)c temabs (dp,sc) - temperature on the absolute scalec

2.2. Subroutine UserPL (Writing Your Own Plasticity Laws)

ANSYS, Inc. recommends using current-technology elements and the UserMat subroutine for definingyour own material model. However, if you are using a legacy element type and wish to define a plasticityor viscoplasticity material model, the UserPL subroutine is applicable to legacy elements SOLID62 andSOLID65.

*deck,userpl USERSDISTRIB subroutine userpl (elem,intpt,mat,ncomp,kfirst,kfsteq,e,nu,dens, x prop,d,ktform,timval,timinc,tem,dtem,toffst,flu,dflu,epel,eppl, x statev,usvr,epeq,plwork,sigepl,sigrat,depeq,dt)cc *** primary function: allow users to write their own plasticity laws.c this logic is accessed with tb,user.c the below demonstration logic is the same as usingc tb,bkin, without adaptive descent (nropt,,,off).c Other plasticity rules may require internal c iterations and/or the more general definition ofc plasticity theory, discussed in the Theoryc Manual.c *** secondary function: demonstrate the use of user-written plasticity lawsc in this routine:c a. update the nonlinear strain historyc b. compute the material tangent matrix if requestedcc *** Notice - This file contains ANSYS Confidential information ***ccc *** ansys(r) copyright(c) 2009c *** ansys, inc.cc input arguments:c variable (type,sze,intent) descriptioncc elem (int,sc,in) - element number (label)



c intpt (int,sc,in) - element integration point numberc mat (int,sc,in) - material reference numberc ncomp (int,sc,in) - no. of stress/strain components (1,4 or 6)c 1 - xc 4 - x,y,z,xyc 6 - x,y,z,xy,yz,xzc kfirst (int,sc,in) - 1 if first time through, 0 otherwisec (useful for initializing state variablesc to a non-zero value)c kfsteq (int,sc,in) - 1 if first equilibrium iteration of ac substep, 0 otherwisecc e (dp,sc,in) - average elastic modulusc nu (dp,sc,in) - average poisson ratioc dens (dp,sc,in) - current material density (mass/volume)c prop - linear material property arrayc (dp,ar(9),in) (ex,ey,ez, gxy,gyz,gxz, nuxy,nuyz,nuxz)c (dp,ar(1),in) if ncomp=1 (ex)c d (dp,ar(ncomp,ncomp),in)- elastic stress-strain matrixc ktform (int,sc,in) - request key for tangent matrix formationc (=1, form tangent .ne.1, do not form)cc timval (dp,sc,in) - current time valuec timinc (dp,sc,in) - time increment over this substepcc tem (dp,sc,in) - temperature at the end of this substepc dtem (dp,sc,in) - temperature increment over this substepc toffst (dp,sc,in) - temperature offset from absolute zeroc flu (dp,sc,in) - fluence at the end of this substepc dflu (dp,sc,in) - fluence increment over this substepcc epel (dp,ar(ncomp),inout)- modified total strain (trial strain)c epel = eptot - eppl - eptherm - ...c if a large strain analysis, epel isc rotation neutralized and is the henckyc (i.e. log) strainc eppl (dp,ar(ncomp),inout)- plastic strain from previous substepcc statev (dp,ar(ncomp,6),inout)- state variables from previous substepc usvr (dp,ar(nuval,nintp),inout)- additional state variables fromc previous equilibrium iteration (savedc if the nsvr command is used)cc epeq (dp,sc,inout) - effective plastic strain from prev substepc plwork (dp,sc,inout) - accumulated plastic work from prev substepcc output arguments:c variable (type,sze,intent) descriptioncc epel (dp,ar(ncomp),inout)- elastic strainc eppl (dp,ar(ncomp),inout)- updated plastic straincc statev (dp,ar(ncomp,6),inout)- updated state variablesc usvr (dp,ar(nuval,nintp),inout)- updated additional state variablescc epeq (dp,sc,inout) - updated effective plastic strainc plwork (dp,sc,inout) - updated accumulated plastic workcc sigepl (dp,sc,out) - stress value on stress-strain curve at epeqc sigrat (dp,sc,out) - ratio of trial stress to yield stressc depeq (dp,sc,out) - increment in plastic strain (equivalent)c (used for auto time stepping - time stepc is reduced if it exceeds .05)cc dt (dp,ar(ncomp,ncomp),out)- material tangent moduluscc fortran parameters (to be defined by the user):c variable (type) descriptionc numinp (int) - number of data items in the user-definedc data table (tbdat commands)c nuval (int) - number of additional state variables perc integration point



Subroutine UserPL (Writing Your Own Plasticity Laws)

c nintp (int) - maximum number of integration points ofc an element to be used with this routinec (14 is the maximum)c note: nuval x nintp = nstv(on nsvr command); cannot exceed 840!cc internal variables:c variable (type,sze) descriptionc b (dp,ar(6,6)) - 2nd derivative of the yield functionc c (dp,ar(6,12)) - part of deffc con (dp,sc) - temporary variablec deppl (dp,ar(6)) - plastic strain incrementc dfds (dp,ar(6)) - derivative of the yield function (normal)c dlamb (dp,sc) - plastic multiplierc ep (dp,ar(6)) - shifted strainc epshfo (dp,ar(6)) - initial shift strain (center of the yield surf)c epshft (dp,ar(6)) - shift strain (center of the yield surface)c et (dp,sc) - tangent modulus (stress/total strain)c h (dp,sc) - plastic tangent modulus (stress/plastic strain)c n2 (int,sc) - ncomp squared, ncomp*ncompc seqtr (dp,sc) - equivalent (von mises) trial stressc sigtr (dp,ar(6)) - trial stressc sigy (dp,sc) - yield stressc vect (dp,ar(6)) - temporary vectorc

2.3. Subroutine UserVisLaw (Defining Viscosity Laws)

*deck,UserVisLaw USERSDISTRIB subroutine UserVisLaw x (dudx,dudy,dudz, x dvdx,dvdy,dvdz, x dwdx,dwdy,dwdz, x u,v,w,x,y,z,kGeom, x Vis,Temp,Tref,Pres,Pref,Cf, x MFrac,DfNSpec,Time,VisNew,toffst)

C Primary function: to provide a user defined viscosityC relationship in terms of the following:C pressure, temperature, position, time,C velocity, & velocity-gradientC This routine is for use with the FLOTRAN C elements, Fluid141 and Fluid142 only.CC In order to activate this subroutine the user must issueC FLDA,PROT,VISC,USRV command.CC In addition the initial value of viscosity must be specified viaC FLDA,PROP,IVIS,value. This value is not available in this routine.CC Optionally the user may specify 4 additional coefficientsC which are available in this routine by the commands:C FLDA,NOMI,VISC,value1C FLDA,COF1,VISC,value1C FLDA,COF2,VISC,value2C FLDA,COF3,VISC,value3Cc *** copyright(c) 2009 SAS IP, Inc. All rights reserved.c *** ansys, inc.CC input arguments:C variable (typ,siz,intent) descriptionC dudx (dp,sc,in) velocity gradient componentC dudy (dp,sc,in) velocity gradient componentC dudz (dp,sc,in) velocity gradient componentC dvdx (dp,sc,in) velocity gradient componentC dvdy (dp,sc,in) velocity gradient componentC dvdz (dp,sc,in) velocity gradient componentC dwdx (dp,sc,in) velocity gradient componentC dwdy (dp,sc,in) velocity gradient componentC dwdz (dp,sc,in) velocity gradient component



C u (dp,sc,in) velocity componentC v (dp,sc,in) velocity componentC w (dp,sc,in) velocity componentC x (dp,sc,in) position componentC y (dp,sc,in) position componentC z (dp,sc,in) position componentC kGeom (int,sc,in) analysis typeC Vis (dp,sc,in) old viscosityC Temp (dp,sc,in) absolute temperatureC Tref (dp,sc,in) reference temperature (Absolute also) C Pres (dp,sc,in) pressureC Pref (dp,sc,in) reference pressureC Cf (dp,ar(4),in) input coefficientsC Mfrac (dp,ar(6),in) species mass fractionsC DfNSpec (int,sc,in) defined number of speciesC Time (dp,sc,in) timeC toffst (dp,sc,in) Temperature offset for absolute scale.C output arguments:C variable (typ,siz,intent) descriptionC VisNew (dp,sc,out) new viscosityC

2.4. Subroutine usflex (Computes the flexibility factor for PIPE16 and

PIPE18)

Legacy pipe elements PIPE16 and PIPE18 are described in Part III:Legacy Elements (p. 75).

*deck,usflex USERSDISTRIB subroutine usflex (etype,elem,rvrm,kff,prs,ex, flexi,flexo)c *** primary function: to (re)compute the flexibility factor c for pipe16, pipe17, pipe18, and pipe60c this is accessed by inputting the flexibility factorc as any negative number.c *** secondary functions: nonecc *** Notice - This file contains ANSYS Confidential information ***cc *** copyright(c) 2009 SAS IP, Inc. All rights reserved.c *** ansys, inc.cc typ=int,dp,log,chr,dcp siz=sc,ar(n) intent=in,out,inoutcc input arguments:c variable (typ,siz,intent) descriptionc etype (int,sc,in) - pipe element type (16, 17, 18 or 60)c elem (int,sc,in) - element numberc rvrm (dp,ar(*),in) - real constantsc kff (int,sc,in) - keyopt for flexibility factorc (not used for pipe16 or pipe17)c prs (dp,ar(5),in) - pressuresc ex (dp,sc,in) - young's Modulusc flexi (dp,sc,inout) - effective in-plane flexibility factorc flexo (dp,sc,inout) - effective out-of-plane flexibility factorc (not used for pipe16 or pipe17)cc output arguments:c variable (typ,siz,intent) descriptionc flexi (dp,sc,inout) - effective in-plane flexibility factorc flexo (dp,sc,inout) - effective out-of-plane flexibility factorc (not used for pipe16 or pipe17)c



Subroutine usflex (Computes the flexibility factor for PIPE16 and PIPE18)


Chapter 3: Restarting a Direct Coupled-Field Analysis

To restart a direct coupled-field analysis, ANSYS Inc. recommends using a singleframe restart. Directcoupled-field analyses use a coupled-field element containing all necessary degrees of freedom. Seethe Coupled-Field Analysis Guide for more information on this type of coupled-field analysis.

3.1. Singleframe Restart

A traditional restart requires that certain files from the initial run of the job are present, and requiresthat you make any changes to the input before the SOLVE command.

3.1.1. Singleframe Restart Requirements

When restarting from a static or full transient analysis, the following files must be available from theinitial run:

• Jobname.DB - The database file saved immediately after the initial SOLVE. If you save the databaseat any point later in the analysis, boundary conditions and other variables may be changed fromtheir initial values, which would prevent the restart from running properly. (For non-convergedsolutions, the database file is saved automatically; see the note below.)

• Jobname.EMAT - Element matrices (if created).

• Jobname.ESAV or .OSAV - Element saved data (.ESAV) or old element saved data (.OSAV).Jobname.OSAV is required only if the .ESAV file is missing, incomplete, or otherwise corruptedbecause of a diverging solution; because the displacement limit was exceeded; or because of anegative pivot (see Table 3.1: Restart Information for Nonlinear Analyses (p. 16)). It is written if KSTOPis set to 1 (default) or 2 on the NCNV command, or if automatic time stepping is active. If the.OSAV file is required, you must rename it as Jobname.ESAV before restarting the analysis.

• Results file - Not required, but if available, results from the restart run will be appended to it withthe proper, sequential load step and substep numbers. If the initial run terminated because thenumber of results sets on the results file were exceeded, you will need to rename the initial resultsfile to a different name before restarting. To do so, issue the /ASSIGN command (Utility Menu>

File> ANSYS File Options).

When restarting from a mode-superposition transient analysis, the following files must be availablefrom the initial run:

• Jobname.DB -- The database file saved immediately after the initial solve operation (SOLVE). If yousave the database at any point later in the analysis, boundary conditions and other variables may bechanged from their initial values, which would prevent the restart from running properly.

• Jobname.RDSP -- The reduced displacement file with information from the last substep of the lastload step needed for restart.



Note

In a nonlinear analysis, if the program terminates due to nonconvergence, time limits, theabort file (Jobname.ABT ), or other program-detected failure, the database is automaticallysaved, and the solution output (Jobname.OUT ) will list the files and other information re-quired for restarting. See also Table 3.1: Restart Information for Nonlinear Analyses (p. 16) fora list of termination causes and the element saved data file needed to restart.

If the files .RDB, .LDHI , or .R nnn/.Mnnn were accidentally created from a previous run,you must delete them before performing a singleframe restart.

In interactive mode, an existing database file is first written to a backup file (Jobname.DBB ).In batch mode, an existing database file is replaced by the current database information withno backup.

Table 3.1 Restart Information for Nonlinear Analyses

Required Corrective ActionElement Saved

Data File

Cause of Termination

Add more load steps at the end of your job.Job-name.ESAV

Normal (i.e., no errors)

Define a smaller time step, change the adaptivedescent option, or take other action to enhance

Job-name.OSAV

Nonconvergence

convergence. Rename Jobname.OSAV as Job-name.ESAV before restarting.

If the solution was converging, allow more equilib-rium equations (NEQIT command).

Job-name.ESAV

Nonconvergence due toinsufficient equilibriumiterations

Increase ITLIM on NCNV command.Job-name.ESAV

Cumulative iterationlimit exceeded (NCNV

command)

None (simply restart the analysis). (If you were run-ning the analysis interactively and you want to re-

Job-name.ESAV

Time limit exceeded(NCNV)

start it from within the same ANSYS session, youmust reset the time limits before attempting therestart.)

(Same as for nonconvergence.)Job-name.OSAV

Displacement limit ex-ceeded (NCNV)

(Same as for nonconvergence.)Job-name.OSAV

Negative pivot

Make whatever changes are necessary to addressthe behavior that caused you to voluntarily termin-ate the analysis.

Job-name.ESAV,Job-name.OSAV

Jobname.ABT

• if solution was con-verging

• if solution was diver-ging



Required Corrective ActionElement Saved

Data File

Cause of Termination

Could indicate a problem - check settings on CN-

VTOL, DELTIM, and NSUBST, or KEYOPT(7) forJob-name.ESAV

Maximum number ofdata sets on the resultsfile exceeded. contact elements. Or, specify larger number of res-

ults allowed on results file [/CONFIG,NRES] before

solution or reduce the number of results to beoutput. Also rename results file (/ASSIGN).

No restart is possible.Not applicable"Killed" job (systembreak), system crash, orsystem time-limit ex-ceeded

Note

Singleframe restart does not support surface-to-surface, node-to-surface, line-to-line, or line-to-surface contact. Use multiframe restart if your model contains any of the following contactelements: CONTA171, CONTA172, CONTA173, CONTA174, CONTA175, CONTA176, CONTA177.

3.1.2. Singleframe Restart Procedure

If you are performing a mode-superposition transient analysis, ANSYS sets up the parameters for asingleframe restart by default.

The procedure for performing the restart analysis is as follows:

1. Enter the ANSYS program and specify the same jobname that was used in the initial run with/FILNAME (Utility Menu> File> Change Jobname).

2. Enter the SOLUTION processor using /SOLU (Main Menu> Solution), then resume the databasefile using RESUME (Utility Menu> File> Resume Jobname.db).

3. Indicate that this is a restart analysis by issuing ANTYPE,,REST (Main Menu> Solution> Restart).

4. Specify revised or additional loads as needed. Modified ramped loads start from their previousvalues. Newly applied ramped loads are ramped from zero; newly applied body loads start frominitial values. Deleted loads which are reapplied are treated as new, not modified, loads. In staticand full transient analyses, surface and body loads to be deleted should be ramped to zero, or tothe initial value, so that the Jobname.ESAV and Jobname.OSAV files are consistent with thedatabase.

For a mode-superposition transient analysis, steps 5, 6, 7, and 8 below do not apply.

Take whatever corrective action is necessary if you are restarting from a convergence failure.

5. If you are running a linear static or linear full transient analysis (with AUTOTS,OFF and the timestepfixed) using the sparse solver, you can realize additional savings by using the KeepFile field onthe EQSLV command. Setting KeepFile = KEEP on your initial solve will force ANSYS to keepall necessary files from the sparse solver in the working directory. In the subsequent singleframerestart, the sparse matrix files are available for reuse in conjunction with KUSE,1 (Main Menu>

Preprocessor> Loads> Other> Reuse LN22 Matrix).

By default, the ANSYS program calculates a new factorized matrix for the first load step of arestart run. By issuing the KUSE,1 command, you can force the program to reuse the existing



Singleframe Restart

matrix at the first solve of the restart and at all subsequent solves, thereby saving a significantamount of computer time. However, you can reuse factorized files such as Jobname.LN xxonly under certain conditions, in particular if the specified DOF constraints have not changedand it is a linear analysis. See the Mechanical APDL Theory Reference for details.

By issuing KUSE,-1, you can cause ANSYS to redo the element matrices. This can be usefulfor debugging analyses and for handling error cases.

Sometimes, you may have to analyze the same model for different constraint conditions, forinstance a quarter-symmetry model with symmetry-symmetry (SS), symmetry-antisymmetry(SA), antisymmetry-symmetry (AS), and antisymmetry-antisymmetry (AA) conditions. In sucha situation, keep the following points in mind:

• All four cases (SS, SA, AS, AA) require a new factorized matrix.

• You can use substructuring (with the constrained nodes as master DOF) to minimizecomputing time. (See "Substructuring" in the Advanced Analysis Techniques Guide.)

6. Initiate the restart solution by issuing the SOLVE command. (See Obtaining the Solution for details.)

7. Repeat steps 4 and 6 for additional load steps, if any. For static and full transient analyses, youcan also use the load step file method to create and solve multiple load steps (not supported formode superposition transient analyses). Use the following commands:

Command(s): LSWRITE

GUI: Main Menu> Preprocessor> Loads> Write LS File

Main Menu> Solution> Write LS File

Command(s): LSSOLVE

GUI: Main Menu> Solution> From LS Files

8. Postprocess as desired, then exit the ANSYS program.

A sample restart input listing is shown below.

! Restart run:/FILNAME,... ! JobnameRESUME/SOLUANTYPE,,REST ! Specify restart of previous analysis!! Specify new loads, new load step options, etc. ! Take appropriate corrective action for nonlinear analyses.!SOLVE ! Initiate restart solutionSAVE ! Optional SAVE for possible subsequent singleframe restartFINISH!! Postprocess as desired!/EXIT,NOSAV

3.1.3. Restarting a Nonlinear Analysis From an Incompatible Database

Sometimes, postprocessing is performed prior to a restart. If you issue SET and SAVE commands duringthis postprocessing, the boundary conditions in your database might be altered and become inconsistentwith those needed for a restart. By default, the program saves your file automatically when you exit. Atthe end of solution, the boundary conditions for the last load step are stored in the database memory.(The database contains only one set of boundary conditions.)



A SET command in POST1 (other than SET,LAST) reads the boundary conditions for the specified resultsinto the database, and overwrites the database stored in memory. If you subsequently save your file orexit, ANSYS overwrites the boundary conditions in the database file with the D's and F's from the currentresults file. However, to perform a restart which ramps boundary conditions from the last solved substep,you need the boundary conditions for the last successfully solved load substep.

3.1.3.1. Re-establishing Boundary Conditions

To re-establish the correct boundary conditions for the restart, first run a "dummy" load step. The pro-cedure is as follows:

1. Rename Jobname.OSAV as Jobname.ESAV .

2. Enter the ANSYS program and specify the same jobname that was used in the initial run with/FILNAME (Utility Menu> File> Change Jobname).

3. Enter the SOLUTION processor using /SOLU (Main Menu> Solution), then resume the databasefile using RESUME (Utility Menu> File> Resume Jobname.db).

4. Indicate that this is a restart analysis by issuing ANTYPE,,REST (Main Menu> Solution> Restart).

5. Respecify boundary conditions from the last substep that was successfully solved. One substepis sufficient since the solution will converge immediately.

6. Issue SOLVE (Main Menu> Solution> Current LS or Main Menu> Solution> Run FLOTRAN).

7. Apply final loads and load step options as desired. You will need to adjust the number of substeps(or time step size) if this load step is a "continuation" of the previous (before the dummy) loadstep. Time step numbering may be altered from your initial intent. Use a small time increment instep 6 if you need to preserve the time step numbering (such as for a transient analysis).

8. Continue the procedure as outlined in Restarting an Analysis.



Singleframe Restart


Chapter 4: Partial Solution Procedure

When you initiate a solution, the ANSYS program goes through a predefined series of steps to calculatethe solution; it formulates element matrices, triangularizes matrices, and so on. The partial solutionprocedure, which is initiated by the PSOLVE command, allows you to exercise each such step individually,completing just a portion of the solution sequence each time. (The PSOLVE command is described inPart II:Legacy Commands (p. 25).) For example, you can stop at the element matrix formulation stepand go down a different path to perform inertia relief calculations. Or, you can stop at the Guyan reduc-tion step (matrix reduction) and go on to calculate reduced eigenvalues.

Some possible uses of the PSOLVE approach are listed below.

• You can use the results of an intermediate solution step as input to another software package oruser-written program.

• If you are interested just in inertia relief calculations or some such intermediate result, the PSOLVEapproach is useful.

The following topics concerning the partial solution procedure are available:4.1. Partial Inertia Relief Calculations4.2. Comparison of Linear Perturbation and Partial Solution Procedures4.3. Surface Solution

4.1. Partial Inertia Relief Calculations

You can do a partial inertia relief calculation using the PSOLVE command (PSOLVE is described inPart II:Legacy Commands (p. 25)). Use the partial solution method as shown in the command input below:

/PREP7 ... ...MP,DENS,... ! Generate model, define density ... ...FINISH

/SOLUD,... ! Specify only minimum no. of constraintsF,... ! Other loadsSF,...OUTPR,ALL,ALL ! Activates printout of all itemsIRLF,1 ! Can also be set to -1 for precise mass and ! load summary only, no inertia reliefPSOLVE,ELFORM ! Calculates element matricesPSOLVE,ELPREP ! Modifies element matrices and calculates ! inertia relief termsIRLIST ! Lists the mass summary and total load summary tablesFINISH

See the OUTPR, IRLF, and IRLIST commands in the Command Reference. See also the PSOLVE commandin Part II:Legacy Commands (p. 25).



4.2. Comparison of Linear Perturbation and Partial Solution Procedures

A partial solution procedure (PSOLVE) is available for performing a mode frequency analysis based onprior linear or nonlinear static or full transient analyses. The procedure can be used when the baseanalysis is a small-deflection analysis, and is similar to a prestressed modal analysis.

However, the partial solution procedure has limitations when compared to the linear perturbationprocedure. Therefore, it is recommended that you use the linear perturbation procedure instead. Thefollowing table outlines the advantages of the linear perturbation procedure.

Table 4.1 Linear Perturbation vs. Partial Solution Procedures

Partial Solution ProcedureLinear Perturbation Procedure

A modal analysis can be done only at the lastsubstep of the last load step of the prior analys-is.

A modal analysis can be done at any time pointduring the prior analysis as long as the multi-frame restart file is made available.

The stress expansion pass is done assuming thematerial property is linear for the entire model.

The stress expansion pass uses linear materialproperties and is always allowed.

If it contains hyperelasticity or another nonlinearmaterial that does not have an easy segregationfrom the linear material property in the con-stitutive law, the stress expansion pass is notallowed.

The stress expansion pass does not have anyeffects of the previous nonlinear analysis; any

All nonlinear effects, including history depend-ent and large rotation effects, are taken into

nonlinear history-dependent properties andlarge rotation effects are lost.

consideration and handled consistently, guaran-teeing correct results for the linear perturbationanalysis.

The nodal coordinate update for the originalmesh is done by an external UPCOORD com-mand (and is optional).

The nodal coordinate update is done automat-ically at the beginning of the second phase ofthe solution; the stress expansion is done basedon the updated geometry.

All prestress and spin-softening effects are in-voked by the commands PSTRES, OMEGA, and

All prestress effects are included automatically(independent of PSTRES, OMEGA, or CMO-

CMOMEGA at the earlier stage of the analysis,as well as in the PSOLVE phase.

MEGA command settings) in the phases of alinear perturbation analysis. Also, even thoughthe base analysis is linear, the prestress effectsare still taken into account in the subsequentlinear perturbation analysis.

For the QRDAMP eigensolver, the solution maybe less accurate compared to the UNSYM eigen-solver.

If the base analysis includes geometric nonlin-earity (NLGEOM,ON), the solution accuracy froma QR damped (MODOPT,QRDAMP) linear per-turbation analysis is greatly improved. The linearperturbation architecture enables this improve-ment on the QRDAMP eigensolver.

Requires knowing ahead of time that aprestressed modal analysis is needed and re-

The EMATWRITE command is unnecessary.

quires the use of the EMATWRITE commandto force writing of the .EMAT file.



Partial Solution ProcedureLinear Perturbation Procedure

Eigenvalue buckling analysis is not supportedEigenvalue buckling analysis is supported. Thebase analysis can a be linear or nonlinear, andcan be a static or full transient analysis.

Full harmonic analysis is not fully supported.Full harmonic analysis is supported, includingstress/strain calculations during the harmonicsubsteps. The contact status from the baseanalysis is frozen and maintained in the fullharmonic phase of the analysis.

4.3. Surface Solution

Surface output is available in the output listing on certain free surfaces of legacy solid elements. A freesurface is a surface not connected to any other element and not having any degree-of-freedom constraintor nodal force load on the surface.

Surface Output Limitations

The following limitations apply to surface output:

• Not valid on surfaces which are not free or for elements having nonlinear material properties

• Not valid for elements deactivated (EKILL) and then reactivated (EALIVE)

• Does not include large-strain effects

The surface output is automatically suppressed if the element has nonlinear material properties. Surfacecalculations are of the same accuracy as the displacement calculations. Values are not extrapolated tothe surface from the integration points but are calculated from the nodal displacements, face load, andthe material property relationships. Transverse surface shear stresses are assumed to be zero. The surfacenormal stress is set equal to the surface pressure. Surface output should not be requested on condensedfaces or on the zero-radius face (center line) of an axisymmetric model.

For 3-D solid elements, the face coordinate system has the x-axis in the same general direction as thefirst two nodes of the face, as defined with pressure loading. The exact direction of the x-axis is on theline connecting the midside nodes or midpoints of the two opposite edges. The y-axis is normal to thex-axis, in the plane of the face.

The following table lists output available via the ETABLE command using the Sequence Numbermethod (Item = SURF). See the appropriate table in the individual element descriptions for definitionsof the output quantities.

Table 4.2 Output Available via ETABLE

Element Dimensionality

Axisymm2-D3-Dsnum

FACEFACEFACE1

AREAAREAAREA2

TEMPTEMPTEMP3

PRESPRESPRES4

EPPAREPPAREPX5



Surface Solution

Element Dimensionality

Axisymm2-D3-Dsnum

EPPEREPPEREPY6

EPZEPZEPZ7

EPSH [1]0EPXY8

SPARSPARSX9

SPERSPERSY10

SZSZSZ11

00SXY12

00013

SSH [1]0014

S1S1S115

S2S2S216

S3S3S317

SINTSINTSINT18

SEQVSEQVSEQV19

1. Axiharmonic only

If an additional face has surface output requested, then snum 1-19 are repeated as snum 20-38.

Convection heat flow output may be given on convection surfaces of solid thermal elements. Outputis valid on interior as well as exterior surfaces. Convection conditions should not be defined on condensedfaces or on the zero-radius face (center line) of an axisymmetric model.



Legacy Commands

Following is the archived documentation for legacy commands.

BELLOW, NLOC, LENG, STIFF, FLEX, ELEM

Defines a bellows in a piping run.

PREP7:Piping

MP ME ST PR PRN <> <> <> <> <> <> PP <> EME MFS

NLOCNode where bellows is to be placed. Defaults to current run starting point (RUN).

LENGLength of bellows (defaults to average pipe OD).

STIFFAxial stiffness value (defaults to that of equivalent straight pipe).

FLEXBending flexibility factor (defaults to 1.0).

ELEMElement number to be assigned to bellows (defaults to the previous maximum element number (MAXEL)+ 1).

Notes

Defines a bellows (straight-pipe element PIPE16 with adjusted specifications and loadings) at a givenlocation in a piping run.

Menu Paths

This command cannot be accessed from a menu.




BEND, NEL1, NEL2, RAD, NDIV, ESTRT, EINC

Defines a bend in a piping run.

PREP7:Piping


NEL1, NEL2Element numbers of the two intersecting straight pipes. Defaults to the last two straight pipe elementsnearest the intersection of the last two runs.

RADBend radius. If LR, use long radius standard (1.5 x nominal diameter) (default). If SR, use short radiusstandard (1.0 x nominal diameter).

NDIVNumber of divisions (elements) along bend (defaults to 2). A node is generated at the end of each division.

ESTRTNumber to be assigned to first element of bend (defaults to MAXEL + 1).

EINCElement number increment (defaults to 1).

Notes

Defines a bend of curved (elbow) pipe elements (PIPE18) in place of the intersection of two previouslydefined straight pipe elements (RUN). Two new nodes are generated at the ends of the bend (at thetangency points). A node is also generated at the center of curvature point. The two straight pipes areautomatically "shortened" to meet the ends of the bend. The bend specifications and loadings are takenfrom the corresponding two straight pipes. The flexibility factors are calculated from the internal pressureand EX (evaluated at TAVE) based on the current PPRES and PTEMP command specifications when theelement is generated.

Menu Paths





BRANCH, NODE, X, Y, Z

Defines the starting point for a piping branch.

PREP7:Piping


NODEStart branch at this node.

X, Y, ZStart branch at this location (in the active coordinate system). Used only if NODE is not input or inputbut the node itself is not previously defined. In either case a node is generated at this location and as-signed the number NODE (or 1 + previous maximum node number if NODE is not input).

Notes

See the RUN command in Part II:Legacy Commands (p. 25) for information relating to piping models.

Menu Paths





FLANGE, NLOC, LENG, MASS, SIF, FLEX, ARINS, ELEM

Defines a flange in a piping run.

PREP7:Piping


NLOCNode where flange is to be placed (as described below). Defaults to current piping run starting point.

LENGLength of flange (defaults to larger pipe OD).

MASSDry mass (weight/gravity) of flange without insulation (defaults to equivalent straight pipe mass). Notethat acceleration [ACEL] must be nonzero for weight to be calculated.

SIFStress intensification factor (defaults to 1.0).


ARINS

Insulation surface area (defaults to equivalent straight pipe insulation area). Units (length2) must beconsistent with the smallest unit of the system used (not mixed) regardless of the PUNIT option.

ELEMElement number to be assigned to flange (defaults to the previous maximum element number (MAXEL)+ 1).

Notes

Defines a flange (straight-pipe element PIPE16 with adjusted specifications and loadings) at a givenlocation in a piping run. (See the RUN command, and other commands described here, in Part II:Legacy

Commands (p. 25).)

The FLANGE command is similar to the VALVE command except for a different flexibility factor default.The location may be 1) between two adjacent colinear straight pipes, 2) between an adjacent straightpipe and a different piping component, or 3) at the end of a straight pipe.

For Case 1, two new nodes are generated at the ends of the flange. The two straight pipes are automat-ically "shortened" to meet the ends of the flange. The flange specifications and loadings are taken fromthe corresponding two straight pipes.

For Case 2, one new node is generated at one end of the flange. The straight pipe is automatically"shortened" to meet this end of the flange. The other end of the flange meets the other piping com-ponent. The flange specifications and loadings are taken from the straight pipe.

For Case 3, one new node is generated at the free end of the flange. The other end of the flange meetsthe straight pipe. The flange specifications and loadings are taken from the straight pipe.

Menu Paths





MITER, NEL1, NEL2, RAD, NDIV, ESTRT, EINC

Defines a mitered bend in a piping run.

PREP7:Piping


NEL1, NEL2Element numbers of the two intersecting straight pipes. Defaults to the last two straight pipe elementsnearest the intersection of the last two runs.

RADBend radius. If LR, use long radius standard (1.5 x OD) (default). If SR, use short radius standard (1.0 xOD).

NDIVNumber of divisions (elements) along bend (defaults to 2). A node is generated at the end of each division.

ESTRTNumber to be assigned to first element of bend (defaults to MAXEL + 1).


Notes

Defines a mitered bend of piecewise straight-pipe PIPE16 elements in place of the intersection of twopreviously defined straight pipe elements (RUN). This command is similar to the BEND command exceptthat straight pipe elements are used to form the bend instead of curved (elbow) elements. (See theRUN and BEND command descriptions in Part II:Legacy Commands (p. 25).)

Menu Paths





PCORRO, CTK

Specifies the allowable exterior corrosion thickness for a piping run.

PREP7:Piping


CTKAllowable corrosion thickness.

Notes

Specifies the allowable exterior corrosion thickness for a piping run. (See the RUN command descriptionin Part II:Legacy Commands (p. 25).)

Menu Paths





PDRAG, PX1, PY1, PZ1, H1, PX2, PY2, PZ2, H2, Kcord

Defines the external fluid drag loading for a piping run.

PREP7:Piping


PX1, PY1, PZ1External fluid drag pressure (global Cartesian components) at height H1.

H1Height (along Kcord coordinate) for first drag pressure.

PX2, PY2, PZ2External fluid drag pressure (global Cartesian components) at height H2.

H2Height (along Kcord coordinate) for second drag pressure.

KcordCoordinate direction for height value (in the global Cartesian coordinate system):

X

X coordinate.

Y

Y coordinate (default).

Z

Z coordinate.

Notes

Defines the external fluid drag loading (pressure) as a function of height for a piping run. (See the RUNcommand description in Part II:Legacy Commands (p. 25).) The element drag pressure is determinedfrom the centroid height and linear interpolation. Pressures are assigned to the elements as they aregenerated.

Menu Paths





PFLUID, DENS

Defines the contained fluid density for a piping run.

PREP7:Piping


DENSDensity of the contained fluid.

Notes

See the RUN command description in Part II:Legacy Commands (p. 25).

Distributed ANSYS Restriction This command is not supported in Distributed ANSYS.

Menu Paths





PGAP, NLOC, K, DX, DY, DZ, GAP, ELEM

Defines a spring-gap constraint in a piping run.

PREP7:Piping


NLOCNode where gap is to be placed. Defaults to current run starting point.

KSpring constant value (must be positive).

DX, DY, DZIncrement (in terms of the active coordinate system components) to determine gap ground point. Elementlength must not be zero. Constraints are automatically generated at the ground point.

GAPGap size (defaults to the element length).

ELEMElement number to be assigned to gap (defaults to MAXEL + 1).

Notes

Defines a spring-gap constraint (gap element CONTAC52) at a given location in a piping run. Givesspring constraint resistance after a specified gap is closed. (See the RUN command description inPart II:Legacy Commands (p. 25).)

Menu Paths





PINSUL, DENS, ITK

Defines the external insulation constants in a piping run.

PREP7:Piping


DENSInsulation density.

ITKInsulation thickness.

Command Default

No insulation.

Notes

Defines the external insulation constants in a piping run. (See the RUN command description inPart II:Legacy Commands (p. 25).)

Menu Paths





PIPE

Specifies "Pipe modeling" as the subsequent status topic.

PREP7:Status

MP ME ST PR PRN <> <> FL EM EH DY PP <> EME MFS

Notes

This is a status topic command. If status is requested for some items, it appears in the log file (Job-name.LOG). This command should be followed immediately by a STAT command, which reports thestatus for the specified topic.

Menu Paths





POPT, Lop1

Selects the piping analysis standard for a piping run.

PREP7:Piping


Lop1Option label:

B31.1

for ANSI B31.1.

NC

for ASME Section III NC, Class 2.

Command Default

ANSI B31.1.

Notes

Selects the piping analysis standard for a piping run (RUN). Affects only the flexibility and stress intens-ification factors applied to the curved pipe elements. (See the RUN command description inPart II:Legacy Commands (p. 25).)

Menu Paths





PPRES, PRESS

Defines the internal pressure for a piping run.

PREP7:Piping


PRESSPipe internal pressure.

Notes

Defines the pipe internal pressure for a piping run (RUN). These pressures are assigned to the elementsas they are generated. (See the RUN command description in Part II:Legacy Commands (p. 25).)

Menu Paths





PSOLVE, Lab, Rkey

Directs the program to perform a partial solution.

SOLUTION: Analysis Options

MP ME ST <> PRN <> <> <> <> <> <> PP <> EME MFS

LabValid labels defining the solution step. All characters are required:

EIGDAMP

Calculates the eigenvalues and eigenvectors using the damped eigensolver. Requires Jobname.FULLfrom MODOPT,UNSYM or MODOPT,DAMP options. Produces Jobname.MODE.

EIGQRDA

Calculates eigenvalues and eigenvectors using the QR damped eigensolver. Requires Jobname.EMATfrom MODOPT,QRDAMP option. Produces Jobname.MODE.

EIGEXP

Expands the eigenvector solution. Requires Jobname.ESAV and Jobname.MODE. Produces Job-name.RST.

EIGLANB

Calculates the eigenvalues and eigenvectors using Block Lanczos. Requires Jobname.EMAT fromMODOPT,LANB option. Produces Jobname.MODE.

EIGLANPCG

Calculates the eigenvalues and eigenvectors using PCG Lanczos. Requires Jobname.EMAT fromMODOPT,LANPCG option. Produces Jobname.MODE.

EIGSNODE

Calculates the eigenvalues and eigenvectors using the Supernode method. Requires Jobname.EMATfrom MODOPT,SNODE option. Produces Jobname.MODE. (See the MODOPT command for moreinformation on the SNODE modal solver.)

EIGREDUC

Calculates the eigenvalues and eigenvectors using Householder. Requires Jobname.REDM. ProducesJobname.MODE.

EIGUNSYM

Calculates the eigenvalues and eigenvectors using the unsymmetric eigensolver. Requires Job-name.EMAT from MODOPT,UNSYM or MODOPT,DAMP options. Produces Jobname.MODE.

ELFORM

Creates the element matrices. Produces Jobname.EMAT and Jobname.ESAV .

Note

If you want to include prestress effects (PSTRES,ON) from a previous prestress ana-lysis, the ELFORM option requires the Jobname.EMAT and Jobname.ESAV filesgenerated by that analysis.

ELPREP

Modifies element matrices for solution and calculates inertia relief terms (IRLF). Requires Job-name.EMAT. Produces Jobname.EROT.



REDWRITE

Writes the reduced matrix to a file. Requires Jobname.REDM. Produces Jobname.SUB .

TRIANG

Triangularizes the matrices completely. This option is required prior to performing a partial solutionusing the EIGREDUC option.

RkeyKey for initial contact results:

CNDI

Write initial contact configuration to the results file. This option is only valid for Lab = ELFORM.

Notes

Directs the program to perform a partial solution (that is, one step of an analysis sequence). Predefinedanalysis types (ANTYPE) perform a defined subset of these solution steps in a predefined sequence.You can use the partial-solution procedure to repeat a certain step of an analysis or to restart an ana-lysis.

Not all steps are valid for all analysis types. The order of the steps may vary depending on the resultyou desire. See the Basic Analysis Guide for a description of how to perform partial and predefinedsolutions.

An example of a prestressed modal analysis is given below. The Jobname.EMAT and Jobname.ESAVfiles from a prior static analysis must be available.

The example is provided for illustration purposes only, as the linear perturbation analysis method isrecommended in place of this partial-solution method.

! Prestressed modal analysis!/SOLUANTYPE,MODAL ! Modal analysisUPCOORD,1.0,ON ! Display mode shapes relative to deformed geometry ! in the postprocessor.PSTRES,ON ! Prestress effects ONMODOPT,LANB ! Select eigensolverPSOLVE,EIGLANB ! Calculate the eigenvalues and eigenvectors. ! EIGxxx label must be consistent with mode extraction method on MODOPT command.FINISH/SOLU !Additional solution step for expansion.EXPASS,ONMXPAND,... ! Specify the number of modes to expand, if desired.PSOLVE,EIGEXP ! Expand the eigenvector solution. (Required if you ! want to review mode shapes in the postprocessor.)FINISH

In a cyclic symmetry analysis, PSOLVE,EIGLANB or PSOLVE,EIGLANPCG performs the modal analysis atmultiple load steps, one for each nodal-diameter specified via the CYCOPT command. In addition, theeigenvector solution is expanded at each nodal-diameter solution, eliminating the need for a separateexpansion pass (PSOLVE,EIGEXP).

If issuing PSOLVE,ELFORM and PSOLVE,ELPREP using the Jacobi Conjugate Gradient solver, do so onlyafter issuing PSOLVE,CGSOL; otherwise, unpredictable results may occur.

Although documented to work, using the PSOLVE commands with an iterative solver is not likely todecrease solution-processing time.


PSOLVE

If Jobname.EMAT is required, run the prior analysis with EMATWRITE,YES to ensure that a Job-name.EMAT is generated.

In a prestressed modal analysis, issue a PSOLVE,TRIANG command immediately before a PSOLVE,EIGRE-DUC command to ensure that ANSYS creates a proper .FULL file. The PSOLVE ,EIGUNSYM;PSOLVE,EIGLANB; PSOLVE,EIGDAMP; PSOLVE,EIGQRDA; PSOLVE,EIGLANPCG; and PSOLVE,EIGSNODEcommands do not require a preceding PSOLVE,TRIANG command and should not be preceded by aPSOLVE,TRIANG command.

Distributed ANSYS Restriction Only the EIGLANB, and EIGLANPCG options on this command aresupported in Distributed ANSYS.

Menu Paths




PSOLVE


PSPEC, MAT, DNOM, SCHED, OD, TK

Defines pipe material and dimensions.

PREP7:Piping


MATMaterial number referring to a material property [MP]. Material number must be between 1 and 40.

DNOM, SCHEDNominal diameter of pipe and schedule rating. Only valid ratings accepted. If these are specified, theOD and TK values are found from an internal table.

Valid values for DNOM are: 1, 1.5, 2, 2.5, 3, 3.5, 4, 5, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32,34, and 36.

Valid ratings for SCHED are: 5, 5S, 10, 10S, 20, 30, 40, 40S, 60, 80 80S, 100, 120, 140, 160, XS, XXS,and STD.

ODOuter diameter of pipe (if DNOM not specified). If both DNOM and OD are not specified, OD and TK retaintheir previous values.

TKWall thickness of pipe (if OD specified).

Notes

Defines pipe material and dimensions. (See the RUN command description in Part II:Legacy Com-

mands (p. 25).)

Menu Paths





PSPRNG, NLOC, TYPE, K, DX, DY, DZ, ELEM

Defines a spring constraint in a piping run.

PREP7:Piping


NLOCNode where spring is to be placed. Defaults to current run starting point.

TYPEType of spring:

TRAN

Translational (default).

ROT

Rotational.

KSpring constant value (must be positive).

DX, DY, DZIncrement (in terms of the active coordinate system components) to determine spring ground point.Spring length must not be zero. Constraints are automatically generated at the ground point.

ELEMElement number to be assigned to spring (defaults to the previous maximum element number (MAXEL+ 1)).

Notes

Defines a spring constraint (spring element COMBIN14) at a given location in a piping run. (See theRUN command description in Part II:Legacy Commands (p. 25).)

Menu Paths





PTEMP, TOUT, TIN

Defines the pipe wall temperatures in a piping run.

PREP7:Piping


TOUTOuter pipe wall temperature. If NONE, reset temperature specification to none (BFUNIF will be assigned).

TINInner pipe wall temperature (defaults to TOUT).

Command Default

Assign uniform temperature BFUNIF to elements.

Notes

Defines the pipe wall temperatures in a piping run. These temperatures are assigned to the elementsas they are generated. (See the RUN command description in Part II:Legacy Commands (p. 25).)

Menu Paths





PUNIT, KOPT

Selects the system of length units to be used in a piping run.

PREP7:Piping


KOPTUnits key:

0

Input units are consistent (no conversions are done) (default).

FTIN or 1

English units (feet A, inch B, fraction of inch C/D). Use A+B+C/D format for PDRAG, BRANCH, RUN,BEND, MITER, REDUCE, VALVE, BELLOW, FLANGE, PSPRNG, and PGAP commands. Precede by "-'' signfor negative coordinates. (Example: 5+6+7/16 for 5 ft. 6-7/16 in., +3 for 3 in., -0+3 for -3 in., +0+9/16for 9/16 in.).

The two signs should not be consecutive. A, B, C, and D must be integers. Use B+C/D formatfor PSPEC, PINSUL, and PCORRO commands. (Example: 2 for 2 in., 3+1/2 for 3-1/2 in., +3/8 for3/8 in.)

METRIC or 2

Metric units (meter A, centimeter B, fraction of cm C/D). Use as explained for English units. (Example:5+6+7/10 for 5 m 6-7/10 cm with PDRAG command.)

Command Default

Input units are consistent (no conversions are done).

Notes

Selects the system of length units to be used for the piping commands. Mixed length units require a+ sign to delimit (or position) the units in the system and are converted to the smallest unit of thesystem (inches or centimeters) upon input.

This conversion is local only to pure length units of the piping commands listed. Other units and unitsfor other commands must be input to be consistent with the smallest length unit of the system used.

Menu Paths





REDUCE, NLOC, LENG, ELEM

Defines a reducer in a piping run.

PREP7:Piping


NLOCNode where two straight pipes intersect at center of reducer. Defaults to previous run starting point.

LENGLength of reducer (defaults to average pipe OD).

ELEMElement number to be assigned to reducer (defaults to MAXEL + 1).

Notes

Defines a reducer (straight-pipe element PIPE16 with averaged specifications) in place of the intersectionof two previously defined straight pipe elements in a piping run. (See the RUN command descriptionin Part II:Legacy Commands (p. 25).) Two new nodes are generated at the ends of the reducer. The twostraight pipes are automatically "shortened" to meet the ends of the reducer. The reducer specificationsand loadings are taken from the corresponding two straight pipes.

Menu Paths





RUN, DX, DY, DZ, NDIV, NEND, ESTRT, EINC

Defines a pipe run.

PREP7:Piping


DX, DY, DZIncrement (in terms of the active coordinate system components) to determine run end point. Incrementis applied to branch starting point (BRANCH) or end point of previous run (whichever was later).

NDIVNumber of divisions (elements) along branch (defaults to 1). A node is generated at the end of each di-vision.

NENDNumber to be assigned to end node of branch (defaults to MAXNP + NDIV).

ESTRTNumber to be assigned to first element of branch (defaults to the previous maximum element number(MAXEL) + 1).


Notes

Defines a pipe run from a previous point to an incremental point. Nodes (and elements) are generatedstraight (in the active coordinate system). Elements are of type PIPE16 straight pipes. Material properties,real constants, and loads are derived from the previously defined piping specifications. Piping loadsand specifications are defined via PCORRO, PDRAG, PFLUID, PINSUL, POPT, PPRES, PSPEC, PTEMP, andPUNIT commands.

Generated items may be listed (or displayed) with the standard commands (NLIST, ELIST, NPLOT,EPLOT, ETLIST, RLIST, etc.).

Items may also be modified (NMODIF, EMODIF, RMODIF, etc.) or redefined as desired.

See Piping Models (p. 3) for more information.

Menu Paths





SSTIF, Key

Activates stress stiffness effects in a nonlinear analysis.

SOLUTION: Nonlinear Options


KeyStress stiffening key:

OFF

No stress stiffening is included (default unless NLGEOM,ON).

ON

Stress stiffening is included (default if NLGEOM,ON).

Command Default

SSTIF will be turned on if NLGEOM,ON; otherwise it will be turned off.

Notes

Activates stress stiffness effects in a nonlinear analysis (ANTYPE,STATIC or TRANS). (The PSTRES commandalso controls the generation of the stress stiffness matrix and therefore should not be used in conjunctionwith SSTIF.) If used within the solution processor, this command is valid only within the first load step.

When SOLCONTROL and NLGEOM are ON, SSTIF defaults to ON. This normally forms all of the consistenttangent matrix. However, for some special nonlinear cases, this can lead to divergence caused by someelements which do not provide a complete consistent tangent (notably, elements outside the 18xfamily). In such a case, ANSYS recommends issuing an SSTIF,OFF command to achieve convergence.For current-technology elements, setting SSTIF,OFF when NLGEOM is ON has no effect (because stressstiffness effects are always included).

The default values given for this command assume SOLCONTROL,ON (the default). See the descriptionof SOLCONTROL for a complete listing of the defaults set by SOLCONTROL,ON and SOLCONTROL,OFF.

This command is also valid in PREP7.

Menu Paths





TEE, NCENT, TYPE, ELEM, EINC, L1, L2, L3

Defines a tee in a piping run.

PREP7:Piping


NCENTNode where three straight pipes intersect forming a tee (or "Y"). Defaults to last starting branch node(BRANCH).

TYPEType of tee:

WT

Welding tee (default).

r = (D0 - tw) / 2

h = 4.4 tw/ r

SIF = 0.9 / (h2/3)

If (SIF < 1) SIF = 1

UFT

Unreinforced fabricated tee.

r = (D0 - tw) / 2

h = tw/ r

SIF = 0.9 / (h2/3)

If (SIF < 1) SIF = 1

ELEMElement number to be assigned to first tee leg (defaults to the previous maximum element number(MAXEL) + 1).


L1, L2, L3Tee leg lengths (corresponding in order of increasing straight pipe element numbers). Must be less thanthe straight pipe length. Defaults to 2 x OD of straight pipe (for each leg).

Notes

Defines a tee in place of the tee intersection of three previously defined straight pipe elements. (Seethe RUN command description in Part II:Legacy Commands (p. 25).)

The new tee is also composed of three PIPE16 straight pipe elements, but of the leg lengths specifiedand with the appropriate tee factors calculated.

Three new nodes are generated at the ends of the tee.



The original three straight pipes are automatically "shortened" to meet the ends of the tee. The teespecifications and loadings are taken from the corresponding three straight pipes.

Menu Paths



TEE

VALVE, NLOC, LENG, MASS, SIF, FLEX, ARINS, ELEM

Defines a valve in a piping run.

PREP7:Piping


NLOCNode where valve is to be placed (as described below). Defaults to current run starting point.

LENGLength of valve (defaults to larger pipe OD).

MASSDry mass (weight/gravity) of valve without insulation (defaults to equivalent straight pipe mass). Note,acceleration (ACEL) must be nonzero for weight to be calculated.

SIFStress intensification factor (defaults to 1.0).


ARINS

Insulation surface area (defaults to equivalent straight pipe insulation area). Units (length2) must beconsistent with the smallest unit of the system used (not mixed) regardless of the PUNIT option.

ELEMElement number to be assigned to valve (defaults to the previous maximum element number (MAXEL)+ 1).

Notes

Defines a valve (straight-pipe element PIPE16 with adjusted specifications and loadings) at a givenlocation in a piping run. (See the RUN command description in Part II:Legacy Commands (p. 25).) Thelocation may be 1) between two adjacent colinear straight pipes, 2) between an adjacent straight pipeand a different piping component, or 3) at the end of a straight pipe.

For Case 1, two new nodes are generated at the ends of the valve. The two straight pipes are automat-ically "shortened" to meet the ends of the valve. The valve specifications and loadings are taken fromthe corresponding two straight pipes.

For Case 2, one new node is generated at one end of the valve. The straight pipe is automatically"shortened" to meet this end of the valve. The other end of the valve meets the other piping component.The valve specifications and loadings are taken from the straight pipe.

For Case 3, one new node is generated at the free end of the valve. The other end of the valve meetsthe straight pipe. The valve specifications and loadings are taken from the straight pipe.

Menu Paths





Legacy Elements

Following is the archived documentation for legacy elements.

BEAM4

3-D Elastic Beam

MP ME ST PR PRN DS DSS <> <> <> <> PP <> EME MFSProduct Restrictions

BEAM4 Element Description

Although this legacy element is available for use in your analysis, ANSYS recommends using a current-technology element such as BEAM188 (KEYOPT(3) = 3).

BEAM4 is a uniaxial element with tension, compression, torsion, and bending capabilities. The elementhas six degrees of freedom at each node: translations in the nodal x, y, and z directions and rotationsabout the nodal x, y, and z axes. Stress stiffening and large deflection capabilities are included. A con-sistent tangent stiffness matrix option is available for use in large deflection (finite rotation) analyses.A tapered unsymmetrical elastic beam is described in BEAM44 and a 3-D plastic beam in BEAM24.

Figure 1 BEAM4 Geometry

Z

J

Θz

z

zΘ

Θ Θ

Θ

Θ

z

y

Y

y

Θ

x

x

x

X

K (optional)

I

J

J

T5

T6T7

T3T2

T1T4

T8

I

y

J

I

I y

(If node K is omitted and Θ = 0°,

the element y axis is parallel to

the global X-Y plane.)

2

4

1

5

3x

Θ

T1,T5

T2,T6 T3,T7

T4,T8

TKZ

TKY

IYYJ y

z

IZZ1

2

5



BEAM4 Input Data

The geometry, node locations, and coordinate systems for this element are shown in Figure 1 (p. 77).The element is defined by two or three nodes, the cross-sectional area, two area moments of inertia(IZZ and IYY), two thicknesses (TKY and TKZ), an angle of orientation (θ) about the element x-axis, thetorsional moment of inertia (IXX), and the material properties. For stiffness purposes, the torsional momentof inertia, if IXX is equal to 0.0 or not specified, is assumed to be equal to the polar moment of inertia(IYY + IZZ). For inertial purposes, the torsional (rotational) moment of inertia used is the polar momentof inertia, and is therefore not affected by the value entered for IXX. The IXX value should be positiveand is usually less than the polar moment of inertia. An added mass per unit length may be input withthe ADDMAS value.

The element x-axis is oriented from node I toward node J. For the two-node option, the default (θ = 0°)orientation of the element y-axis is automatically calculated to be parallel to the global X-Y plane. Sev-eral orientations are shown in Figure 1 (p. 77). For the case where the element is parallel to the globalZ axis (or within a 0.01 percent slope of it), the element y axis is oriented parallel to the global Y axis(as shown). For user control of the element orientation about the element x-axis, use the θ angle (THETA)or the third node option. If both are defined, the third node option takes precedence. The third node(K), if used, defines a plane (with I and J) containing the element x and z axes (as shown). If this elementis used in a large deflection analysis, it should be noted that the location of the third node (K), or theangle (THETA), is used only to initially orient the element. (For information about orientation nodes andbeam meshing, see Meshing Your Solid Model in the Modeling and Meshing Guide.)

The initial strain in the element (ISTRN) is given by ∆/L, where ∆ is the difference between the elementlength, L, (as defined by the I and J node locations) and the zero strain length. The shear deflectionconstants (SHEARZ and SHEARY) are used only if shear deflection is to be included. A zero value ofSHEAR_ may be used to neglect shear deflection in a particular direction.

KEYOPT(2) is used to activate the consistent tangent stiffness matrix (i.e., a matrix composed of themain tangent stiffness matrix plus the consistent stress stiffness matrix) in large deflection analyses[NLGEOM,ON]. You can often obtain more rapid convergence in a geometrically nonlinear analysis,such as a nonlinear buckling or postbuckling analysis, by activating this option. However, you shouldnot use this option if you are using the element to simulate a rigid link or a group of coupled nodes.The resulting abrupt changes in stiffness within the structure make the consistent tangent stiffnessmatrix unsuitable for such applications.

KEYOPT(7) is used to compute an unsymmetric gyroscopic damping matrix (often used for rotordynamicanalyses). The rotational frequency is input with the SPIN real constant (radians/time, positive in thepositive element x direction). The element must be symmetric with this option (e.g., IYY = IZZ andSHEARY = SHEARZ).

Element loads are described in Nodal Loading. Pressures may be input as surface loads on the elementfaces as shown by the circled numbers on Figure 1 (p. 77). Positive normal pressures act into the element.Lateral pressures are input as a force per unit length. End "pressures" are input as a force. Temperaturesmay be input as element body loads at the eight "corner" locations shown in Figure 1 (p. 77). The firstcorner temperature T1 defaults to TUNIF. If all other temperatures are unspecified, they default to T1.If only T1 and T2 are input, T3 defaults to T2 and T4 defaults to T1. If only T1 and T4 are input, T2 defaultsto T1 and T3 defaults to T4. In both cases, T5 through T8 default to T1 through T4. For any other inputpattern, unspecified temperatures default to TUNIF.

KEYOPT(9) is used to request output at intermediate locations. It is based on equilibrium (free body ofa portion of the element) considerations and is not valid if:


BEAM4

• stress stiffening is turned on [SSTIF,ON]

• more than one component of angular velocity is applied [OMEGA]

• any angular velocities or accelerations are applied with the CGOMGA, DOMEGA, or DCGOMG

commands.

A summary of the element input is given in "BEAM4 Input Summary" (p. 79). A general description ofelement input is given in Element Input.

BEAM4 Input Summary

Nodes

I, J, K (K orientation node is optional)

Degrees of Freedom

UX, UY, UZ, ROTX, ROTY, ROTZ

Real Constants

AREA, IZZ, IYY, TKZ, TKY, THETAISTRN, IXX, SHEARZ, SHEARY, SPIN, ADDMASSee Table 1: BEAM4 Real Constants (p. 80) for a description of the real constants.

Material Properties

EX, ALPX (or CTEX or THSX), DENS, GXY, BETD, ALPD

Surface Loads

Pressures --

face 1 (I-J) (-Z normal direction)face 2 (I-J) (-Y normal direction)face 3 (I-J) (+X tangential direction)face 4 (I) (+X axial direction)face 5 (J) (-X axial direction)(use negative value for opposite loading)

Body Loads

Temperatures --

T1, T2, T3, T4, T5, T6, T7, T8

Special Features

Stress stiffeningLarge deflectionBirth and death

KEYOPT(2)

Stress stiffening option:

0 --

Use only the main tangent stiffness matrix when NLGEOM is ON. (Stress stiffening effects used inlinear buckling or other linear prestressed analyses must be activated separately with PSTRES,ON.)

1 --

Use the consistent tangent stiffness matrix (i.e., a matrix composed of the main tangent stiffnessmatrix plus the consistent stress stiffness matrix) when NLGEOM is ON. (SSTIF,ON will be ignored



BEAM4

for this element when KEYOPT(2) = 1 is activated.) Note that if SOLCONTROL is ON and NLGEOM

is ON, KEYOPT(2) is automatically set to 1; i.e., the consistent tangent will be used.

2 --

Turn off consistent tangent stiffness matrix (i.e., a matrix composed of the main tangent stiffnessmatrix plus the consistent stress stiffness matrix) when SOLCONTROL is ON. Sometimes it is necessaryto turn off the consistent tangent stiffness matrix if the element is used to simulate rigid bodies byusing a very large real constant number . KEYOPT(2) = 2 is the same as KEYOPT(2) = 0, however,KEYOPT(2) = 0 is controlled by SOLCONTROL, ON or OFF, while KEYOPT(2) = 2 is independent ofSOLCONTROL.

KEYOPT(6)

Member force and moment output:

0 --

No printout of member forces or moments

1 --

Print out member forces and moments in the element coordinate system

KEYOPT(7)

Gyroscopic damping matrix:

0 --

No gyroscopic damping matrix

1 --

Compute gyroscopic damping matrix. Real constant SPIN must be greater than zero. IYY must equalIZZ.

KEYOPT(9)

Output at intermediate points between ends I and J:

N --

Output at N intermediate locations (N = 0, 1, 3, 5, 7, 9)

Table 1 BEAM4 Real Constants

DescriptionNameNo.

Cross-sectional areaAREA1

Area moment of inertiaIZZ2

Area moment of inertiaIYY3

Thickness along Z axisTKZ4

Thickness along Y axisTKY5

Orientation about X axisTHETA6

Initial strainISTRN7

Torsional moment of inertiaIXX8

Shear deflection constant Z [1]SHEARZ9

Shear deflection constant Y [2]SHEARY10

Rotational frequency (required if KEYOPT(7) = 1)SPIN11

Added mass/unit lengthADDMAS12

1. SHEARZ goes with IZZ; if SHEARZ = 0, there is no shear deflection in the element Y direction.


BEAM4

2. SHEARY goes with IYY; if SHEARY = 0, there is no shear deflection in the element Z direction.

BEAM4 Output Data

The solution output associated with the element is in two forms:

• Nodal displacements included in the overall nodal solution

• Additional element output as shown in Table 2: BEAM4 Element Output Definitions (p. 81).

Several items are illustrated in Figure 2 (p. 81).

The maximum stress is computed as the direct stress plus the absolute values of both bending stresses.The minimum stress is the direct stress minus the absolute value of both bending stresses. A generaldescription of solution output is given in Solution Output. See the Basic Analysis Guide for ways to viewresults.

Figure 2 BEAM4 Stress Output

SDIR

J

SBZT

x

SBYB

I J

y

xI

SDIR

z

The Element Output Definitions table uses the following notation:

A colon (:) in the Name column indicates that the item can be accessed by the Component Namemethod (ETABLE, ESOL). The O column indicates the availability of the items in the file Jobname.OUT .The R column indicates the availability of the items in the results file.

In either the O or R columns, “Y” indicates that the item is always available, a number refers to a tablefootnote that describes when the item is conditionally available, and “-” indicates that the item is not

available.

Table 2 BEAM4 Element Output Definitions

RODefinitionName

YYElement numberEL

YYElement node number (I and J)NODES

YYMaterial number for the elementMAT

Y-Element volumeVOLU:

3YLocation where results are reportedXC, YC, ZC

YYTemperatures at integration points T1, T2, T3, T4, T5, T6,T7, T8

TEMP



BEAM4

RODefinitionName

YYPressure P1 at nodes I, J; OFFST1 at I, J; P2 at I, J; OFFST2at I, J; P3 at I, J; OFFST3 at I, J; P4 at I; P5 at J

PRES

11Axial direct stressSDIR

11Bending stress on the element +Y side of the beamSBYT

11Bending stress on the element -Y side of the beamSBYB

11Bending stress on the element +Z side of the beamSBZT

11Bending stress on the element -Z side of the beamSBZB

11Maximum stress (direct stress + bending stress)SMAX

11Minimum stress (direct stress - bending stress)SMIN

11Axial elastic strain at the endEPELDIR

11Bending elastic strain on the element +Y side of the beamEPELBYT

11Bending elastic strain on the element -Y side of the beamEPELBYB

11Bending elastic strain on the element +Z side of the beamEPELBZT

11Bending elastic strain on the element -Z side of the beamEPELBZB

11Axial thermal strain at the endEPTHDIR

11Bending thermal strain on the element +Y side of the beamEPTHBYT

11Bending thermal strain on the element -Y side of the beamEPTHBYB

11Bending thermal strain on the element +Z side of the beamEPTHBZT

11Bending thermal strain on the element -Z side of the beamEPTHBZB

11Initial axial strain in the elementEPINAXL

Y2Member forces in the element coordinate system X, Y, Zdirections

MFOR(X, Y,Z)

Y2Member moments in the element coordinate system X, Y,Z directions

MMOM(X, Y,Z)

1. The item repeats for end I, intermediate locations (see KEYOPT(9)), and end J.

2. If KEYOPT(6) = 1.

3. Available only at centroid as a *GET item.

The following tables list output available through the ETABLE command using the Sequence Numbermethod. See The General Postprocessor (POST1) of the Basic Analysis Guide and The Item and SequenceNumber Table of this manual for more information. The following notation is used in Table 3: BEAM4

Item and Sequence Numbers (KEYOPT(9) = 0) (p. 83) through Table 8: BEAM4 Item and Sequence Numbers

(KEYOPT(9) = 9) (p. 89):

Name

output quantity as defined in the Table 2: BEAM4 Element Output Definitions (p. 81)

Item

predetermined Item label for ETABLE command

E

sequence number for single-valued or constant element data


BEAM4

I,J

sequence number for data at nodes I and J

ILNsequence number for data at Intermediate Location N

Table 3 BEAM4 Item and Sequence Numbers (KEYOPT(9) = 0)

ETABLE and ESOL Command InputOutput

Quant-

ity

Name

JIEItem

61-LSSDIR

72-LSSBYT

83-LSSBYB

94-LSSBZT

105-LSSBZB

61-LEPELEPELDIR

72-LEPELEPELBYT

83-LEPELEPELBYB

94-LEPELEPELBZT

105-LEPELEPELBZB

31-NMISCSMAX

42-NMISCSMIN

61-LEPTHEPTHDIR

72-LEPTHEPTHBYT

83-LEPTHEPTHBYB

94-LEPTHEPTH-BZT

105-LEPTHEPTH-BZB

--11LEPTHEPINAXL

71-SMISCMFORX

82-SMISCMFORY

93-SMISCMFORZ

104-SMISCMMOMX

115-SMISCMMOMY

126-SMISCMMOMZ

1413-SMISCP1

1615-SMISCOFFST1

1817-SMISCP2

2019-SMISCOFFST2



BEAM4


Quant-

ity

Name

JIEItem

2221-SMISCP3

2423-SMISCOFFST3

-25-SMISCP4

26--SMISCP5

Pseudo Node

87654321

87654321LBFETEMP



Quant-

ity

Name

JIL1IEItem

1161-LSSDIR

1272-LSSBYT

1383-LSSBYB

1494-LSSBZT

15105-LSSBZB

1161-LEPELEPELDIR

1272-LEPELEPELBYT

1383-LEPELEPELBYB

1494-LEPELEPELBZT

15105-LEPELEPELBZB

531-NMISCSMAX

642-NMISCSMIN

1161-LEPTHEPTHDIR

1272-LEPTHEPTHBYT

1383-LEPTHEPTHBYB

1494-LEPTHEPTH-BZT

15105-LEPTHEPTH-BZB

---16LEPTHEPINAXL

1371-SMISCMFORX

1482-SMISCMFORY

1593-SMISCMFORZ


BEAM4


Quant-

ity

Name

JIL1IEItem

16104-SMISCMMOMX

17115-SMISCMMOMY

18126-SMISCMMOMZ

20-19-SMISCP1

22-21-SMISCOFFST1

24-23-SMISCP2

26-25-SMISCOFFST2

28-27-SMISCP3

30-29-SMISCOFFST3

--31-SMISCP4

32---SMISCP5

Pseudo Node

87654321

87654321LBFETEMP



Quant-

ity

Name

JIL3IL2IL1IEItem

21161161-LSSDIR

22171272-LSSBYT

23181383-LSSBYB

24191494-LSSBZT

252015105-LSSBZB

21161161-LEPELEPELDIR

22171272-LEPELEPELBYT

23181383-LEPELEPELBYB

24191494-LEPELEPELBZT

252015105-LEPELEPELBZB

97531-NMISCSMAX

108642-NMISCSMIN

21161161-LEPTHEPTHDIR

22171272-LEPTHEPTHBYT

23181383-LEPTHEPTHBYB



BEAM4


Quant-

ity

Name

JIL3IL2IL1IEItem

24191494-LEPTHEPTH-BZT

252015105-LEPTHEPTH-BZB

-----26LEPTHEPINAXL

25191371-SMISCMFORX

26201482-SMISCMFORY

27211593-SMISCMFORZ

282216104-SMISCMMOMX

292317115-SMISCMMOMY

302418126-SMISCMMOMZ

32---31-SMISCP1

34---33-SMISCOFFST1

36---35-SMISCP2

38---37-SMISCOFFST2

40---39-SMISCP3

42---41-SMISCOFFST3

---43-SMISCP4

44-----SMISCP5

Pseudo Node

87654321

87654321LBFETEMP



Quant-

ity

Name

JIL5IL4IL3IL2IL1IEItem

312621161161-LSSDIR

322722171272-LSSBYT

332823181383-LSSBYB

342924191494-LSSBZT

3530252015105-LSSBZB





BEAM4


Quant-

ity

Name

JIL5IL4IL3IL2IL1IEItem



131197531-NMISCSMAX

1412108642-NMISCSMIN





3530252015105-LEPTHEPTH-BZB

-------36LEPTHEPINAXL

373125191371-SMISCMFORX

383226201482-SMISCMFORY

393327211593-SMISCMFORZ

4034282216104-SMISCMMOMX

4135292317115-SMISCMMOMY

4236302418126-SMISCMMOMZ

44-----43-SMISCP1

46-----45-SMISCOFFST1

48-----47-SMISCP2


52-----51-SMISCP3


------55-SMISCP4

56-------SMISCP5

Pseudo Node

87654321

87654321LBFETEMP



Quant-

ity

Name

JIL7IL6IL5IL4IL3IL2IL1IEItem

4136312621161161-LSSDIR



BEAM4


Quant-

ity

Name

JIL7IL6IL5IL4IL3IL2IL1IEItem

4237322722171272-LSSBYT

4338332823181383-LSSBYB

4439342924191494-LSSBZT

45403530252015105-LSSBZB






1715131197531-NMISCSMAX

18161412108642-NMISCSMIN





45403530252015105-LEPTHEPTH-BZB

---------46LEPTHEPINAXL

4943373125191371-SMISCMFORX

5044383226201482-SMISCMFORY

5145393327211593-SMISCMFORZ

52464034282216104-SMISCMMOMX

53474135292317115-SMISCMMOMY

54484236302418126-SMISCMMOMZ

56-------55-SMISCP1

58-------57-SMISCOFFST1

60-------59-SMISCP2


64-------63-SMISCP3


--------67-SMISCP4

68---------SMISCP5


BEAM4

Pseudo Node

87654321

87654321LBFETEMP



Quant-

ity

Name

JIL9IL8IL7IL6IL5IL4IL3IL2IL1IEItem

51464136312621161161-LSSDIR

52474237322722171272-LSSBYT

53484338332823181383-LSSBYB

54494439342924191494-LSSBZT

555045403530252015105-LSSBZB

51464136312621161161-LEPELEPELDIR

52474237322722171272-LEPELEPELBYT

53484338332823181383-LEPELEPELBYB

54494439342924191494-LEPELEPELBZT

555045403530252015105-LEPELEPELBZB

21191715131197531-NMISCSMAX

222018161412108642-NMISCSMIN

51464136312621161161-LEPTHEPTHDIR

52474237322722171272-LEPTHEPTHBYT

53484338332823181383-LEPTHEPTHBYB

54494439342924191494-LEPTHEPTH-BZT

555045403530252015105-LEPTHEPTH-BZB

-----------56LEPTHEPINAXL

61554943373125191371-SMISCMFORX

62565044383226201482-SMISCMFORY

63575145393327211593-SMISCMFORZ

645852464034282216104-SMISCMMOMX

655953474135292317115-SMISCMMOMY

666054484236302418126-SMISCMMOMZ

68---------67-SMISCP1

70---------69-SMISCOFFST1

72---------71-SMISCP2


76---------75-SMISCP3



BEAM4


Quant-

ity

Name

JIL9IL8IL7IL6IL5IL4IL3IL2IL1IEItem


----------79-SMISCP4

80-----------SMISCP5

Pseudo Node

87654321

87654321LBFETEMP

BEAM4 Assumptions and Restrictions

• The beam must not have a zero length or area. The moments of inertia, however, may be zero if largedeflections are not used.

• The beam can have any cross-sectional shape for which the moments of inertia can be computed. Thestresses, however, will be determined as if the distance between the neutral axis and the extreme fiberis one-half of the corresponding thickness.

• The element thicknesses are used only in the bending and thermal stress calculations.

• The applied thermal gradients are assumed to be linear across the thickness in both directions andalong the length of the element.

• If you use the consistent tangent stiffness matrix (KEYOPT(2) = 1), take care to use realistic (that is, "toscale") element real constants. This precaution is necessary because the consistent stress-stiffeningmatrix is based on the calculated stresses in the element. If you use artificially large or small cross-sec-tional properties, the calculated stresses will become inaccurate, and the stress-stiffening matrix willsuffer corresponding inaccuracies. (Certain components of the stress-stiffening matrix could evenovershoot to infinity.) Similar difficulties could arise if unrealistic real constants are used in a linearprestressed or linear buckling analysis [PSTRES,ON].

• Eigenvalues calculated in a gyroscopic modal analysis can be very sensitive to changes in the initialshift value, leading to potential error in either the real or imaginary (or both) parts of the eigenvalues.

BEAM4 Product Restrictions

When used in the product(s) listed below, the stated product-specific restrictions apply to this elementin addition to the general assumptions and restrictions given in the previous section.

ANSYS Professional

• The SPIN real constant (R11) is not available. Input R11 as a blank.

• KEYOPT(2) can only be set to 0 (default).


• The only special features allowed are stress stiffening and large deflections.


BEAM4

CONTAC12

2-D Point-to-Point Contact

MP ME ST PR PRN <> <> <> <> <> <> PP <> EME MFSProduct Restrictions

CONTAC12 Element Description

Although this legacy element is available for use in your analysis, ANSYS recommends using a current-tech-nology element such as CONTA178.To use CONTA178 as you would CONTAC12, constrain the UZ degree offreedom to simulate 2-D behavior. CONTA178 does not support the circular gap option of CONTAC12.

CONTAC12 represents two surfaces which may maintain or break physical contact and may slide relativeto each other. The element is capable of supporting only compression in the direction normal to thesurfaces and shear (Coulomb friction) in the tangential direction. The element has two degrees of freedomat each node: translations in the nodal x and y directions.

The element may be initially preloaded in the normal direction or it may be given a gap specification.A specified stiffness acts in the normal and tangential directions when the gap is closed and not sliding.

Figure 1 CONTAC12 Geometry

Positive Slide

(STAT or START = +2)Nodes may be coincident

X

Y

x

I

n

J

s

θ determines element

orientation

θ

I J

L δ < 0

I J

δ > 0

s

I

n

CONTAC12 Input Data

The geometry, node locations, and the coordinate system for this element are shown in Figure 1 (p. 91).The element is defined by two nodes, an angle to define the interface, two stiffnesses (KN and KS), aninitial displacement interference or gap (INTF), and an initial element status (START). An element coordin-ate system (s-n) is defined on the interface. The angle θ (THETA) is input (or calculated) in degrees andis measured from the global X axis to the element s-axis. The orientation of the interface may be defined(KEYOPT(2)) by THETA or by the node locations.

The normal stiffness, KN, should be based upon the stiffness of the surfaces in contact. See Performinga Node-to-Node Contact Analysis in the Contact Technology Guide for guidelines on choosing a valuefor KN. In some cases (such as initial interference analyses, nonconvergence, or over penetration), itmay be useful to change the KN value between load steps or in a restart in order to obtain an accurate,converged solution. The sticking stiffness, KS, represents the stiffness in the tangential direction whenelastic Coulomb friction is selected (µ > 0.0 and KEYOPT(1) = 0). The coefficient of friction µ is input asmaterial property MU and is evaluated at the average of the two node temperatures. Stiffnesses may



also be computed from the maximum expected force divided by the maximum allowable surface dis-placement. KS defaults to KN. Stiffnesses should be on a full 360° basis for an axisymmetric analysis.

The initial displacement interference, ∆, defines the displacement interference (if positive) or the gapsize (if negative). The value may be input as a real constant (INTF) or automatically calculated from theinput node locations if KEYOPT(4) = 1. Stiffness is associated with a zero or positive interference. Theinitial element status (START) is used to define the "previous" condition of the interface to be used atthe start of the first substep. This input is used to override the condition implied by the interferencespecification and is useful in anticipating the final interface configuration and in reducing the numberof iterations required for convergence.

The force deflection relationships for the interface element can be separated into the normal and tan-gential (sliding) directions as shown in Figure 2 (p. 95). The element condition at the beginning of thefirst substep is determined from the START parameter. If the interface is open, no stiffness is associatedwith this element for this substep. If the interface is closed and sticking, KN is used in the gap resistanceand KS is used in the sliding resistance. If the interface is closed but sliding, KN is used in the gap res-istance and the limit friction force µFN is used for the sliding resistance.

In the normal direction, when the normal force (FN) is negative, the interface remains in contact andresponds as a linear spring. As the normal force becomes positive, contact is broken and no force istransmitted.

KEYOPT(3) can be used to specify a "weak spring" across an open interface, which is useful for preventingrigid body motion that could occur in a static analysis. The weak spring stiffness is computed by mul-tiplying the normal stiffness KN by a reduction factor. The default reduction factor of 1E-6 can beoverridden with real constant REDFACT.

In the tangential direction, for FN < 0 and the absolute value of the tangential force (FS) less than(µ|FN|), the interface sticks and responds as a linear spring in the tangential direction. For FN < 0 andFS = µ|FN|, sliding occurs.

If KEYOPT(1) = 1, rigid Coulomb friction is selected, KS is not used, and the elastic sticking capability isremoved. This option is useful for displacement controlled problems or for certain dynamic problemswhere sliding dominates. With this option, no tangential resistance is assumed for the first substep.

The only material property used is the interface coefficient of friction MU. A zero value should be usedfor frictionless surfaces. Temperatures may be input at the element nodes (for material property evaluationonly). The node I temperature T(I) defaults to TUNIF. The node J temperature defaults to T(I). The circulargap option (KEYOPT(2)) is useful where the final contact point (and thus the orientation angle) is notknown, such as with concentric cylinders. With this option the angular orientation THETA is initially setto 0.0 and then internally calculated from the relative displacements of the nodes at the end of thesubstep for use in the next substep. The user specified THETA (if any) is ignored. A negative interference(gap) and a zero coefficient of friction is used with this option.

For analyses involving friction, using NROPT,UNSYM is useful (and, in fact, sometimes required) forproblems where the normal and tangential (sliding) motions are strongly coupled, such as in a wedgeinsertion problem.

A summary of the element input is given in "CONTAC12 Input Summary" (p. 93). A general descriptionof element input is given in Element Input.


CONTAC12

CONTAC12 Input Summary

Nodes

I, J

Degrees of Freedom

UX, UY

Real Constants

See Table 1: CONTAC12 Real Constants (p. 94) for details on these real constants

Material Properties

MU

Surface Loads

None

Body Loads

Temperatures --

T(I), T(J)

Special Features

NonlinearAdaptive descent

KEYOPT(1)

Type of friction (only with MU > 0.0):

0 --

Elastic coulomb friction (KS used for sticking stiffness)

1 --

Rigid coulomb friction (resisting force only)

KEYOPT(2)

Orientation angle:

0 --

Orientation angle based on Theta real constant

1 --

Circular gap option (THETA orientation determined from direction of motion) (ignore THETA realconstant)

KEYOPT(3)

Weak spring across open gap:

0 --

No weak spring across an open gap

1 --

Use a weak spring across an open gap

KEYOPT(4)

Interference or gap:

0 --

Interference (or gap) based on INTF real constant

1 --

Interference (or gap) based on initial node locations (ignore INTF real constant)



CONTAC12

KEYOPT(7)

Element level time incrementation control. Note that this option should be activated first at the procedurelevel if SOLCONTROL is ON. SOLCONTROL,ON,ON is the most frequent usage with this element. IfSOLCONTROL,ON,OFF, this keyoption is not activated.

0 --

Predictions are made to achieve the minimum time (or load) increment whenever a change in contactstatus occurs

1 --

Predictions are made to maintain a reasonable time (or load) increment (recommended)

Table 1 CONTAC12 Real Constants

DescriptionNameNo.

Interference angleTHETA1

Normal stiffnessKN2

Initial displacement interference or gap. A negative INTF (inter-ference) assumes an initially open gap.

INTF3

Initial element statusSTART4

If = 0.0 or blank, initial condition of gap status is determ-ined from real constant INTFIf = 1.0, gap is initially closed and not sliding (if MU ≠ 0.0),or sliding node J is positive (if MU = 0.0)If = 2.0, gap is initially closed and node J is sliding to theright of node IIf = -2.0, gap is initially closed and node J is sliding to theleft of node IIf = 3.0, gap is initially open

Sticking stiffnessKS5

KN reduction factorREDFACT6

CONTAC12 Output Data


• nodal displacements included in the overall nodal solution

• additional element output as shown in Table 2: CONTAC12 Element Output Definitions (p. 95).


The value of USEP is determined from the normal displacement (un) (in the element x-direction) between

the interface nodes at the end of this substep. That is: USEP = (un) J - (un) I - ∆. This value is used in

determining the normal force, FN. For an axisymmetric analysis, the element forces are expressed on afull 360° basis. The value represented by UT is the total translational displacement. The maximum valueprinted for the sliding force, FS, is µ|FN|. STAT describes the status of the element at the end of thissubstep. If STAT = 1, the gap is closed and no sliding occurs. If STAT = 3, the gap is open. A value ofSTAT = +2 indicates the node J slides positive relative to node I as shown in Figure 4.12-1. STAT = -2indicates a negative slide. For a frictionless surface (µ = 0.0), the element status is either STAT = ±2 or3. The value of THETA is either the input orientation angle (if KEYOPT(2) = 0), or the calculated angle


CONTAC12

(if KEYOPT(2) = 1). A general description of solution output is given in Solution Output. See the Basic

Analysis Guide for ways to view results.

Figure 2 CONTAC12 Force-Deflection Relationship

1

FN

1

FS

(a) (b)

KS

KN

unJ - unI - δ

µ | FN |

usJ - usI

µ | FN |

or < 0, d o

revered lodig




available.

Table 2 CONTAC12 Element Output Definitions

RODefinitionName

YYElement NumberEL

YYNodes - I, JNODES

3YLocation where results are reportedXC, YC

YYTemperatures T(I), T(J)TEMP

YYGap size or interferenceUSEP

YYNormal forceFN

11Element statusSTAT

11Stat value of the previous time stepOLDST

YYOrientation angleTHETA

22Coefficient of frictionMU

22Relative displacement in tangential direction(positive for node J moving to right of node I)

UT

22Tangential forceFS

1. Element status values:



CONTAC12

1 - Contact, no sliding

2 - Sliding contact with node J moving to right of node I

-2 - Sliding contact with node J moving to left of node I

3 - Gap open

2. Only if MU > 0.0 and KEYOPT(2) = 0.


Table 3: CONTAC12 Item and Sequence Numbers (p. 96) lists output available through the ETABLE commandusing the Sequence Number method. See The General Postprocessor (POST1) of the Basic Analysis Guide

and The Item and Sequence Number Table of this manual for more information. The following notationis used in Table 3: CONTAC12 Item and Sequence Numbers (p. 96):

Name

output quantity as defined in the Table 2: CONTAC12 Element Output Definitions (p. 95)

Item


E


Table 3 CONTAC12 Item and Sequence Numbers

ETABLE and

ESOL Command

Input

Output

Quant-

ity

Name EItem

1SMISCFN

2SMISCFS

1NMISCSTAT

2NMISCOLDST

3NMISCUSEP

4NMISCUT

5NMISCMU

6NMISCTHETA

CONTAC12 Assumptions and Restrictions

• The 2-D interface element must be defined in an X-Y plane and the Y-axis must be the axis of symmetryfor axisymmetric analyses. An axisymmetric structure should be modeled in the +X quadrants.

• The element operates bilinearly only in a static or a nonlinear transient dynamic analysis.

• If used in other analysis types, the element maintains its initial status throughout the analysis.

• The element is nonlinear and requires an iterative solution.

• Convergence is also based on forces when friction or the circular gap option is present.


CONTAC12

• Nodes I and J may be coincident since the orientation of the interface is defined only by the angleTHETA.

• The orientation of the interface does not change (with KEYOPT(2) = 0) during a large deflection analysis.Use CONTA175 if this effect is desired.

• No moment effects due to noncoincident nodes are included. That is, if the nodes are offset from a lineperpendicular to the interface, moment equilibrium may not be satisfied.

• The element is defined such that a positive normal displacement (in the element coordinate system)of node J relative to node I tends to open the gap, as shown in Figure 1 (p. 91). If, for a given set ofconditions, node I and J are interchanged, or if the interface is rotated by 180°, the gap element actsas a hook element, i.e., the gap closes as the nodes separate. The element may have rotated nodal co-ordinates since a displacement transformation into the element coordinate system is included.

• The element stiffness KN cannot be exactly zero.

• Unreasonably high stiffness values also should be avoided.

• The rate of convergence decreases as the stiffness increases. Note that, although it is permissible tochange KN, it is not permissible to change any other real constants between load steps. Therefore, ifyou plan to change KN, you cannot allow the value of KS to be defined by default, because the programwould then attempt to redefine KS as KN changed.

• You must explicitly define KS whenever KN changes, to maintain a consistent value throughout all loadsteps.

• The element may not be deactivated with the EKILL command.

• If µ is nonzero, the element is nonconservative as well as nonlinear. Nonconservative elements requirethat the load be applied very gradually, along the actual load history path, and in the proper sequence(if multiple loadings exist).

CONTAC12 Product Restrictions


ANSYS Professional

• This element is frictionless. Specifically, MU is not allowed as a material property and KS is not al-lowed as a real constant.

• Temperature body loads are not applicable.

• KEYOPT(1) is not applicable.



CONTAC12


PIPE16

Elastic Straight Pipe


PIPE16 Element Description

Although this legacy element is available for use in your analysis, ANSYS recommends using a current-tech-nology element such as PIPE288.

PIPE16 is a uniaxial element with tension-compression, torsion, and bending capabilities. The elementhas six degrees of freedom at two nodes: translations in the nodal x, y, and z directions and rotationsabout the nodal x, y, and z axes. See PIPE16 - Elastic Straight Pipe (p. 206) for more details about thiselement.

Figure 1 PIPE16 Geometry

X

If node K is omitted, the element y-axis

is parallel to the global X-Y plane

x

y

z

x

y

z

ZK

J

PX

PY

z

Iy

x

x

yz

PZ

4

3

2

x, y, z defines the element

coordinate system orientation

Y

1T180

T90

Tu

T

Tvu

5

PIPE16 Input Data

The geometry, node locations, and the coordinate system for this element are shown in Figure 1 (p. 99).The element input data include two or three nodes, the pipe outer diameter and wall thickness, stressintensification and flexibility factors, internal fluid density, exterior insulation density and thickness,corrosion thickness allowance, insulation surface area, pipe wall mass, axial pipe stiffness, rotordynamicspin, and the isotropic material properties.



The element X-axis is oriented from node I toward node J. For the two-node option, the element Y-axisis automatically calculated to be parallel to the global X-Y plane. Several orientations are shown in Figure

1 (p. 99). For the case where the element is parallel to the global Z-axis (or within a 0.01 percent slopeof it), the element Y-axis is oriented parallel to the global Y-axis (as shown). For user control of theelement orientation about the element X-axis, use the third node option. The third node (K), if used,defines a plane (with I and J) containing the element X and Z axes (as shown). Input and output locationsaround the pipe circumference identified as being at 0° are located along the element Y-axis, and sim-ilarly 90° is along the element Z-axis.

The stress intensification factor (SIF) modifies the bending stress. Stress intensification factors may beinput at end I (SIFI) and end J (SIFJ), if KEYOPT(2) = 0, or determined by the program using a tee-jointcalculation if KEYOPT(2) = 1, 2, or 3. SIF values less than 1.0 are set equal to 1.0. The flexibility factor(FLEX) is divided into the cross-sectional moment of inertia to produce a modified moment of inertiafor the bending stiffness calculation. FLEX defaults to 1.0 but may be input as any positive value.

The element mass is calculated from the pipe wall material, the external insulation, and the internalfluid. The insulation and the fluid contribute only to the element mass matrix. The corrosion thicknessallowance contributes only to the stress calculations. A positive wall mass real constant overrides thepipe wall mass calculation. A nonzero insulation area real constant overrides the insulation surface areacalculation (from the pipe outer diameter and length). A nonzero stiffness real constant overrides thecalculated axial pipe stiffness.

Element loads are described in Nodal Loading. Pressures may be input as surface loads on the elementfaces as shown by the circled numbers on Figure 1 (p. 99). Internal pressure (PINT) and external pressure(POUT) are input as positive values. The internal and external pressure loads are designed for closed-loop static pressure environments and therefore include pressure loads on fictitious "end caps" so thatthe pressure loads induce an axial stress and/or reaction in the pipe system. If a dynamic situation needsto be represented, such as a pipe venting to a lower pressure area or the internal flow is past a constric-tion in the pipe, these end cap loads may need to be modified by applying a nodal force normal to thecross-section of the pipe with the magnitude representing the change in pressure. Alternatively, theprecomputed end cap loads can be removed using KEYOPT(8) = 1 and the appropriate end cap loadsadded by the user. The transverse pressures (PX, PY, and PZ) may represent wind or drag loads (perunit length of the pipe) and are defined in the global Cartesian directions. Positive transverse pressuresact in the positive coordinate directions. The normal component or the projected full pressure may beused (KEYOPT(5)). Tapered pressures are not recognized. Only constant pressures are supported for thiselement. See PIPE16 - Elastic Straight Pipe (p. 206) for more information.

Temperatures may be input as element body loads at the nodes. Temperatures may have wall gradientsor diametral gradients (KEYOPT(1)). The average wall temperature at θ = 0° is computed as 2 * TAVG -T(180) and the average wall temperature at θ = -90° is computed as 2 * TAVG - T(90). The elementtemperatures are assumed to be linear along the length. The first temperature at node I (TOUT(I) orTAVG(I)) defaults to TUNIF. If all temperatures after the first are unspecified, they default to the first. Ifall temperatures at node I are input, and all temperatures at node J are unspecified, the node J temper-atures default to the corresponding node I temperatures. For any other pattern of input temperatures,unspecified temperatures default to TUNIF.

For piping analyses, the PIPE module of PREP7 may be used to generate the input for this element.KEYOPT(4) is used to identify the element type for output labeling and for postprocessing operations.

KEYOPT(7) is used to compute an unsymmetric gyroscopic damping matrix (often used for rotordynamicanalyses). The rotational frequency is input with the SPIN real constant (radians/time, positive in thepositive element x direction).


PIPE16

A summary of the element input is given in "PIPE16 Input Summary" (p. 101). A general description ofelement input is given in Element Input.

PIPE16 Input Summary

Nodes

I, J, K (K, the orientation node, is optional)

Degrees of Freedom


Real Constants

OD, TKWALL, SIFI, SIFJ, FLEX, DENSFL,DENSIN, TKIN, TKCORR, AREAIN, MWALL, STIFF,SPINSee Table 1: PIPE16 Real Constants (p. 103) for a description of the real constants

Material Properties

EX, ALPX (or CTEX or THSX),

PRXY (or NUXY), DENS, GXY, BETD, ALPD

Surface Loads

Pressures --

1-PINT, 2-PX, 3-PY, 4-PZ, 5-POUT

Body Loads

Temperatures --

TOUT(I), TIN(I), TOUT(J), TIN(J) if KEYOPT (1) = 0, orTAVG(I), T90(I), T180(I), TAVG(J), T90(J), T180(J) if KEYOPT (1) = 1

Special Features


KEYOPT(1)

Temperatures represent:

0 --

The through-wall gradient

1 --

The diametral gradient

KEYOPT(2)

Stress intensification factors:

0 --

Stress intensity factors from SIFI and SIFJ

1 --

Stress intensity factors at node I from tee joint calculation

2 --

Stress intensity factors at node J from tee joint calculation



PIPE16

3 --

Stress intensity factors at both nodes from tee joint calculation

KEYOPT(4)

Element identification (for output and postprocessing):

0 --

Straight pipe

1 --

Valve

2 --

Reducer

3 --

Flange

4 --

Expansion joint

5 --

Mitered bend

6 --

Tee branch

KEYOPT(5)

PX, PY, and PZ transverse pressures:

0 --

Use only the normal component of pressure

1 --

Use the full pressure (normal and shear components)

KEYOPT(6)


0 --

Do not print member forces or moments

2 --

Print member forces and moments in the element coordinate system

KEYOPT(7)

Gyroscopic damping matrix:

0 --

No gyroscopic damping matrix

1 --

Compute gyroscopic damping matrix. Real constant SPIN must be greater than zero. DENSFL andDENSIN must be zero.

Note

The real constant MWALL is not used to compute the gyroscopic damping matrix.

KEYOPT(8)

End cap loads:


PIPE16

0 --

Internal and external pressures cause loads on end caps

1 --

Internal and external pressures do not cause loads on end caps

Table 1 PIPE16 Real Constants

DescriptionNameNo.

Pipe outer diameterOD1

Wall thicknessTKWALL2

Stress intensification factor (node I)SIFI3

Stress intensification factor (node J)SIFJ4

Flexibility factorFLEX5

Internal fluid densityDENSFL6

Exterior insulation densityDENSIN7

Insulation thicknessTKIN8

Corrosion thickness allowanceTKCORR9

Insulation surface area (replaces program-calculated value)AREAIN10

Pipe wall mass (replaces program-calculated value)MWALL11

Axial pipe stiffness (replaces program-calculated value)STIFF12

Rotordynamic spin (required if KEYOPT(7) = 1)SPIN13

PIPE16 Output Data



• Additional element output as shown in Table 2: PIPE16 Element Output Definitions (p. 104)


The direct stress (SAXL) includes the internal pressure (closed end) effect. The direct stress does notinclude the axial component of the transverse thermal stress (STH). The principal stresses and the stressintensity include the shear force stress component, and are based on the stresses at the two extremepoints on opposite sides of the neutral axis. These quantities are computed at the outer surface andmight not occur at the same location around the pipe circumference. Angles listed in the output aremeasured as shown (θ) in Figure 2 (p. 104). A general description of solution output is given in SolutionOutput. See the Basic Analysis Guide for ways to view results.



PIPE16

Figure 2 PIPE16 Stress Output

J

SDIR

SBEND

SAXL

Torsional

Moment

Shear

Force

SH

STJ

θ




available.

Table 2 PIPE16 Element Output Definitions

RODefinitionName

YYElement NumberEL

YYNodes - I, JNODES

YYMaterial numberMAT

Y-VolumeVOLU:


11Corrosion thickness allowanceCORAL

22TOUT(I), TIN(I), TOUT(J), TIN(J)TEMP

33TAVG(I), T90(I), T180(I), TAVG(J), T90(J), T180(J)TEMP

YYPINT, PX, PY, PZ, POUTPRES

YYStress intensification factors at nodes I and JSFACTI, SFACTJ

YYStress due to maximum thermal gradient throughthe wall thickness

STH

Y-Hoop pressure stress for code calculationsSPR2

Y-Moment stress at nodes I and J for code calculationsSMI, SMJ

Y-Direct (axial) stressSDIR

Y-Maximum bending stress at outer surfaceSBEND

Y-Shear stress at outer surface due to torsionST

Y-Shear stress due to shear forceSSF


PIPE16

RODefinitionName

YYMaximum principal stress, minimum principal stress,maximum stress intensity, maximum equivalent

S:(1MX, 3MN, INT-MX, EQVMX)

stress (over eight points on the outside surface atboth ends of the element)

44Axial, radial, hoop, and shear stressesS:(AXL, RAD, H, XH)

44Maximum principal stress, minimum principal stress,stress intensity, equivalent stress

S:(1, 3, INT, EQV)

44Axial, radial, hoop, and shear strainsEPEL:(AXL, RAD, H,XH)

44Axial, radial, and hoop thermal strainEPTH:(AXL, RAD, H)

Y5Member forces for nodes I and J (in the elementcoordinate system)

MFOR:(X, Y, Z)

Y5Member moments for nodes I and J (in the elementcoordinate system)

MMOM:(X, Y, Z)

1. If the value is greater than 0.

2. If KEYOPT(1) = 0

3. If KEYOPT(1) = 1

4. The item repeats at 0°, 45°, 90°, 135°, 180°, 225°, 270°, 315° at node I, then at node J, all at the outersurface.

5. If KEYOPT(6) = 2


The following tables list output available through the ETABLE command using the Sequence Numbermethod. See The General Postprocessor (POST1) in the Basic Analysis Guide and The Item and SequenceNumber Table of this manual for more information. The following notation is used in Table 3: PIPE16

Item and Sequence Numbers (Node I) (p. 105) through Table 5: PIPE16 Item and Sequence Numbers (p. 107):

Name

output quantity as defined in the Table 2: PIPE16 Element Output Definitions (p. 104)

Item


E


I, J


Table 3 PIPE16 Item and Sequence Numbers (Node I)


Quant-

ity

Name

Circumferential LocationEItem

315°270°225°180°135°90°45°0°

2925211713951-LSSAXL



PIPE16


Quant-

ity

Name


315°270°225°180°135°90°45°0°

30262218141062-LSSRAD

31272319151173-LSSH

32282420161284-LSSXH

2925211713951-LEPELEPELAXL

30262218141062-LEPELEPELRAD

31272319151173-LEPELEPELH

32282420161284-LEPELEPELXH

2925211713951-LEPTHEPTHAXL

30262218141062-LEPTHEP-THRAD

31272319151173-LEPTHEPTHH

--------1SMISCMFORX

--------2SMISCMFORY

--------3SMISCMFORZ

--------4SMISCMMOMX

--------5SMISCMMOMY

--------6SMISCMMOMZ

--------13SMISCSDIR

--------14SMISCST

36312621161161-NMISCS1

38332823181383-NMISCS3

39342924191494-NMISCSINT

403530252015105-NMISCSEQV

--------90NMISCSBEND

--------91NMISCSSF

-3-2-1-4-LBFETOUT

-7-6-5-8-LBFETIN

Table 4 PIPE16 Item and Sequence Numbers (Node J)


Quant-

ity

Name


315°270°225°180°135°90°45°0°

6157534945413733-LSSAXL

6258545046423834-LSSRAD

6359555147433935-LSSH


PIPE16


Quant-

ity

Name


315°270°225°180°135°90°45°0°

6460565248444036-LSSXH



6359555147433935-LEPELEPELH

6460565248444036-LEPELEPELXH



6359555147433935-LEPTHEPTHH

--------7SMISCMFORX

--------8SMISCMFORY

--------9SMISCMFORZ

--------10SMISCMMOMX

--------11SMISCMMOMY

--------12SMISCMMOMZ

--------15SMISCSDIR

--------16SMISCST

7671666156514641-NMISCS1

7873686358534843-NMISCS3

7974696459544944-NMISCSINT

8075706560555045-NMISCSEQV


--------93NMISCSSF

-11-10-9-12-LBFETOUT

-15-14-13-16-LBFETIN

Table 5 PIPE16 Item and Sequence Numbers

ETABLE and

ESOL Command

Input

Output

Quant-

ity

Name EItem

17SMISCSTH

18SMISCPINT

19SMISCPX

20SMISCPY

21SMISCPZ



PIPE16

ETABLE and

ESOL Command

Input

Output

Quant-

ity

Name EItem

22SMISCPOUT

81NMISCSFACTI

82NMISCSFACTJ

83NMISCSPR2

84NMISCSMI

85NMISCSMJ

86NMISCS1MX

87NMISCS3MN

88NMISCSINTMX

89NMISCSEQVMX

PIPE16 Assumptions and Restrictions

• The pipe must not have a zero length or wall thickness. In addition, the OD must not be less than orequal to zero, the ID must not be less than zero, and the corrosion thickness allowance must be lessthan the wall thickness.

• The element temperatures are assumed to vary linearly along the length.

• The element may be used for both thin and thick-walled situations; however, some of the stress calcu-lations are based on thin-wall theory.

• The pipe element is assumed to have "closed ends" so that the axial pressure effect is included.

• Shear deflection capability is also included in the element formulation.

• Eigenvalues calculated in a gyroscopic modal analysis can be very sensitive to changes in the initialshift value, leading to potential error in either the real or imaginary (or both) parts of the eigenvalues.

PIPE16 Product Restrictions


ANSYS Professional

• The SPIN real constant (R13) is not available.

• The only special features allowed are stress stiffening and large deflections.

• KEYOPT(7) (gyroscopic damping) is not allowed.


PIPE16

PIPE18

Elastic Curved Pipe



Although this legacy element is available for use in your analysis, ANSYS recommends using a current-tech-nology element such as ELBOW290.

PIPE18, also known as an elbow element, is a circularly uniaxial element with tension, compression,torsion, and bending capabilities. The element has six degrees of freedom at each node: translationsin the nodal x, y, and z directions and rotations about the nodal x, y, and z axes.

Options are available to include various flexibility and stress intensification factors in the formulation.The element can account for insulation, contained fluid, and a corrosion allowance. See PIPE18 - Elastic

Curved Pipe (p. 217) for more details about this element.


+

Radius of

Curvature

4

PzPy

K

I

zy

x

Px

2

Z

X

Y

3

Th lmn x-z cn

n h I, J, K pln

K

J

1T180

T90 z

T

Tn

TgP

Pn

5

J

PIPE18 Input Data

The geometry, node locations, and the coordinate system for this element are shown in Figure 1 (p. 109).The element input data include three nodes, the pipe outer diameter, wall thickness, radius of curvature,optional stress intensification and flexibility factors, internal fluid density, exterior insulation densityand thickness, corrosion thickness allowance, and the isotropic material properties. The internal fluidand external insulation constants are used only to determine the added mass effects for these compon-ents.

Although the curved pipe element has only two endpoints (nodes I and J), the third node (K) is requiredto define the plane in which the element lies. This node must lie in the plane of the curved pipe andon the center-of-curvature side of line I-J. A node point belonging to another element (such as the



other node of a connecting straight pipe element) may be used. Input and output locations around thepipe circumference identified as being at 0° are located along the element y-axis, and similarly 90° isalong the element z-axis.

Only the lumped mass matrix is available.

The flexibility and stress intensification factors included in the element are calculated as follows:

ANSYS Flexibility Factor = 1.65/(h(1 + PrXk/tE)) or 1.0 (whichever is greater) (used if

KEYOPT(3) = 0 or 1 and FLXI not input)

Karman Flexibility Factor = (10 + 12h2)/(1 + 12h2) (used if KEYOPT(3) = 2 and FLXI notinput)

User Defined Flexibility Factors = FLXI (in-plane) and FLXO (out-of-plane) (may be inputas any positive value)

FLXO defaults to FLXI for all cases.

Stress Intensification Factor = 0.9/h2/3 or 1.0 (whichever is greater) (used for SIFI or SIFJif factor not input or if input less than 1.0 (must be positive))

where:

h = tR/r2

t = thicknessR = radius of curvaturer = average radiusE = modulus of elasticity

Xk = 6 (r/t)4/3 (R/r)1/3 if KEYOPT(3) = 1 and R/r ≥ 1.7, otherwise Xk = 0

P = Pi - Po if Pi - Po > 0, otherwise P = 0, Pi = internal pressure, Po = external pressure

Do not use KEYOPT(3) = 1 if the included angle of the complete elbow is less than 360/(π(R/r)) degrees.

Element loads are described in Nodal Loading. Pressures may be input as surface loads on the elementfaces as shown by the circled numbers on Figure 1 (p. 109). Internal pressure (PINT) and external pressure(POUT) are input as positive values. The internal and external pressure loads are designed for closed-loop static pressure environments and therefore include pressure loads on fictitious "end caps" so thatthe pressure loads induce an axial stress and/or reaction in the pipe system. If a dynamic situation needsto be represented, such as a pipe venting to a lower pressure area or the internal flow is past a constric-tion in the pipe, these end cap loads may need to be modified by applying a nodal force normal to thecross-section of the pipe with the magnitude representing the change in pressure. Alternatively, theprecomputed end cap loads can be removed using KEYOPT(8) = 1 and the appropriate end cap loadsadded by the user. Note that when using KEYOPT(8) = 1, the pressure load will be acting on only thewall of the elbow element so that the total pressure load will not be self-equilibrating. The transversepressures (PX, PY, and PZ) may represent wind or drag loads (per unit length of the pipe) and are definedin the global Cartesian directions. Positive transverse pressures act in the positive coordinate directions.Tapered pressures are not recognized. Only constant pressures are supported for this element.

Temperatures may be input as element body loads at the nodes. Temperatures may have wall gradientsor diametral gradients (KEYOPT(1)). The average wall temperature at θ = 0° is computed as 2 * TAVG -T(180) and the average wall temperature at θ = -90° is computed as 2 * TAVG - T(90). The element


PIPE18

temperatures are assumed to be linear along the length. The first temperature at node I (TOUT(I) orTAVG(I)) defaults to TUNIF. If all temperatures after the first are unspecified, they default to the first. Ifall temperatures at node I are input, and all temperatures at node J are unspecified, the node J temper-atures default to the corresponding node I temperatures. For any other pattern of input temperatures,unspecified temperatures default to TUNIF.

For piping analyses, the PIPE module of PREP7 may be used to generate the input for this element.

A summary of the element input is given below. A general description of element input is given inElement Input.


Nodes

I, J, K - where node K is in the plane of the elbow, on the center of curvature side of line I-J

Degrees of Freedom


Real Constants

OD, TKWALL, RADCUR, SIFI, SIFJ, FLXI,DENSFL, DENSIN, TKIN, TKCORR, (Blank), FLXOSee Table 1: PIPE18 Real Constants (p. 112) for a description of the real constants

Material Properties

EX, ALPX (or CTEX or THSX), PRXY (or NUXY), DENS, GXY, ALPD, BETD

Surface Loads

Pressures --


Body Loads

Temperatures --

TOUT(I), TIN(I), TOUT(J), TIN(J) if KEYOPT (1) = 0, orTAVG(I), T90(I), T180(I), TAVG(J), T90(J), T180(J) if KEYOPT (1) = 1

Special Features

Large deflectionBirth and death

KEYOPT(1)


0 --


1 --


KEYOPT(3)

Flex factor (if FLEX is not specified):

0 --

Use ANSYS flexibility factor (without pressure term)



PIPE18

1 --

Use ANSYS flexibility factor (with pressure term)

2 --

Use KARMAN flexibility factor

KEYOPT(6)


0 --

Do not print member forces or moments

2 --


KEYOPT(8)

End cap loads:

0 --


1 --



DescriptionNameNo.

Pipe outer diameterOD1

Wall thicknessTKWALL2

Radius of curvatureRADCUR3

Stress intensification factor (node I)SIFI4

Stress intensification factor (node J)SIFJ5

Flexibility factor (in-plane)FLXI6

Internal fluid densityDENSFL7

Exterior insulation densityDENSIN8

Insulation thicknessTKIN9

Corrosion thickness allowanceTKCORR10

--(Blank)11

Flexibility factor (out-of-plane). FLXO defaults to FLXI in all cases.FLXO12

PIPE18 Output Data





The stresses are computed with the outer diameter of the pipe reduced by twice the corrosion thicknessallowance. The direct stress includes the internal pressure (closed end) effect. Also printed for each endare the maximum and minimum principal stresses and the stress intensity. These quantities are computed


PIPE18

at the outer surface and may not occur at the same location around the pipe circumference. Some ofthese stresses are shown in Figure 2 (p. 113). The direct stress does not include the axial component ofthe transverse thermal stress. The principal stresses and the stress intensity include the shear forcestress component. Angles listed in the output are measured (θ) as shown in Figure 2 (p. 113). A generaldescription of solution output is given in Solution Output. See the Basic Analysis Guide for ways to viewresults.


J

SDIR

SBEND

hear

Force

θST

SHSAXL

Tsinl

Mmnt

J




available.


RODefinitionName

YYElement NumberEL

YYNodes - I, JNODES


Y-VolumeVOLU:


11Corrosion thickness allowanceCORAL

22TOUT(I), TIN(I), TOUT(J), TIN(J)TEMP

33TAVG(I), T90(I), T180(I), TAVG(J), T90(J), T180(J)TEMP

YYPINT, PX, PY, PZ, POUTPRES

Y-Element flexibility factorFFACT

Y4Member forces for nodes I and J (in the elementcoordinate system)

MFOR(X, Y, Z)

Y4Member moments for nodes I and J (in the elementcoordinate system)

MMOM(X, Y, Z)



PIPE18

RODefinitionName

YYStress intensification factors at nodes I and JSFACTI, SFACTJ


STH

Y-Hoop pressure stress for code calculationsSPR2

Y-Moment stress at nodes I and J for code calculationsSMI, SMJ

Y-Direct (axial) stressSDIR

Y-Maximum bending stress at outer surfaceSBEND

Y-Shear stress at outer surface due to torsionST

Y-Shear stress due to shear forceSSF

YYMaximum principal stress, minimum principal stress,maximum stress intensity, maximum equivalent

S(1MX, 3MN,INTMX,EQVMX)



S(1, 3, INT, EQV)

55Axial, radial, hoop, and shear stressesS(AXL, RAD, H, XH)

55Axial, radial, hoop, and shear strainsEPEL(AXL, RAD, H,XH)

55Axial, radial, and hoop thermal strainEPTH(AXL, RAD, H)

1. If the value is greater than 0.

2. If KEYOPT(1) = 0

3. If KEYOPT(1) = 1

4. If KEYOPT(6) = 2

5. The item repeats at 0°, 45°, 90°, 135°, 180°, 225°, 270°, 315° at node I, then at node J (all at the outersurface)


The following tables list output available through the ETABLE command using the Sequence Numbermethod. See The General Postprocessor (POST1) in the Basic Analysis Guide and The Item and SequenceNumber Table of this manual for more information. The following notation is used in Table 3: PIPE18

Item and Sequence Numbers (Node I) (p. 115) through Table 5: PIPE18 Item and Sequence Numbers (p. 117):

Name


Item


E



PIPE18

I,J




Quant-

ity

Name


315°270°225°180°135°90°45°0°

2925211713951-LSSAXL

30262218141062-LSSRAD

31272319151173-LSSH

32282420161284-LSSXH








36312621161161-NMISCS1

38332823181383-NMISCS3

39342924191494-NMISCSINT

403530252015105-NMISCSEQV


--------92NMISCSSF

--------1SMISCMFORX

--------2SMISCMFORY

--------3SMISCMFORZ

--------4SMISCMMOMX

--------5SMISCMMOMY

--------6SMISCMMOMZ

--------13SMISCSDIR

--------14SMISCST

-3-2-1-4-LBFETOUT



PIPE18


Quant-

ity

Name


315°270°225°180°135°90°45°0°

-7-6-5-8-LBFETIN



Quant-

ity

Name


315°270°225°180°135°90°45°0°

6157534945413733-LSSAXL

6258545046423834-LSSRAD

6359555147433935-LSSH

6460565248444036-LSSXH



6359555147433935-LEPELEPELH

6460565248444036-LEPELEPELXH



6359555147433935-LEPTHEPTHH

7671666156514641-NMISCS1

7873686358534843-NMISCS3

7974696459544944-NMISCSINT

8075706560555045-NMISCSEQV


--------94NMISCSSF

--------7SMISCMFORX

--------8SMISCMFORY

--------9SMISCMFORZ




--------15SMISCSDIR

--------16SMISCST



PIPE18


Quant-

ity

Name


315°270°225°180°135°90°45°0°

-15-14-13-16-LBFETIN

Table 5 PIPE18 Item and Sequence Numbers

ETABLE and

ESOL Command

Input

Output

Quant-

ity

Name EItem

81NMISCSFACTI

82NMISCSFACTJ

83NMISCSPR2

84NMISCSMI

85NMISCSMJ

86NMISCS1MX

87NMISCS3MN

88NMISCSINTMX

89NMISCSEQVMX

90NMISCFFACT

17SMISCSTH

18SMISCPINT

19SMISCPX

20SMISCPY

21SMISCPZ

22SMISCPOUT


• The curved pipe must not have a zero length or wall thickness. In addition, the OD must not be lessthan or equal to zero and the ID must not be less than zero.

• The corrosion allowance must be less than the wall thickness.

• The element is limited to having an axis with a single curvature and a subtended angle of 0° < θ ≤ 90°.

• Shear deflection capability is also included in the element formulation.

• The elbow is assumed to have "closed ends" so that the axial pressure effect is included.

• When used in a large deflection analysis, the location of the third node (K) is used only to initially orientthe element.

• The element temperatures are assumed to be linear along the length. The average wall temperatureat θ = 0° is computed as 2 * TAVG - T(180) and the average wall temperature at θ = -90° is computedas 2 * TAVG - T(90).



PIPE18

• Stress intensification factors input with values less than 1.0 are set to 1.0.

• The element formulation is based upon thin-walled theory. The elbow should have a large radius-to-thickness ratio since the integration points are assumed to be located at the midthickness of the wall.

• Only the lumped mass matrix is available.



ANSYS Professional

• The ALPD and BETD material properties are not allowed.

• The only special feature allowed is large deflection.


PIPE18

PLANE42

2-D Structural Solid


PLANE42 Element Description

Although this legacy element is available for use in your analysis, ANSYS recommends using a current-tech-nology element such as PLANE182 (KEYOPT(1) = 3).

PLANE42 is used for 2-D modeling of solid structures. The element can be used either as a plane element(plane stress or plane strain) or as an axisymmetric element. The element is defined by four nodeshaving two degrees of freedom at each node: translations in the nodal x and y directions. The elementhas plasticity, creep, swelling, stress stiffening, large deflection, and large strain capabilities.

An option is available to suppress the extra displacement shapes. See PLANE183 for a multi-node versionof this element. See SOLID272 for an axisymmetric version that accepts nonaxisymmetric loading.

Figure 1 PLANE42 Geometry

X (or radial)

Y

(or axial)

1

4

2

3

L K

I

J

K, L

I

J

Tngu Optn -

nt ecmmene

Eement cnte

system shwn f

KEOPT1 = 1

x

y

PLANE42 Input Data

The geometry, node locations, and the coordinate system for this element are shown in Figure 1 (p. 119).The element input data includes four nodes, a thickness (for the plane stress option only) and the or-thotropic material properties. Orthotropic material directions correspond to the element coordinatedirections. The element coordinate system orientation is as described in Coordinate Systems.

Element loads are described in Nodal Loading. Pressures may be input as surface loads on the elementfaces as shown by the circled numbers on Figure 1 (p. 119). Positive pressures act into the element.Temperatures and fluences may be input as element body loads at the nodes. The node I temperatureT(I) defaults to TUNIF. If all other temperatures are unspecified, they default to T(I). For any other inputpattern, unspecified temperatures default to TUNIF. Similar defaults occurs for fluence except that zerois used instead of TUNIF.

The nodal forces, if any, should be input per unit of depth for a plane analysis (except for KEYOPT(3) =3) and on a full 360° basis for an axisymmetric analysis. KEYOPT(2) is used to include or suppress theextra displacement shapes.



KEYOPT(5) and KEYOPT(6) provide various element printout options. (See Element Solution.)

You cannot set initial state conditions (INISTATE) using this element. You can set initial state conditionsusing current-technology elements (such as LINK180,SHELL181). To continue using initial state conditionsin future versions of ANSYS, consider using a current element technology. For more information, seeLegacy vs. Current Element Technologies in the Element Reference. For more information about settinginitial state values, see the INISTATE command documentation and Initial State Loading in the Basic

Analysis Guide.

You can include the effects of pressure load stiffness in a geometric nonlinear analysis using SOLCON-

TROL,,,INCP. Pressure load stiffness effects are included in linear eigenvalue buckling automatically. Ifan unsymmetric matrix is needed for pressure load stiffness effects, use NROPT,UNSYM.

A summary of the element input is given in "PLANE42 Input Summary" (p. 120). A general description ofelement input is given in Element Input. For axisymmetric applications see Harmonic AxisymmetricElements.

PLANE42 Input Summary

Nodes

I, J, K, L

Degrees of Freedom

UX, UY

Real Constants

None, if KEYOPT(3) = 0, 1, or 2THK - Thickness if KEYOPT(3) = 3

Material Properties

EX, EY, EZ, PRXY, PRYZ, PRXZ (or NUXY, NUYZ, NUXZ),ALPX, ALPY, ALPZ (or CTEX, CTEY, CTEZ or THSX, THSY, THSZ), DENS, GXY, BETD, ALPD

Surface Loads

Pressures --

face 1 (J-I), face 2 (K-J), face 3 (L-K), face 4 (I-L)

Body Loads

Temperatures --

T(I), T(J), T(K), T(L)

Fluences --

FL(I), FL(J), FL(K), FL(L)

Special Features

Plasticity (BISO, MISO, BKIN, MKIN, KINH, DP, ANISO)Creep (CREEP, RATE)Swelling (SWELL)Elasticity (MELAS)Other material (USER)Stress stiffeningLarge deflectionLarge strain


PLANE42

Birth and deathAdaptive descent

Items in parentheses refer to data tables associated with the TB command.

KEYOPT(1)

Element coordinate system defined:

0 --

Element coordinate system is parallel to the global coordinate system

1 --

Element coordinate system is based on the element I-J side

KEYOPT(2)

Extra displacement shapes:

0 --

Include extra displacement shapes

1 --

Suppress extra displacement shapes

KEYOPT(3)

Element behavior:

0 --

Plane stress

1 --

Axisymmetric

2 --

Plane strain (Z strain = 0.0)

3 --

Plane stress with thickness input

KEYOPT(5)

Extra stress output:

0 --

Basic element solution

1 --

Repeat basic solution for all integration points

2 --

Nodal stress solution

KEYOPT(6)

Extra surface output:

0 --


1 --

Surface solution for face I-J also.

2 --

Surface solution for both faces I-J and K-L also. (Surface solution available for linear materials only)



PLANE42

3 --

Nonlinear solution at each integration point also.

4 --

Surface solution for faces with nonzero pressure

PLANE42 Output Data



• Additional element output as shown in Table 1: PLANE42 Element Output Definitions (p. 122)


The element stress directions are parallel to the element coordinate system. Surface stresses are availableon any face. Surface stresses on face IJ, for example, are defined parallel and perpendicular to the IJline and along the Z axis for a plane analysis or in the hoop direction for an axisymmetric analysis. Ageneral description of solution output is given in Solution Output. See the Basic Analysis Guide for waysto view results.

Figure 2 PLANE42 Stress Output

X (or radial)

Y

(or axial)

1

4

2

3L K

I

J

S

S

Stress directions shown are for KEYOPT(1) = 0




available.

Table 1 PLANE42 Element Output Definitions

RODefinitionName

YYElement NumberEL

YYNodes - I, J, K, LNODES


PLANE42

RODefinitionName


YYAverage thicknessTHICK

YYVolumeVOLU:


YYPressures P1 at nodes J,I; P2 at K,J; P3 at L,K; P4at I,L

PRES

YYTemperatures T(I), T(J), T(K), T(L)TEMP

YYFluences FL(I), FL(J), FL(K), FL(L)FLUEN

YYStresses (SZ = 0.0 for plane stress elements)S:X, Y, Z, XY

-YPrincipal stressesS:1, 2, 3

-YStress intensityS:INT

YYEquivalent stressS:EQV

YYElastic strainsEPEL:X, Y, Z, XY

-YPrincipal elastic strainEPEL:1, 2, 3

Y-Equivalent elastic strain [4]EPEL:EQV

YYAverage thermal strainEPTH:X, Y, Z, XY

Y-Equivalent thermal strain [4]EPTH:EQV

11Plastic strainEPPL:X, Y, Z, XY

1-Equivalent plastic strain [4]EPPL:EQV

11Creep strainsEPCR:X, Y, Z, XY

1-Equivalent creep strains [4]EPCR:EQV

11Swelling strainEPSW:

11Equivalent plastic strainNL:EPEQ

11Ratio of trial stress to stress on yield surfaceNL:SRAT

11Equivalent stress on stress-strain curveNL:SEPL

1-Hydrostatic pressureNL:HPRES

22Face labelFACE

22Surface elastic strains (parallel, perpendicular,Z or hoop)

EPEL(PAR, PER,Z)

22Surface average temperatureTEMP

22Surface stresses (parallel, perpendicular, Z orhoop)

S(PAR, PER, Z)

22Surface stress intensitySINT

22Surface equivalent stressSEQV

Y-Integration point locationsLOCI:X, Y, Z

1. Nonlinear solution, output only if the element has a nonlinear material.

2. Surface output (if KEYOPT(6) is 1,2, or 4)




PLANE42

4. The equivalent strains use an effective Poisson's ratio: for elastic and thermal this value is set by theuser (MP,PRXY); for plastic and creep this value is set at 0.5.

Table 2 PLANE42 Miscellaneous Element Output

RONames of Items OutputDescription

-YTEMP, SINT, SEQV, EPEL(1, 2,3), S(X, Y, Z, XY), S(1, 2, 3)

Integration Point Solution(KEYOPT(5) = 1)

-YTEMP, S(X, Y, Z, XY), S(1, 2,3), SINT, SEQV

Nodal Stress Solution (KEY-OPT(5) = 2)

-1EPPL, EPEQ, SRAT, SEPL,HPRES, EPCR, EPSW

Nonlinear Integration PointSolution (KEYOPT(6) = 3)

1. Valid if the element has a nonlinear material and KEYOPT(6) = 3

Note

For axisymmetric solutions with KEYOPT(1) = 0, the X, Y, Z, and XY stress and strain outputscorrespond to the radial, axial, hoop, and in-plane shear stresses and strains, respectively.

Table 3: PLANE42 Item and Sequence Numbers (p. 124) lists output available through the ETABLE commandusing the Sequence Number method. See The General Postprocessor (POST1) in the Basic Analysis Guide

and The Item and Sequence Number Table of this manual for more information. The following notationis used in Table 3: PLANE42 Item and Sequence Numbers (p. 124):

Name

output quantity as defined in the Table 1: PLANE42 Element Output Definitions (p. 122)

Item


E


I,J,K,L

sequence number for data at nodes I,J,K,L

Table 3 PLANE42 Item and Sequence Numbers


Quant-

ity

Name

LKJIEItem

--12-SMISCP1

-34--SMISCP2

56---SMISCP3

8--7-SMISCP4

161161-NMISCS:1

171272-NMISCS:2

181383-NMISCS:3


PLANE42


Quant-

ity

Name

LKJIEItem

191494-NMISCS:INT

2015105-NMISCS:EQV

24232221-NMISCFLUEN

----25NMISCTHICK

See Surface Solution for the item and sequence numbers for surface output for the ETABLE command.

PLANE42 Assumptions and Restrictions

• The area of the element must be nonzero.

• The element must lie in a global X-Y plane as shown in Figure 1 (p. 119) and the Y-axis must be the axisof symmetry for axisymmetric analyses. An axisymmetric structure should be modeled in the +X quadrants.

• A triangular element may be formed by defining duplicate K and L node numbers (see DegeneratedShape Elements).

• The extra shapes are automatically deleted for triangular elements so that a constant strain elementresults.

• Surface stress printout is valid only if the conditions described in Element Solution are met.

PLANE42 Product Restrictions


ANSYS Professional

• Fluence body loads are not applicable.

• The only special feature allowed is stress stiffening.

• KEYOPT(6) = 3 is not applicable.



PLANE42


SOLID45

3-D Structural Solid


SOLID45 Element Description

Although this legacy element is available for use in your analysis, ANSYS recommends using a current-tech-nology element such as SOLID185 (KEYOPT(2) = 3).

SOLID45 is used for the 3-D modeling of solid structures. The element is defined by eight nodes havingthree degrees of freedom at each node: translations in the nodal x, y, and z directions.

The element has plasticity, creep, swelling, stress stiffening, large deflection, and large strain capabilities.A reduced integration option with hourglass control is available. A higher-order version of the SOLID45element is SOLID186.

Figure 1 SOLID45 Geometry

I

P

K

J

NM

L

Z

X

Y

5

2

4

3

1

6

O

M O,P

I K,L

J

N

Prism Option

I

Teahedal -

ec eded

y

x

Surf Coorint Sstm

x

y

zy

x

Elee c dae

ye (h w

ET() = )

SOLID45 Input Data

The geometry, node locations, and the coordinate system for this element are shown in Figure 1 (p. 127).The element is defined by eight nodes and the orthotropic material properties. Orthotropic materialdirections correspond to the element coordinate directions. The element coordinate system orientationis as described in Coordinate Systems.

Element loads are described in Nodal Loading. Pressures may be input as surface loads on the elementfaces as shown by the circled numbers on Figure 1 (p. 127). Positive pressures act into the element.Temperatures and fluences may be input as element body loads at the nodes. The node I temperatureT(I) defaults to TUNIF. If all other temperatures are unspecified, they default to T(I). For any other input



temperature pattern, unspecified temperatures default to TUNIF. Similar defaults occurs for fluence exceptthat zero is used instead of TUNIF.

KEYOPT(1) is used to include or suppress the extra displacement shapes. KEYOPT(5) and KEYOPT(6)provide various element printout options (see Element Solution).

This element also supports uniform reduced (1 point) integration with hourglass control when KEYOPT(2)= 1. Using uniform reduced integration provides the following advantages when running a nonlinearanalysis:

• Less cpu time is required for element stiffness formation and stress/strain calculations to achievea comparable accuracy to the FULL integration option.

• The length of the element history saved record (.ESAV and .OSAV) is about 1/7th as much as whenthe full integration (2 X 2 X 2) is used for the same number of elements.

• Nonlinear convergence characteristic of the option is generally far superior to the default full integ-ration with extra displacement shape; that is, KEYOPT(1) = 0, KEYOPT(2) = 0.

• The analysis will not suffer from volumetric locking which can be caused by plasticity or other in-compressible material properties.

An analysis using uniform reduced integration can have the following disadvantages:

• The analysis is not as accurate as the full integration method, which is apparent in the linear ana-lysis for the same mesh.

• The analysis cannot capture the bending behavior with a single layer of elements; for example, inthe case of a fixed-end cantilever with a lateral point load, modeled by one layer of elements laterally.Instead, four elements are usually recommended.

When the uniform reduced integration option is used (KEYOPT(2) = 1 - this option is the same as SOL-ID185 with KEYOPT(2) = 1), you can check the accuracy of the solution by comparing the total energy(SENE label in ETABLE) and the artificial energy (AENE label in ETABLE) introduced by hourglass control.If the ratio of artificial energy to total energy is less than 5%, the solution is generally acceptable. If theratio exceeds 5%, refine the mesh. The total energy and artificial energy can also be monitored by usingthe OUTPR,VENG command in the solution phase. For more details, see Energies in the Mechanical

APDL Theory Reference.


Analysis Guide.



A summary of the element input is given in "SOLID45 Input Summary" (p. 129). A general description ofelement input is given in Element Input.


SOLID45

SOLID45 Input Summary

Nodes

I, J, K, L, M, N, O, P

Degrees of Freedom

UX, UY, UZ

Real Constants

HGSTF - Hourglass control factor needed only when KEYOPT(2) = 1.

Note

The valid value for this real constant is any positive number; default = 1.0. We recommendthat you use a value between 1 and 10.

Material Properties

EX, EY, EZ, PRXY, PRYZ, PRXZ (or NUXY, NUYZ, NUXZ), GXY, GYZ, GXZ, ALPX, ALPY, ALPZ (or CTEX,CTEY, CTEZ or THSX, THSY, THSZ), DENS, BETD, ALPD

Surface Loads

Pressures --

face 1 (J-I-L-K), face 2 (I-J-N-M), face 3 (J-K-O-N), face 4 (K-L-P-O), face 5 (L-I-M-P), face 6 (M-N-O-P)

Body Loads

Temperatures --

T(I), T(J), T(K), T(L), T(M), T(N), T(O), T(P)

Fluences --

FL(I), FL(J), FL(K), FL(L), FL(M), FL(N), FL(O), FL(P)

Special Features

Plasticity (BISO, MISO, BKIN, MKIN, KINH, DP, ANISO)Creep (CREEP, RATE)Swelling (SWELL)Elasticity (MELAS)Other material (USER)Stress stiffeningLarge deflectionLarge strainBirth and deathAdaptive descentInitial stress import


KEYOPT(1)

Include or suppress extra displacement shapes:

0 --

Include extra displacement shapes

1 --

Suppress extra displacement shapes



SOLID45

KEYOPT(2)

Integration option:

0 --

Full integration with or without extra displacement shapes, depending on the setting of KEYOPT(1)

1 --

Uniform reduced integration with hourglass control; suppress extra displacement shapes (KEYOPT(1)is automatically set to 1).

KEYOPT(4)

Element coordinate system:

0 --

Element coordinate system is parallel to the global coordinate system

1 --

Element coordinate system is based on the element I-J side

KEYOPT(5)

Extra element output:

0 --


1 --


2 --

Nodal Stress Solution

KEYOPT(6)


0 --


1 --

Surface solution for face I-J-N-M also

2 --

Surface solution for face I-J-N-M and face K-L-P-O (Surface solution available for linear materials only)

3 --

Include nonlinear solution at each integration point

4 --


KEYOPT(9)

Initial stress subroutine option (available only through direct input of the KEYOPT command):

0 --

No user subroutine to provide initial stress (default)

1 --

Read initial stress data from user subroutine INISTATE (see the Guide to ANSYS User Programmable

Features for user written subroutines)

SOLID45 Output Data



SOLID45


• Additional element output as shown in Table 1: SOLID45 Element Output Definitions (p. 131)

Several items are illustrated in Figure 2 (p. 131). The element stress directions are parallel to the elementcoordinate system. The surface stress outputs are in the surface coordinate systems and are availablefor any face (KEYOPT(6)). The coordinate systems for faces IJNM and KLPO are shown in Figure 1 (p. 127).The other surface coordinate systems follow similar orientations as indicated by the pressure face nodedescription. Surface stress printout is valid only if the conditions described in Element Solution are met.A general description of solution output is given in Solution Output. See the Basic Analysis Guide forways to view results.

Figure 2 SOLID45 Stress Output

SZ

X

Y

I

P

K

J

NM

L

Z

X

Y

O

Stress directions shown are for KEYOPT(4) = 0

When KEYOPT(2) = 1 (the element is using uniform reduced integration), all the outputs for the elementintegration points are output in the same style as the full integration outputs. The number of pointsfor full integration is used for consistency of output within the same element type.




available.

Table 1 SOLID45 Element Output Definitions

RODefinitionName

YYElement NumberEL

YYNodes - I, J, K, L, M, N, O, PNODES



SOLID45

RODefinitionName


YYVolumeVOLU:


YYPressures P1 at nodes J, I, L, K; P2 at I, J, N, M; P3 atJ, K, O, N; P4 at K, L, P, O; P5 at L, I, M, P; P6 at M, N,O, P

PRES

YYTemperatures T(I), T(J), T(K), T(L), T(M), T(N), T(O), T(P)TEMP

YYFluences FL(I), FL(J), FL(K), FL(L), FL(M), FL(N), FL(O),FL(P)

FLUEN

YYStressesS:X, Y, Z, XY, YZ, XZ

YYPrincipal stressesS:1, 2, 3

YYStress intensityS:INT


YYElastic strainsEPEL:X, Y, Z, XY, YZ,XZ

-YPrincipal elastic strainsEPEL:1, 2, 3

YYEquivalent elastic strain [4]EPEL:EQV

5-Average thermal strainsEPTH:X, Y, Z, XY, YZ,XZ

5-Equivalent thermal strain [4]EPTH:EQV

11Average plastic strainsEPPL:X, Y, Z, XY, YZ,XZ

11Equivalent plastic strain [4]EPPL:EQV

11Average creep strainsEPCR:X, Y, Z, XY, YZ,XZ

11Equivalent creep strain [4]EPCR:EQV

11Average swelling strainEPSW:

11Average equivalent plastic strainNL:EPEQ


11Average equivalent stress from stress-strain curveNL:SEPL

1Hydrostatic pressureNL:HPRES

22Face labelFACE

22Face areaAREA


22Surface elastic strains (X ,Y, XY)EPEL

22Surface pressurePRESS

22Surface stresses (X-axis parallel to line defined byfirst two nodes which define the face)

S(X, Y, XY)

22Surface principal stressesS(1, 2, 3)



SOLID45

RODefinitionName



1. Nonlinear solution, output only if the element has a nonlinear material

2. Surface output (if KEYOPT(6) is 1, 2, or 4)

3. Available only at centroid as a *GET item


5. Output only if element has a thermal load.

Table 2 SOLID45 Miscellaneous Element Output


-1EPPL, EPEQ, SRAT, SEPL,HPRES, EPCR, EPSW

Nonlinear Integration Pt.Solution

-2TEMP, S(X, Y, Z, XY, YZ, XZ),SINT, SEQV, EPEL

Integration Point StressSolution

-3TEMP, S(X, Y, Z, XY, YZ, XZ),SINT, SEQV, EPEL


1. Output at each of eight integration points, if the element has a nonlinear material and KEYOPT(6) = 3

2. Output at each integration point, if KEYOPT(5) = 1

3. Output at each node, if KEYOPT(5) = 2

Table 3: SOLID45 Item and Sequence Numbers (p. 133) lists output available through the ETABLE commandusing the Sequence Number method. See The General Postprocessor (POST1) in the Basic Analysis Guide

and The Item and Sequence Number Table of this manual for more information. The following notationis used in Table 3: SOLID45 Item and Sequence Numbers (p. 133):

Name

output quantity as defined in the Table 1: SOLID45 Element Output Definitions (p. 131)

Item


I,J,...,P

sequence number for data at nodes I,J,...,P

Table 3 SOLID45 Item and Sequence Numbers


Quant-

ity

Name

PONMLKJIItem

----3412SMISCP1

--78--65SMISCP2

-1112--109-SMISCP3



SOLID45


Quant-

ity

Name

PONMLKJIItem

1516--1413--SMISCP4

20--1917--18SMISCP5

24232221----SMISCP6

36312621161161NMISCS:1

37322722171272NMISCS:2

38332823181383NMISCS:3

39342924191494NMISCS:INT

403530252015105NMISCS:EQV

4847464544434241NMISCFLUEN


SOLID45 Assumptions and Restrictions

• Zero volume elements are not allowed.

• Elements may be numbered either as shown in Figure 1 (p. 127) or may have the planes IJKL andMNOP interchanged.

• The element may not be twisted such that the element has two separate volumes. This occursmost frequently when the elements are not numbered properly.

• All elements must have eight nodes.

– A prism-shaped element may be formed by defining duplicate K and L and duplicate O and Pnode numbers (see Degenerated Shape Elements).

– A tetrahedron shape is also available. The extra shapes are automatically deleted for tetrahedronelements.

SOLID45 Product Restrictions


ANSYS Professional





SOLID45

CONTAC52

3-D Point-to-Point Contact

MP ME ST PR PRN <> <> <> <> <> <> <> PP <> EME MFSProduct Restrictions

CONTAC52 Element Description

Although this legacy element is available for use in your analysis, ANSYS recommends using a current-tech-nology element such as CONTA178.

CONTAC52 represents two surfaces which may maintain or break physical contact and may slide relativeto each other. The element is capable of supporting only compression in the direction normal to thesurfaces and shear (Coulomb friction) in the tangential direction. The element has three degrees offreedom at each node: translations in the nodal x, y, and z directions.

The element may be initially preloaded in the normal direction or it may be given a gap specification.A specified stiffness acts in the normal and tangential directions when the gap is closed and not sliding.

Figure 1 CONTAC52 Geometry

Gap

J

I

αz

z

x

x

y

y

z x

y

β

xz

y

Z

X

Y

CONTAC52 Input Data

The geometry, node locations, and the coordinate system for this element are shown in Figure 1 (p. 135).The element is defined by two nodes, two stiffnesses (KN and KS), an initial gap or interference (GAP),and an initial element status (START). The orientation of the interface is defined by the node locations,or by a user-specified gap direction. The interface is assumed to be perpendicular to the I-J line or tothe specified gap direction. The element coordinate system has its origin at node I and the x-axis is



directed toward node J or in the user-specified gap direction. The interface is parallel to the elementy-z plane.

The normal stiffness, KN, should be based upon the stiffness of the surfaces in contact. See NonlinearStructural Analysis in the Structural Analysis Guide for guidelines on choosing a value for KN. In somecases (such as initial interference analyses, nonconvergence, or over penetration), it may be useful tochange the KN value between load steps or in a restart in order to obtain an accurate, convergedsolution. The sticking stiffness, KS, represents the stiffness in the tangential direction when elasticCoulomb friction is selected (µ > 0.0 and KEYOPT(1) = 0). The coefficient of friction µ is input as materialproperty MU and is evaluated at the average of the two node temperatures. Stiffnesses may also becomputed from the maximum expected force divided by the maximum allowable surface displacement.KS defaults to KN.

The initial gap defines the gap size (if positive) or the displacement interference (if negative). This inputis the opposite of that used for CONTAC12 (described in the Feature Archive). If you do not specify thegap direction (by means of real constants NX, NY, and NZ), an interference causes the nodes to separate.The gap size may be input as a real constant (GAP) or automatically calculated from the input nodelocations (as the distance between node I and node J) if KEYOPT(4) = 1. Interference must be input asa real constant. Stiffness is associated with a zero or negative gap. The initial element status (START) isused to define the "previous" condition of the interface to be used at the start of the first substep. Thisinput is used to override the condition implied by the interference specification and is useful in anticip-ating the final interface configuration and in reducing the number of iterations required for convergence.

You can specify the gap direction by means of real constants NX, NY, and NZ (the global Cartesian X,Y, and Z components of the gap direction vector). If you do not specify the gap direction, the programwill calculate the direction based on the initial positions of the I and J nodes, such that a positive normaldisplacement (in the element coordinate system) of node J relative to node I tends to open the gap.You should always specify the gap direction if nodes I and J have the same initial coordinates, if themodel has an initial interference condition in which the underlying elements' geometry overlaps, or ifthe initial open gap distance is very small. If the gap is initially geometrically open, the correct normal(NX, NY, NZ) usually points from node I toward node J.

The only material property used is the interface coefficient of friction µ. A zero value should be usedfor frictionless surfaces. Temperatures may be specified at the element nodes (for material propertyevaluation only). The node I temperature T(I) defaults to TUNIF. The node J temperature defaults to T(I).

The force deflection relationships for the interface element can be separated into the normal and tan-gential (sliding) directions as shown in Figure 2 (p. 139). The element condition at the beginning of thefirst substep is determined from the START parameter. If the interface is closed and sticking, KN is usedin the gap resistance and KS is used for sticking resistance. If the interface is closed but sliding, KN isused in the gap resistance and the constant friction force µFN is used for the sliding resistance.

In the normal direction, when the normal force (FN) is negative, the interface remains in contact andresponds as a linear spring. As the normal force becomes positive, contact is broken and no force istransmitted.

KEYOPT(3) can be used to specify a "weak spring" across an open interface, which is useful for preventingrigid body motion that could occur in a static analysis. The weak spring stiffness is computed by mul-tiplying the normal stiffness KN by a reduction factor. The default reduction factor of 1E-6 can beoverridden with real constant REDFACT.


CONTAC52

This "weak spring" capability is not analogous to overlaying an actual spring element (such as COMBIN14)with a low stiffness value. The REDFACT capability will not limit gap separation when a tensile force isapplied.

In the tangential direction, for FN < 0 and the absolute value of the tangential force (FS) less than µ|FN|,the interface sticks and responds as a linear spring. For FN < 0 and FS = µ|FN|, sliding occurs. If contactis broken, FS = 0.

If KEYOPT(1) = 1, rigid Coulomb friction is selected, KS is not used, and the elastic sticking capability isremoved. This option is useful for displacement controlled problems or for certain dynamic problemswhere sliding dominates.

For analyses involving friction, using NROPT,UNSYM is useful (and, in fact, sometimes required) forproblems where the normal and tangential (sliding) motions are strongly coupled, such as in a wedgeinsertion problem.

A summary of the element input is given in "CONTAC52 Input Summary" (p. 137). A general descriptionof element input is given in Element Input.

CONTAC52 Input Summary

Nodes

I, J

Degrees of Freedom

UX, UY, UZ

Real Constants

KN, GAP, START, KS, REDFACT, NX,NY, NZ

See Table 1: CONTAC52 Real Constants (p. 138) for details on these real constants.

Material Properties

MU

Surface Loads

None

Body Loads

Temperatures --

T(I), T(J)

Special Features

NonlinearAdaptive descent

KEYOPT(1)

Sticking stiffness if MU > 0.0:

0 --

Elastic Coulomb friction (KS used for sticking stiffness)

1 --

Rigid Coulomb friction (resisting force only)



CONTAC52

KEYOPT(3)

Weak spring across open gap:

0 --

No weak spring across an open gap

1 --

Use a weak spring across an open gap

KEYOPT(4)

Basis for gap size:

0 --

Gap size based on gap real constant

1 --

Gap size determined from initial node locations (ignore gap real constant)

KEYOPT(7)

Element-level time incrementation control. Note that this option should be activated first at the procedurelevel if SOLCONTROL is ON. SOLCONTROL,ON,ON is the most frequent usage with this element. IfSOLCONTROL,ON,OFF, this keyoption is not activated.

0 --

Change in contact predictions made to achieve the minimum time/load increment whenever achange in contact status occurs

1 --

Change in contact predictions made to maintain a reasonable time/load increment (recommended)

Table 1 CONTAC52 Real Constants

DescriptionNameNo.

Normal stiffnessKN1

Initial gap size; a negative value assumes an initial interferencecondition.

GAP2

Initial condition:

START3

If = 0.0 or blank, initial status of element is determinedfrom gap inputIf = 1.0, gap is initially closed and not sliding (if MU ≠ 0.0),or sliding (if MU = 0.0)If = 2.0, gap is initially closed and slidingIf = 3.0, gap initially open

Sticking stiffnessKS4

Default reduction factor 1E-6REDFACT5

Defined gap normal - X componentNX6

Defined gap normal - Y componentNY7

Defined gap normal - Z componentNZ8

CONTAC52 Output Data



CONTAC52


• Additional element output as shown in Table 2: CONTAC52 Element Output Definitions (p. 140).

Force-deflection curves are illustrated in Figure 2 (p. 139).

The value of USEP is determined from the normal displacement (un) (in the element x-direction) between

the interface nodes at the end of a substep, that is: USEP = (un)J - (un)I + GAP. This value is used in de-

termining the normal force, FN. The values represented by UT(Y, Z) are the total translational displace-ments in the element y and z directions. The maximum value printed for the sliding force, FS, is µ|FN|.Sliding may occur in both the element y and z directions. STAT describes the status of the element atthe end of a substep. If STAT = 1, the gap is closed and no sliding occurs. If STAT = 3, the gap is open.A value of STAT = 2 indicates the node J slides relative to node I. For a frictionless surface (µ = 0.0), theconverged element status is either STAT = 2 or 3.

The element coordinate system orientation angles α and β (shown in Figure 1 (p. 135)) are computedby the program from the node locations. These values are printed as ALPHA and BETA respectively. αranges from 0° to 360° and β from -90° to +90°. Elements lying along the Z-axis are assigned values ofα = 0°, β = ± 90°, respectively. Elements lying off the Z-axis have their coordinate system oriented asshown for the general α, β position. Note, for α = 90°, β → 90°, the element coordinate system flips90° about the Z-axis. The value of ANGLE represents the principal angle of the friction force in the elementy-z plane. A general description of solution output is given in Solution Output. See the Basic Analysis

Guide for ways to view results.

Figure 2 CONTAC52 Force-Deflection Relationship

1

FN

(a)

KN

(un)J - (un)I + GAP (us)J - (us)I

1

FS

KS

−µ FN

µ FN

For FN < 0, ad o

revered loadig

(b)





CONTAC52


available.

Table 2 CONTAC52 Element Output Definitions

RODefinitionName

YYElement NumberEL

YYNodes - I, JNODES


YYT(I), T(J)TEMP

YYGap sizeUSEP

YYNormal force (along I-J line)FN

11Element statusSTAT

YYElement orientation anglesALPHA, BETA

22Coefficient of frictionMU

22Displacement (node J - node I) in element y and z dir-ections

UT(Y, Z)

22Tangential (friction) force (vector sum)FS

22Principal angle of friction force in element y-z planeANGLE

1. If the value of STAT is:

1 - Contact, no sliding

2 - Sliding contact

3 - Gap open

2. If MU > 0.0


Table 3: CONTAC52 Item and Sequence Numbers (p. 141) lists output available through the ETABLE commandusing the Sequence Number method. See The General Postprocessor (POST1) in the Basic Analysis Guide

and The Item and Sequence Number Table of this manual for more information. The following notationis used in Table 3: CONTAC52 Item and Sequence Numbers (p. 141):

Name

output quantity as defined in the Table 2: CONTAC52 Element Output Definitions (p. 140)

Item



CONTAC52

E


Table 3 CONTAC52 Item and Sequence Numbers

ETABLE and

ESOL Command

Input

Output

Quant-

ity

Name EItem

1SMISCFN

2SMISCFS

1NMISCSTAT

2NMISCOLDST

3NMISCUSEP

4NMISCALPHA

5NMISCBETA

6NMISCUTY

7NMISCUTZ

8NMISCMU

9NMISCANGLE

CONTAC52 Assumptions and Restrictions

• The element operates bilinearly only in the static and the nonlinear transient dynamic analyses. Ifused in other analysis types, the element maintains its initial status throughout the analysis.

• The element is nonlinear and requires an iterative solution. Nonconverged substeps are not inequilibrium.

• Unless the gap direction is specified (NX, NY, NZ), nodes I and J may not be coincident since thenodal locations define the interface orientation. The element maintains is original orientation ineither a small or a large deflection analysis.

• The element coordinate system is defined by the initial I and J node locations or by the specifiedgap direction.

• The gap value may be specified independent of the node locations.

• The element may have rotated nodal coordinates since a displacement transformation into theelement coordinate system is included.

• The element stiffness KN should not be exactly zero, and unreasonably high stiffness values alsoshould be avoided. The rate of convergence decreases as the stiffness increases.

• Although it is permissible to change KN, it is not permissible to change any other real constantsbetween load steps. Therefore, if you plan to change KN, you cannot allow the value of KS to bedefined by default, because the program would then attempt to redefine KS as KN changed. Youmust explicitly define KS whenever KN changes, to maintain a consistent value throughout all loadsteps.

• The element may not be deactivated with the EKILL command.



CONTAC52

• If µ is not equal to zero, the element is nonconservative as well as nonlinear. Nonconservativeelements require that the load be applied very gradually, along the actual load history path, andin the proper sequence (if multiple loadings exist).

CONTAC52 Product Restrictions


ANSYS Professional

• This element is frictionless. MU is not allowed as a material property and KS is not allowed as areal constant.

• Temperature body loads are not applicable in a structural analysis.

• KEYOPT(1) is not applicable.


CONTAC52

PIPE59

Immersed Pipe or Cable

MP ME ST <> <> <> <> <> <> <> <> PP <> EME MFSProduct Restrictions


Although this legacy element is available for use in your analysis, ANSYS recommends using a current-tech-nology element such as PIPE288.To apply ocean loading using PIPE288, issue the SOCEAN and ocean com-mands (OCxxxxxx) .

PIPE59 is a uniaxial element with tension-compression, torsion, and bending capabilities, and withmember forces simulating ocean waves and current. The element has six degrees of freedom at eachnode: translations in the nodal x, y, and z directions and rotations about the nodal x, y, and z-axes. Theelement loads include the hydrodynamic and buoyant effects of the water and the element mass includesthe added mass of the water and the pipe internals. A cable representation option is also available withthe element. The element has stress stiffening and large deflection capabilities.


X

x

y

z

x

y

z

Z

J

PX

PY

z

Iy

x

x

yz

PZ

4

3

2

x, y, z defines the element

coordinate system orientation

Y

1T180

T90

Tu

T

Tvgu

5

PIPE59 Input Data

The geometry, node locations, and the coordinate system for this element are shown in Figure 1 (p. 143).The element input data (see "PIPE59 Input Summary" (p. 144)) includes two nodes, the pipe outer diameterand wall thickness, certain loading and inertial information (described in Table 1: PIPE59 Real Con-

stants (p. 146) and Figure 2 (p. 144)), and the isotropic material properties. An external "insulation" maybe defined to represent ice loads or biofouling. The material VISC is used only to determine Reynoldsnumber of the fluid outside the pipe.



The element x-axis is oriented from node I toward node J. The element y-axis is automatically calculatedto be parallel to the global X-Y plane. Several orientations are shown in Figure 1 (p. 143). For the casewhere the element is parallel to the global Z-axis (or within a 0.01 percent slope of it), the element y-axis is oriented parallel to the global Y-axis (as shown). Input and output locations around the pipecircumference identified as being at 0° are located along the element y-axis, and similarly 90° is alongthe element z-axis.


Z Y

X

Y

X

R

Z

R

φ(i)

θw

Direction of

ave

Global Cartesian

coordinate system

(origin must be

at ater surface)

FSO

Water surface

DEPTH

WL(i)

A(i)

-Z(j)

θ(j) Mud Line

Structure

Direction of

drift current

KEYOPT(1) may be used to convert the element to the cable option by deleting the bending stiffnesses.If the element is not "torque balanced", the twist-tension option may be used (KEYOPT(1) = 2). Thisoption accounts for the twisting induced when a helically wound or armored structure is stretched. TheKEYOPT(2) key allows a reduced mass matrix and load vector formulation (with rotational degrees offreedom terms deleted as described in the Mechanical APDL Theory Reference). This formulation is usefulfor suppressing large deflections and improving bending stresses in long, slender members. It is alsooften used with the twist-tension pipe option for cable structures.

The description of the waves, the current, and the water density are input through the water motiontable. The water motion table is associated with a material number and is explained in detail inTable 2: PIPE59 Water Motion Table (p. 148). If the water motion table is not input, no water is assumedto surround the pipe. Note that even though the word "water" is used to describe various inputquantities, the quantities may actually be characteristic of any fluid. Alternate drag coefficient andtemperature data may also be input through this table.

A summary of the element input is given in "PIPE59 Input Summary" (p. 144). A general description ofelement input is given in Element Input.


Nodes

I, J


PIPE59

Degrees of Freedom

UX, UY, UZ, ROTX, ROTY, ROTZ if KEYOPT(1) ≠ 1, orUX, UY, UZ if KEYOPT(1) = 1

Real Constants

DO, TWALL, CD, CM, DENSO, FSO,CENMPL, CI, CB, CT, ISTR, DENSIN,TKIN, TWISTTENSee Table 1: PIPE59 Real Constants (p. 146) for details.

Material Properties

EX, ALPX (or CTEX or THSX), PRXY (or NUXY), DENS, GXY, BETD, ALPD, VISC

Surface Loads

Pressures --


Body Loads

Temperatures --

TOUT(I), TIN(I), TOUT(J), TIN(J) if KEYOPT(3) = 0TAVG(I), T90(I), T180(I), TAVG(J), T90(J), T180(J) if KEYOPT(3) = 1

Special Features


KEYOPT(1)

Element behavior:

0 --

Pipe option

1 --

Cable option

2 --

Pipe with twist-tension option

KEYOPT(2)

Load vector and mass matrix:

0 --

Consistent mass matrix and load vector

1 --

Reduced mass matrix and load vector

KEYOPT(3)


0 --


1 --




PIPE59

KEYOPT(5)

Wave force modifications:

0 --

Waves act on elements at their actual location

1 --

Elements are assumed to be at wave peak

2 --

Upward vertical wave velocity acts on element

3 --

Downward vertical wave velocity acts on element

4 --

Elements are assumed to be at wave trough

KEYOPT(6)


0 --

No printout of member forces or moments

2 --


KEYOPT(7)


0 --

Basic element printout

1 --

Additional hydrodynamic integration point printout

KEYOPT(8)

End cap loads:

0 --


1 --


KEYOPT(9)

PX, PY, and PZ transverse pressures:

0 --

Use only the normal component of pressure

1 --

Use the full pressure (normal and shear components)


DescriptionNameNo.

Outside diameter (Do)DO1

Wall thickness of the pipe (defaults to Do/2.0)TWALL2


PIPE59

DescriptionNameNo.

Normal drag coefficient (CD). May be overridden by Constants 43through 54 of water motion table (see Table 2: PIPE59 Water Motion

Table)

CD3

Coefficient of inertia (CM)CM4

Internal fluid density (used for pressure effect only) (Mass/Length3)DENSO5

Z coordinate location of the free surface of the fluid on the insideof the pipe (used for pressure effect only)

FSO6

Mass per unit length of the internal fluid and additional hardware(used for mass matrix computation)

CENMPL7

Added-mass-used/added-mass for circular cross section (if blankor 0, defaults to 1; if CI should be 0.0, enter negative number)

CI8

Buoyancy force ratio (Buoyancy-force based on outside diameterand water density) (if blank or 0, defaults to 1; if CB should be 0.0,enter negative number)

CB9

Coefficient of tangential drag (CT). May be overridden by Constants55 through 66 of water motion table (See Table 2: PIPE59 Water

Motion Table).

CT10

Initial strain in axial direction.ISTR11

Density of external insulation[1].DENSIN12

Thickness of external insulation (ti).TKIN13

Twist tension constant (used if KEYOPT(1) = 2) (See Mechanical

APDL Theory Reference for more details).TWISTTEN14

1. Density of external insulation (ρi).

PIPE59 Water Motion Information

The data listed in Table 2: PIPE59 Water Motion Table (p. 148) is entered in the data table with the TB

commands. If the table is not input, no water is assumed to surround the pipe. Constants not input areassumed to be zero. If the table is input, ACELZ must also have a positive value and remain constantfor all load steps. The constant table is started by using the TB command (with Lab = WATER). Up to196 constants may be defined with the TBDATA commands. The constants (C1-C196) entered on theTBDATA commands (6 per command) are:

where:

KWAVE = Wave selection key (see next section)KCRC = Wave/current interaction key (see next section)DEPTH = Depth of water to mud line (DEPTH > 0.0) (Length)

DENSW = Water density, ρw, (DENSW > 0.0) (Mass/Length3)

θw = Wave direction (see Figure 2 (p. 144))

Z(j) = Z coordinate of location j of drift current measurement (see Figure 2 (p. 144)) (locationmust be input starting at the ocean floor (Z(1) = -DEPTH) and ending at the water surface(Z(MAX) = 0.0). If the current does not change with height, only W(1) needs to be defined.)W(j) = Velocity of drift current at location j (Length/Time)θd(j) = Direction of drift current at location j (Degrees) (see Figure 2 (p. 144))



PIPE59

Re(k) = Twelve Reynolds number values (if used, all 12 must be input in ascending order)CD(k) = Twelve corresponding normal drag coefficients (if used, all 12 must be input)CT(k) = Twelve corresponding tangential drag coefficients (if used, all 12 must be input)T(j) = Temperature at Z(j) water depth (Degrees)

A(i) = Wave peak-to-trough height (0.0 ≤ A(i) < DEPTH) (Length) (if KWAVE = 2, A(1) is entirewave height and A(2) through A(5) are not used)τ(i) = Wave period (τ(i) > 0.0) (Time/Cycle)φ(i) = Adjustment for phase shift (Degrees)

WL(i) = Wave length (0.0 ≤ WL(i) < 1000.0*DEPTH) (Length)

(default =

τπ

π2

)Use 0.0 with Stokes theory (KWAVE = 2).

Table 2 PIPE59 Water Motion Table

MeaningConstant

θwDENSWDEPTHKCRCKWAVE1-5

θd(2)W(2)Z(2)θd(1)W(1)Z(1)7-12

θd(4)W(4)Z(4)θd(3)W(3)Z(3)13-18

θd(6)W(6)Z(6)θd(5)W(5)Z(5)19-24

θd(8)W(8)Z(8)θd(7)W(7)Z(7)25-30

Re(6)Re(5)Re(4)Re(3)Re(2)Re(1)31-36

Re(12)Re(11)Re(10)Re(9)Re(8)Re(7)37-42

CD(6)CD(5)CD(4)CD(3)CD(2)CD(1)43-48

CD(12)CD(11)CD(10)CD(9)CD(8)CD(7)49-54

CT(6)CT(5)CT(4)CT(3)CT(2)CT(1)55-60

CT(12)CT(11)CT(10)CT(9)CT(8)CT(7)61-66

T(6)T(5)T(4)T(3)T(2)T(1)67-72

T(8)T(7)73-74

For KWAVE = 0, 1, or 2WL(1)φ(1)τ(1)A(1)79-82

WL(2)φ(2)τ(2)A(2)85-88For KWAVE = 2, useonly A(1), τ(1), φ(1)etc.etc.

WL(20)φ(20)τ(20)A(20)193-196

For KWAVE = 3 (See Dean fordefinitions other than φ(1))

φ(1)Not UsedX(1)/(H*T*G)79-81

DPT/LOX(2)/(H*T*G)85-86

L/LOX(3)/(H*T*G)91-92

H/DPTX(4)/(H*T*G)97-98

Ψ/(G*H*T)X(5)/(H*T*G)103-104

X(6)/(H*T*G)109

etc.etc.

X(20)/(H*T*G)193


PIPE59

The distributed load applied to the pipe by the hydrodynamic effects is computed from a generalizedMorison's equation. This equation includes the coefficient of normal drag (CD) (perpendicular to the

element axis) and the coefficient of tangential drag (CT), both of which are a functions of Reynolds

numbers (Re). These values are input as shown in Table 1: PIPE59 Real Constants (p. 146) and Table 2: PIPE59

Water Motion Table (p. 148).

The Reynolds numbers are determined from the normal and tangential relative particle velocities, thepipe geometry, the water density, and the viscosity µ (input as VISC). The relative particle velocitiesinclude the effects of water motion due to waves and current, as well as motion of the pipe itself. Ifboth Re(1) and CD(1) are positive, the value of CD from the real constant table (Table 1: PIPE59 Real

Constants (p. 146)) is ignored and a log-log table based on Constants 31 through 54 of the water motiontable (Table 2: PIPE59 Water Motion Table (p. 148)) is used to determine CD. If this capability is to be used,

the viscosity, Re, and CD constants must be input and none may be less than or equal to zero.

Similarly, if both Re(1) and CT(1) are positive, the value of CT from the real constant table (Table 1: PIPE59

Real Constants (p. 146)) is ignored, and a log-log table based on Constants 31 through 42 and 55 through66 of the water motion table (Table 2: PIPE59 Water Motion Table (p. 148)) is used to determine CT. If this

capability is to be used, the viscosity, Re, and CT constants must be input and none may be less than

or equal to zero.

Various wave theories may be selected with the KWAVE constant of the water motion table (Table 2: PIPE59

Water Motion Table (p. 148)). These are:

• Small Amplitude Wave Theory with empirical modification of depth decay function (KWAVE = 0)

• Small Amplitude Airy Wave Theory without modifications (KWAVE = 1)

• Stokes Fifth Order Wave Theory (KWAVE = 2)

• Stream Function Wave Theory (KWAVE = 3).

The wave loadings can be altered (KEYOPT(5)) so that horizontal position has no effect on the wave-induced forces.

Wave loading depends on the acceleration due to gravity (ACELZ), and it may not change betweensubsteps or load steps. Therefore, when performing an analysis using load steps with multiple substeps,the gravity may only be "stepped on" [KBC,1] and not ramped.

With the stream function wave theory (KWAVE = 3), the wave is described by alternate Constants 79through 193 as shown in Table 2: PIPE59 Water Motion Table (p. 148). The definitions of the constantscorrespond exactly to those given in the tables in Dean for the forty cases of ratio of wave height andwater depth to the deep water wave length. The other wave-related constants that the user inputsdirectly are the water density (DENSW), water depth (DEPTH), wave direction (Φ), and acceleration dueto gravity (ACELZ). The wave height, length, and period are inferred from the tables. The user shouldverify the input by comparing the interpreted results (the columns headed DIMENSIONLESS under theSTREAM FUNCTION INPUT VALUES printout) with the data presented in the Dean tables. Note that thiswave theory uses the current value defined for time [TIME] (which defaults to 1.0 for the first load step).

Several adjustments to the current profile are available with the KCRC constant of the water motiontable as shown in Figure 3 (p. 150). The adjustments are usually used only when the wave amplitude islarge relative to the water depth, such that there is significant wave/current interaction. Options include

1. use the current profile (as input) for wave locations below the mean water level and the top currentprofile value for wave locations above the mean water level (KCRC = 0)



PIPE59

2. "stretch" (or compress) the current profile to the top of the wave (KCRC = 1)

3. same as (2) but also adjust the current profile horizontally such that total flow continuity ismaintained with the input profile (KCRC = 2) (all current directions (θ(j)) must be the same for thisoption).

Figure 3 PIPE59 Velocity Profiles for Wave-current Interactions

Horizontal arrows represent

input velocities

Mean Water

Surface

Mud Line

Constant (KCRC = 0)

Stretch (KCRC = 1)

Continuity (KCRC = 2)

Water Surface

Z

Nonlinear Stretch (KCRC = 3)

Element loads are described in Nodal Loading. Pressures may be input as surface loads on the elementfaces as shown by the circled numbers on Figure 1 (p. 143). Internal pressure (PINT) and external pressure(POUT) are input as positive values. These pressures are in addition to the linearly varying pressure ofthe fluids on the inside and outside of the pipe. In handling the pressures, each element is assumed tobe capped (that is, have closed ends). The internal and external pressure loads are designed for closed-loop static pressure environments and therefore include pressure loads on fictitious "end caps" so thatthe pressure loads induce an axial stress and/or reaction in the pipe system. If a dynamic situation needsto be represented, such as a pipe venting to a lower pressure area or the internal flow is past a constric-tion in the pipe, these end cap loads may need to be modified by applying a nodal force normal to thecross-section of the pipe with the magnitude representing the change in pressure. Alternatively, theprecomputed end cap loads can be removed using KEYOPT(8) = 1 and the appropriate end cap loadsadded by the user. The transverse pressures (PX, PY, and PZ) may represent wind or drag loads (perunit length of the pipe) and are defined in the global Cartesian directions. Positive transverse pressuresact in the positive coordinate directions. The normal component or the projected full pressure may beused (KEYOPT(9)). See the Mechanical APDL Theory Reference for more details.

Temperatures may be input as element body loads at the nodes. Temperatures may have wall gradientsor diametral gradients (KEYOPT(3)). Diametral gradients are not valid for the cable option. The averagewall temperature at θ = 0° is computed as 2 * TAVG - T(180) and the average wall temperature at θ = -90° is computed as 2 * TAVG - T(90). The element temperatures are assumed to be linear along thelength. The first temperature at node I (TOUT(I) or TAVG(I)) defaults to TUNIF. If all temperatures afterthe first are unspecified, they default to the first. If all temperatures at node I are input, and all temper-


PIPE59

atures at node J are unspecified, the node J temperatures default to the corresponding node I temper-atures. For any other pattern of input temperatures, unspecified temperatures default to TUNIF.

Eight temperatures (T(j)) are read as Constants 67-74 corresponding to the eight water depths (Z(j)) inputas Constants 7-30. These temperatures override any other temperature input (except TREF) unless theelement is entirely out of the water or if all eight temperatures are input as zero. The thermal loadvector from these temperatures may not be scaled in a superelement use pass if an expansion pass isto follow. Constants 31 through 66 may have zero values if desired. The temperatures input as Constants67-74 are used to compute a temperature-dependent viscosity based on linear interpolation (if previousconstants are not all zero). In the case of a solid cross section (inside diameter = 0.0), they are also usedto compute the material properties of the element.

For the mass matrix, the mass per unit length used for axial motion is the mass of the pipe wall (DENS),the external insulation (DENSIN), and the internal fluid together with the added mass of any additionalhardware (CENMPL). The mass per unit length used for motion normal to the pipe is all of the aboveplus the added mass of the external fluid (DENSW).

CI should be 1.0 for a circular cross section. Values for other cross sections may be found in McCormick.The user should remember, however, that other properties of PIPE59 are based on a circular cross section.

PIPE59 Output Data




Several items are illustrated in Figure 4 (p. 152). Note that the output is simplified and reduced if thecable option, KEYOPT(1) = 1, is used.

The principal stresses are computed at the two points around the circumference where the bendingstresses are at a maximum. The principal stresses and the stress intensity include the shear force stresscomponent. The principal stresses and the stress intensity are based on the stresses at two extremepoints on opposite sides of the neutral axis. If KEYOPT(6) = 2, the 12-member forces and moments (6at each end) are also printed (in the element coordinate system).

The axial force (FX) excludes the hydrostatic force component, as does the MFORX member force(printed if KEYOPT(6) = 2). If KWAVE = 2 or 3 (Stokes or Stream Function theory), additional wave inform-ation is also printed. If KEYOPT(7) = 1, detailed hydrodynamic information is printed at the immersedintegration points. Angles listed in the output are measured (θ) as shown in Figure 4 (p. 152). A generaldescription of solution output is given in Solution Output. See the Basic Analysis Guide for ways to viewresults.



PIPE59


J

SDIR

SBEND

SAXL

Torsional

Moment

Shear

Force

SH

STJ

θ

x x




available.


RODefinitionName

YYElement numberEL

YYNodes - I, JNODES


Y-VolumeVOLU:

9-Location where results are reportedXC, YC, ZC

-YLengthLEN

YYPressures PINTE (average effective internal pressure),PX, PY, PZ, POUTE (average effective external pres-sure)

PRES


STH

1-Hoop pressure stress for code calculationsSPR2

1-Moment stress at nodes I and J for code calculationsSMI, SMJ

1-Direct (axial) stressSDIR

1-Maximum bending stress at outer surfaceSBEND

1-Shear stress at outer surface due to torsionST

1-Shear stress due to shear forceSSF

11Maximum principal stress, minimum principal stress,maximum stress intensity, maximum equivalent

S(1MX, 3MN, INT-MX, EQVMX)


PIPE59

RODefinitionName


22Temperatures TOUT(I), TIN(I), TOUT(J), TIN(J)TEMP

33Temperatures TAVG(I), T90(I), T180(I), TAVG(J), T90(J),T180(J)

TEMP


S(1, 3, INT, EQV)

44Axial, radial, hoop, and shear stressesS(AXL, RAD, H, XH)

44Axial, radial, hoop, and shear strainsEPEL(AXL, RAD, H,XH)

44Axial, radial, and hoop thermal strainEPTH(AXL, RAD, H)

77Member forces for nodes I and J (in the elementcoordinate system)

MFOR(X, Y, Z)

55Member moments for nodes I and J (in the elementcoordinate system)

MMOM(X, Y, Z)

66Node I or JNODE

66Axial force (excludes the hydrostatic force)FAXL

66Axial stress (includes the hydrostatic stress)SAXL

66Radial stressSRAD

66Hoop stressSH

66Stress intensitySINT

66Equivalent stress (SAXL minus the hydrostatic stress)SEQV

66Axial, radial, and hoop elastic strains (excludes thethermal strain)

EPEL(AXL, RAD, H)

66TOUT(I), TOUT(J)TEMP

66Axial thermal strains at nodes I and JEPTHAXL

88Radial and vertical fluid particle velocities (VR is al-ways > 0)

VR, VZ

88Radial and vertical fluid particle accelerationsAR, AZ

88Dynamic fluid pressure headPHDYN

88Wave amplitude over integration pointETA

88Fluid temperature (printed if VISC is nonzero)TFLUID

88ViscosityVISC

88Normal and tangential Reynolds numbers (if VISC isnonzero)

REN, RET

88Input coefficients evaluated at Reynolds numbersCT, CD, CM

88CT*DENSW*DO/2, CD*DENSW*DO/2CTW, CDW

88CM*DENSW*PI*DO**2/4CMW

88Tangential (parallel to element axis) and normal rel-ative velocity

URT, URN



PIPE59

RODefinitionName

88Vector sum of normal (URN) velocitiesABURN

88Accelerations normal to the elementAN

88Hydrodynamic forces tangential and normal to ele-ment axis

FX, FY, FZ

88Effective position of integration point (radians)ARGU

1. Output only for the pipe option (KEYOPT(1) = 0 or 2)

2. If KEYOPT(3) = 0 or if KEYOPT(1) = 1

3. If KEYOPT(3) = 1

4. Output only for the pipe option and the item repeats at 0, 45, 90, 135, 180, 225, 270, 315° at node I,then at node J (all at the outer surface)

5. Output only for the pipe option (KEYOPT(1) = 0 or 2) and if KEYOPT(6) = 2

6. Output only for the cable option (KEYOPT(1) = 1)

7. Output only if KEYOPT(6) = 2

8. Hydrodynamic solution (if KEYOPT(7) = 1 for immersed elements at integration points)


Table 4: PIPE59 Item and Sequence Numbers (Node I) (p. 154) lists output available through the ETABLE

command using the Sequence Number method. See The General Postprocessor (POST1) in Basic Analysis

Guide and The Item and Sequence Number Table of this manual for more information. The followingnotation is used in Table 4: PIPE59 Item and Sequence Numbers (Node I) (p. 154):

Name


Item


E


I,J




Quant-

ity

Name


315°270°225°180°135°90°45°0°

2925211713951-LSSAXL

30262218141062-LSSRAD

31272319151173-LSSH

32282420161284-LSSXH




PIPE59


Quant-

ity

Name


315°270°225°180°135°90°45°0°






--------1SMISCMFORX

--------2SMISCMFORY

--------3SMISCMFORZ

--------4SMISCMMOMX

--------5SMISCMMOMY

--------6SMISCMMOMZ

--------13SMISCSDIR

--------14SMISCST

36312621161161-NMISCS1

38332823181383-NMISCS3

39342924191494-NMISCSINT

403530252015105-NMISCSEQV


--------89NMISCSSF

-3-2-1-4-LBFETOUT

-7-6-5-8-LBFETIN



Quant-

ity

Name


315°270°225°180°135°90°45°0°

6157534945413733-LSSAXL

6258545046423834-LSSRAD

6359555147433935-LSSH

6460565248444036-LSSXH



6359555147433935-LEPELEPELH

6460565248444036-LEPELEPELXH



PIPE59


Quant-

ity

Name


315°270°225°180°135°90°45°0°



6359555147433935-LEPTHEPTHH

--------7SMISCMFORX

--------8SMISCMFORY

--------9SMISCMFORZ




--------15SMISCSDIR

--------16SMISCST

7671666156514641-NMISCS1

7873686358534843-NMISCS3

7974696459544944-NMISCSINT

8075706560555045-NMISCSEQV


--------91NMISCSSF


-15-14-13-16-LBFETIN

Table 6 PIPE59 Item and Sequence Numbers (Pipe Options)

ETABLE and

ESOL Command

Input

Output

Quant-

ity

Name EItem

17SMISCSTH

18SMISCPINTE

19SMISCPX

20SMISCPY

21SMISCPZ

22SMISCPOUTE

81NMISCSPR2

82NMISCSMI

83NMISCSMJ

84NMISCS1MX


PIPE59

ETABLE and

ESOL Command

Input

Output

Quant-

ity

Name EItem

85NMISCS3MN

86NMISCSINTMX

87NMISCSEQVMX

Table 7 PIPE59 Item and Sequence Numbers (Cable Option)

ETABLE and ESOL Command In-

putOutput

Quant-

ity

NameNode

J

Node

I

EItem

41LSSAXL

52LSSRAD

63LSSH

41LEPELEPELAXL

52LEPELEPELRAD

63LEPELEPELH

41LEPTHEPTHAXL

91LBFETOUT

135LBFETIN

94NMISCSINT

105NMISCSEQV

61SMISCFAXL

13SMISCSTH

14SMISCPINTE

15SMISCPX

16SMISCPY

17SMISCPZ

18SMISCPOUTE

Table 8: PIPE59 Item and Sequence Numbers (Additional Output) (p. 157) lists additional print and post datafile output available through the ETABLE command if KEYOPT(7) = 1.

Table 8 PIPE59 Item and Sequence Numbers (Additional Output)

ETABLE and ESOL Command InputOutput Quant-

ity Name E- Second Integ-

ration Point

E- First Integra-

tion Point

Item

N + 31, N + 32,N + 33

N + 1, N + 2, N+ 3

NMISCGLOBAL CO-ORD



PIPE59

ETABLE and ESOL Command InputOutput Quant-

ity Name E- Second Integ-

ration Point

E- First Integra-

tion Point

Item

N + 34N + 4NMISCVR

N + 35N + 5NMISCVZ

N + 36N + 6NMISCAR

N + 37N + 7NMISCAZ

N + 38N + 8NMISCPHDY

N + 39N + 9NMISCETA

N + 40N + 10NMISCTFLUID

N + 41N + 11NMISCVISC

N + 42N + 12NMISCREN

N + 43N + 13NMISCRET

N + 44N + 14NMISCCT

N + 45N + 15NMISCCTW

N + 46N + 16NMISCURT

N + 47N + 17NMISCFX

N + 48N + 18NMISCCD

N + 49N + 19NMISCCDW

N + 50, N + 51N + 20, N + 21NMISCURN

N + 52N + 22NMISCABURN

N + 53N + 23NMISCFY

N + 54N + 24NMISCCM

N + 55N + 25NMISCCMW

N + 56, N + 57N + 26, N + 27NMISCAN

N + 58N + 28NMISCFZ

N + 59N + 29NMISCARGU

Note

For the pipe option (KEYOPT(1) = 0 or 2): N = 99. For the cable option (KEYOPT(1) = 1): N =10.

Material Properties -- WATER Specifications

TB,WATER (water motion table data for PIPE59)

NTEMP:

Not used.

NPTS:

Not used.


PIPE59

TBOPT:

Not used.


• The pipe must not have a zero length. In addition, the O.D. must not be less than or equal to zero andthe I.D. must not be less than zero.

• Elements input at or near the water surface should be small in length relative to the wave length.

• Neither end of the element may be input below the mud line (ocean floor). Integration points that movebelow the mud line are presumed to have no hydrodynamic forces acting on them.

• If the element is used out of water, the water motion table (Table 2: PIPE59 Water Motion Table (p. 148))need not be included.

• The element should also be used with caution in the reduced transient dynamic analysis since thisanalysis type ignores the element load vector. Fluid damping, if any, should be handled via the hydro-dynamic load vector rather than α (mass matrix) damping.

• When performing a transient analysis, the solution may be unstable with small time steps due to thenature of Morrison's equation.

• The applied thermal gradient is assumed to vary linearly along the length of the element.

• The same water motion table (Table 2: PIPE59 Water Motion Table (p. 148)) should not be used for differentwave theories in the same problem.

• The lumped mass matrix formulation [LUMPM,ON] is not allowed for PIPE59 when using "added mass"

on the outside of the pipe (CI ≥ 0.0).


There are no product-specific restrictions for this element.



PIPE59


SHELL63

Elastic Shell

MP ME ST PR PRN DS <> <> <> <> <> PP <> EME MFSProduct Restrictions

SHELL63 Element Description

Although this legacy element is available for use in your analysis, ANSYS recommends using a current-tech-nology element such as SHELL181 (KEYOPT(3) = 2).

SHELL63 has both bending and membrane capabilities. Both in-plane and normal loads are permitted.The element has six degrees of freedom at each node: translations in the nodal x, y, and z directionsand rotations about the nodal x, y, and z-axes. Stress stiffening and large deflection capabilities are in-cluded. A consistent tangent stiffness matrix option is available for use in large deflection (finite rotation)analyses. See SHELL63 for more details about this element. Similar elements are SHELL181 (plastic cap-ability) and SHELL281 (midside node capability). The ETCHG command converts SHELL157 elements toSHELL63.

Figure 1 SHELL63 Geometry

zIJ

z

y

LK

5

3

6

2

1

4

xIJ

yIJ

x

K,L

Triangular Option

Z

X

Y

78

xIJ = Element x-axis if ESYS is not supplied.

x = Element x-axis if ESYS is supplied.

SHELL63 Input Data

The geometry, node locations, and the coordinate system for this element are shown in Figure 1 (p. 161).The element is defined by four nodes, four thicknesses, an elastic foundation stiffness, and the ortho-tropic material properties. Orthotropic material directions correspond to the element coordinate direc-tions. The element coordinate system orientation is as described in Coordinate Systems. The elementx-axis may be rotated by an angle THETA (in degrees).



The thickness is assumed to vary smoothly over the area of the element, with the thickness input atthe four nodes. If the element has a constant thickness, only TK(I) need be input. If the thickness is notconstant, all four thicknesses must be input.

The elastic foundation stiffness (EFS) is defined as the pressure required to produce a unit normal de-flection of the foundation. The elastic foundation capability is bypassed if EFS is less than, or equal to,zero.

For certain nonhomogeneous or sandwich shell applications, the following real constants are provided:RMI is the ratio of the bending moment of inertia to be used to that calculated from the input thicknesses.RMI defaults to 1.0. CTOP and CBOT are the distances from the middle surface to the extreme fibers tobe used for stress evaluations. Both CTOP and CBOT are positive, assuming that the middle surface isbetween the fibers used for stress evaluation. If not input, stresses are based on the input thicknesses.ADMSUA is the added mass per unit area.

Element loads are described in Nodal Loading. Pressures may be input as surface loads on the elementfaces as shown by the circled numbers on Figure 1 (p. 161). Positive pressures act into the element. Becauseshell edge pressures are input on a per-unit-length basis, per-unit-area quantities must be multipliedby the shell thickness. The lateral pressure loading may be an equivalent (lumped) element load appliedat the nodes (KEYOPT(6) = 0) or distributed over the face of the element (KEYOPT(6) = 2). The equivalentelement load produces more accurate stress results with flat elements representing a curved surfaceor elements supported on an elastic foundation since certain fictitious bending stresses are eliminated.

Temperatures may be input as element body loads at the "corner" locations (1-8) shown in Figure

1 (p. 161). The first corner temperature T1 defaults to TUNIF. If all other temperatures are unspecified,they default to T1. If only T1 and T2 are input, T1 is used for T1, T2, T3, and T4, while T2 (as input) isused for T5, T6, T7, and T8. For any other input pattern, unspecified temperatures default to TUNIF.

KEYOPT(1) is available for neglecting the membrane stiffness or the bending stiffness, if desired. A reducedout-of-plane mass matrix is also used when the bending stiffness is neglected.

KEYOPT(2) is used to activate the consistent tangent stiffness matrix (that is, a matrix composed of themain tangent stiffness matrix plus the consistent stress stiffness matrix) in large deflection analyses[NLGEOM,ON]. You can often obtain more rapid convergence in a geometrically nonlinear analysis,such as a nonlinear buckling or postbuckling analysis, by activating this option. However, you shouldnot use this option if you are using the element to simulate a rigid link or a group of coupled nodes.The resulting abrupt changes in stiffness within the structure make the consistent tangent stiffnessmatrix unsuitable for such applications.

KEYOPT(3) allows you to include (KEYOPT(3) = 0 or 2) or suppress (KEYOPT(3) = 1) extra displacementshapes. It also allows you to choose the type of in-plane rotational stiffness used:

• KEYOPT(3) = 0 or 1 activates a spring-type in-plane rotational stiffness about the element z-axis

• KEYOPT(3) = 2 activates a more realistic in-plane rotational stiffness (Allman rotational stiffness -the program uses default penalty parameter values of d1 = 1.0E-6 and d2 = 1.0E-3).

Using the Allman stiffness will often enhance convergence behavior in large deflection (finite rotation)analyses of planar shell structures (that is, flat shells or flat regions of shells).

KEYOPT(7) allows a reduced mass matrix formulation (rotational degrees of freedom terms deleted).This option is useful for improved bending stresses in thin members under mass loading.


SHELL63

KEYOPT(8) allows a reduced stress stiffness matrix (rotational degrees of freedom deleted). This optioncan be useful for calculating improved mode shapes and a more accurate load factor in linear bucklinganalyses of certain curved shell structures.

KEYOPT(11) = 2 is used to store midsurface results in the results file for single or multi-layer shell elements.If you use SHELL,MID, you will see these calculated values, rather than the average of the TOP andBOTTOM results. You should use this option to access these correct midsurface results (membrane results)for those analyses where averaging TOP and BOTTOM results is inappropriate; examples include midsur-face stresses and strains with nonlinear material behavior, and midsurface results after mode combinationsthat involve squaring operations such as in spectrum analyses.

A summary of the element input is given in "SHELL63 Input Summary" (p. 163). A general description ofelement input is given in Element Input.

SHELL63 Input Summary

Nodes

I, J, K, L

Degrees of Freedom


Real Constants

TK(I), TK(J), TK(K), TK(L), EFS, THETA,RMI, CTOP, CBOT, (Blank), (Blank), (Blank),(Blank), (Blank), (Blank), (Blank), (Blank), (Blank),ADMSUASee Table 1: SHELL63 Real Constants (p. 165) for a description of the real constants

Material Properties

EX, EY, EZ, (PRXY, PRYZ, PRXZ or NUXY, NUYZ, NUXZ), ALPX, ALPY, ALPZ (or CTEX, CTEY, CTEZ or THSX,THSY, THSZ), DENS, GXY, BETD, ALPD

Surface Loads

Pressures --

face 1 (I-J-K-L) (bottom, in +Z direction), face 2 (I-J-K-L) (top, in -Z direction),face 3 (J-I), face 4 (K-J), face 5 (L-K), face 6 (I-L)

Body Loads

Temperatures --

T1, T2, T3, T4, T5, T6, T7, T8

Special Features


KEYOPT(1)

Element stiffness:

0 --

Bending and membrane stiffness



SHELL63

1 --

Membrane stiffness only

2 --

Bending stiffness only

KEYOPT(2)

Stress stiffening option:

0 --

Use only the main tangent stiffness matrix when NLGEOM is ON. (Stress stiffening effects used inlinear buckling or other linear prestressed analyses must be activated separately with PSTRES,ON.)

1 --

Use the consistent tangent stiffness matrix (that is, a matrix composed of the main tangent stiffnessmatrix plus the consistent stress stiffness matrix) when NLGEOM is ON and when KEYOPT(1) = 0.(SSTIF,ON will be ignored for this element when KEYOPT(2) = 1 is activated.) Note that if SOLCONTROL

is ON and NLGEOM is ON, KEYOPT(2) is automatically set to 1; that is, the consistent tangent will beused.

2 --

Use to turn off consistent tangent stiffness matrix (i.e., a matrix composed of the main tangentstiffness matrix plus the consistent stress stiffness matrix) when SOLCONTROL is ON. Sometimes itis necessary to turn off the consistent tangent stiffness matrix if the element is used to simulate rigidbodies by using a very large real constant number . KEYOPT(2) = 2 is the same as KEYOPT(2) = 0,however, KEYOPT(2) = 0 is controlled by SOLCONTROL, ON or OFF, while KEYOPT(2) = 2 is independ-ent of SOLCONTROL.

KEYOPT(3)

Extra displacement shapes:

0 --

Include extra displacement shapes, and use spring-type in-plane rotational stiffness about the elementz-axis (the program automatically adds a small stiffness to prevent numerical instability for non-warped elements if KEYOPT(1) = 0).

Note

For models with large rotation about the in-plane direction, KEYOPT(3) = 0 results insome transfer of moment directly to ground.

1 --

Suppress extra displacement shapes, and use spring-type in-plane rotational stiffness about the ele-ment z-axis (the program automatically adds a small stiffness to prevent numerical instability fornon-warped elements if KEYOPT(1) = 0).

2 --

Include extra displacement shapes, and use the Allman in-plane rotational stiffness about the elementz-axis). See the Mechanical APDL Theory Reference.

KEYOPT(5)

Extra stress output:

0 --



SHELL63

2 --

Nodal stress printout

KEYOPT(6)

Pressure loading:

0 --

Reduced pressure loading (must be used if KEYOPT(1) = 1)

2 --

Consistent pressure loading

KEYOPT(7)

Mass matrix:

0 --

Consistent mass matrix

1 --

Reduced mass matrix

KEYOPT(8)

Stress stiffness matrix:

0 --

"Nearly" consistent stress stiffness matrix (default)

1 --

Reduced stress stiffness matrix

KEYOPT(9)

Element coordinate system defined:

0 --

No user subroutine to define element coordinate system

4 --

Element x-axis located by user subroutine USERAN

Note

See the Guide to ANSYS User Programmable Features for user written subroutines

KEYOPT(11)

Specify data storage:

0 --

Store data for TOP and BOTTOM surfaces only

2 --

Store data for TOP, BOTTOM, and MID surfaces

Table 1 SHELL63 Real Constants

DescriptionNameNo.

Shell thickness at node ITK(I)1

Shell thickness at node JTK(J)2

Shell thickness at node KTK(K)3



SHELL63

DescriptionNameNo.

Shell thickness at node LTK(L)4

Elastic foundation stiffnessEFS5

Element X-axis rotationTHETA6

Bending moment of inertia ratioRMI7

Distance from mid surface to topCTOP8

Distance from mid surface to bottomCBOT9

- -(Blank)10, ..., 18

Added mass/unit areaADMSUA19

SHELL63 Output Data



• Additional element output as shown in Table 2: SHELL63 Element Output Definitions (p. 167)

Several items are illustrated in Figure 2 (p. 166). Printout includes the moments about the x face (MX),the moments about the y face (MY), and the twisting moment (MXY). The moments are calculated perunit length in the element coordinate system. The element stress directions are parallel to the elementcoordinate system. A general description of solution output is given in Solution Output. See the Basic

Analysis Guide for ways to view results.

Figure 2 SHELL63 Stress Output

zIJ

z

y

L

yIJ

x

K

xIJ

TX

MX

TY

MY

SY

SX

TXY

TXY

MXY

MXY

SX(TOP)

SX (MD)

SX (BOT)


SHELL63

xIJ = Element x-axis if ESYS is not supplied.

x = Element x-axis if ESYS is supplied.




available.

Table 2 SHELL63 Element Output Definitions

RODefinitionName

YYElement NumberEL

YYNodes - I, J, K, LNODES


YYAREAAREA


YYPressures P1 at nodes I, J, K, L; P2 at I, J, K, L; P3at J, I; P4 at K, J; P5 at L, K; P6 at I, L

PRES

YYTemperatures T1, T2, T3, T4, T5, T6, T7, T8TEMP

YYIn-plane element X, Y, and XY forcesT(X, Y, XY)

YYElement X, Y, and XY momentsM(X, Y, XY)

-YFoundation pressure (if nonzero)FOUND.PRESS

YYTop, middle, or bottomLOC

YYCombined membrane and bending stressesS:X, Y, Z, XY

YYPrincipal stressS:1, 2, 3



YYAverage elastic strainEPEL:X, Y, Z, XY


YYAverage thermal strainEPTH:X, Y, Z, XY





SHELL63

2. The equivalent strains use an effective Poisson's ratio: for elastic and thermal this value is set by theuser (MP,PRXY).

Table 3 SHELL63 Miscellaneous Element Output


-1TEMP, S(X, Y, Z, XY), SINT,SEQV

Nodal Stress Solu-tion

1. Output at each node, if KEYOPT(5) = 2, repeats each location

Table 4: SHELL63 Item and Sequence Numbers (p. 168) lists output available through the ETABLE commandusing the Sequence Number method. See The General Postprocessor (POST1) in the Basic Analysis Guide

and The Item and Sequence Number Table in this manual for more information. The following notationis used in Table 4: SHELL63 Item and Sequence Numbers (p. 168):

Name

output quantity as defined in the Table 2: SHELL63 Element Output Definitions (p. 167)

Item


E


I,J,K,L

sequence number for data at nodes I,J,K,L

Table 4 SHELL63 Item and Sequence Numbers


Quant-

ity

Name

LKJIEItem

----1SMISCTX

----2SMISCTY

----3SMISCTXY

----4SMISCMX

----5SMISCMY

----6SMISCMXY

1211109-SMISCP1

16151413-SMISCP2

--1718-SMISCP3

-1920--SMISCP4

2122---SMISCP5

24--23-SMISCP6

Top

161161-NMISCS:1

171272-NMISCS:2


SHELL63


Quant-

ity

Name

LKJIEItem

181383-NMISCS:3

191494-NMISCS:INT

2015105-NMISCS:EQV

Bot

36312621-NMISCS:1

37322722-NMISCS:2

38332823-NMISCS:3

39342924-NMISCS:INT

40353025-NMISCS:EQV

SHELL63 Assumptions and Restrictions

• Zero area elements are not allowed. This occurs most often whenever the elements are not numberedproperly.

• Zero thickness elements or elements tapering down to a zero thickness at any corner are not allowed.

• The applied transverse thermal gradient is assumed to vary linearly through the thickness and vary bi-linearly over the shell surface.

• An assemblage of flat shell elements can produce a good approximation of a curved shell surfaceprovided that each flat element does not extend over more than a 15° arc. If an elastic foundationstiffness is input, one-fourth of the total is applied at each node. Shear deflection is not included in thisthin-shell element.

• A triangular element may be formed by defining duplicate K and L node numbers as described in De-generated Shape Elements. The extra shapes are automatically deleted for triangular elements so thatthe membrane stiffness reduces to a constant strain formulation. For large deflection analyses, if KEY-OPT(1) = 1 (membrane stiffness only), the element must be triangular.

• For KEYOPT(1) = 0 or 2, the four nodes defining the element should lie as close as possible to a flatplane (for maximum accuracy), but a moderate amount of warping is permitted. For KEYOPT(1) = 1, thewarping limit is very restrictive. In either case, an excessively warped element may produce a warningor error message. In the case of warping errors, triangular elements should be used (see DegeneratedShape Elements). Shell element warping is described in detail in Warping Factor in Mechanical APDL

Theory Reference.

• If the lumped mass matrix formulation is specified [LUMPM,ON], the effect of the implied offsets onthe mass matrix is ignored for warped SHELL63 elements.

SHELL63 Product Restrictions


ANSYS Professional




SHELL63

• The only special features allowed are stress stiffening and large deflection.




SHELL63

PLANE82

2-D 8-Node Structural Solid

MP ME ST PR PRN DS <> <> <> <> <> PP <> EME MFSProduct Restrictions

PLANE82 Element Description

Although this legacy element is available for use in your analysis, ANSYS recommends using a current-tech-nology element such as PLANE183.

PLANE82 provides accurate results for mixed (quadrilateral-triangular) automatic meshes and can tolerateirregular shapes without as much loss of accuracy. The eight-node elements have compatible displace-ment shapes and are well suited to model curved boundaries.

The 8-node element is defined by eight nodes having two degrees of freedom at each node: translationsin the nodal x and y directions. The element may be used as a plane element or as an axisymmetricelement. The element has plasticity, creep, swelling, stress stiffening, large deflection, and large straincapabilities. Various printout options are also available. See SOLID273 for a description of an axisymmetricelement which accepts nonaxisymmetric loading.

Figure 1 PLANE82 Geometry

O

K

N

J

M

P

L

I

I

K, L, O

P N

M

Tri OptionX ( adal)

Y

( axal)

3

1

2

4

PLANE82 Input Data

The geometry, node locations, and the coordinate system for this element are shown in Figure 1 (p. 171).

A triangular-shaped element may be formed by defining the same node number for nodes K, L and O.Besides the nodes, the element input data includes a thickness (TK) (for the plane stress option only)and the orthotropic material properties. Orthotropic material directions correspond to the element co-ordinate directions. The element coordinate system orientation is as described in Coordinate Systems.

Element loads are described in Nodal Loading. Pressures may be input as surface loads on the elementfaces as shown by the circled numbers on Figure 1 (p. 171). Positive pressures act into the element.Temperatures and fluences may be input as element body loads at the nodes. The node I temperatureT(I) defaults to TUNIF. If all other temperatures are unspecified, they default to T(I). If all corner nodetemperatures are specified, each midside node temperature defaults to the average temperature of itsadjacent corner nodes. For any other input temperature pattern, unspecified temperatures default toTUNIF. Similar defaults occurs for fluence except that zero is used instead of TUNIF.



The nodal forces, if any, should be input per unit of depth for a plane analysis (except for KEYOPT(3) =3) and on a full 360° basis for an axisymmetric analysis. KEYOPT(5) and KEYOPT(6) parameters providevarious element printout options (see Element Solution).


Analysis Guide.



A summary of the element input is given in "PLANE82 Input Summary" (p. 172). A general description ofelement input is given in Element Input. For axisymmetric applications see Harmonic AxisymmetricElements.

PLANE82 Input Summary

Nodes

I, J, K, L, M, N, O, P

Degrees of Freedom

UX, UY

Real Constants

None, if KEYOPT (3) = 0, 1, or 2THK - Thickness, if KEYOPT (3) = 3

Material Properties

EX, EY, EZ, PRXY, PRYZ, PRXZ (or NUXY, NUYZ, NUXZ),ALPX, ALPY, ALPZ (or CTEX, CTEY, CTEZ or THSX, THSY, THSZ), DENS, GXY, BETD, ALPD

Surface Loads

Pressures --

face 1 (J-I), face 2 (K-J), face 3 (I-K), face 4 (I-L)

Body Loads

Temperatures --

T(I), T(J), T(K), T(L), T(M), T(N), T(O), T(P)

Fluences --

FL(I), FL(J), FL(K), FL(L), FL(M), FL(N), FL(O), FL(P)

Special Features

Plasticity (BISO, MISO, BKIN, MKIN, KINH, DP, ANISO)Creep (CREEP, RATE)Swelling (SWELL)Elasticity (MELAS)Other material (USER)Stress stiffening


PLANE82

Large deflectionLarge strainBirth and deathAdaptive descent


KEYOPT(3)

Element behavior:

0 --

Plane stress

1 --

Axisymmetric

2 --

Plane strain (Z strain = 0.0)

3 --

Plane stress with thickness (TK) real constant input

KEYOPT(5)


0 --


1 --


2 --


KEYOPT(6)


0 --


1 --

Surface solution for face I-J also

2 --

Surface solution for both faces I-J and K-L also (surface solution valid for linear materials only)

3 --

Nonlinear solution at each integration point also

4 --


PLANE82 Output Data



• Additional element output as shown in Table 1: PLANE82 Element Output Definitions (p. 174)




PLANE82

The element stress directions are parallel to the element coordinate system. Surface stresses are availableon any face. Surface stresses on face IJ, for example, are defined parallel and perpendicular to the IJline and along the Z axis for a plane analysis or in the hoop direction for an axisymmetric analysis. Ageneral description of solution output is given in Solution Output. See the Basic Analysis Guide for waysto view results.

Figure 2 PLANE82 Stress Output

O K

N

JM

P

L

I

X (or radial)

Y

(or axial)

S

S




available.

Table 1 PLANE82 Element Output Definitions

RODefinitionName

YYElement NumberEL

YYCorner nodes - I, J, K, LNODES


YYAverage thicknessTHICK

YYVolumeVOLU:


YYPressures P1 at nodes J,I; P2 at K,J; P3 at L,K; P4 atI,L

PRES

YYTemperatures T(I), T(J), T(K), T(L), T(M), T(N), T(O), T(P)TEMP

YYFluences FL(I), FL(J), FL(K), FL(L), FL(M), FL(N), FL(O),FL(P)

FLUEN

YYStresses (SZ = 0.0 for plane stress elements)S:X, Y, Z, XY

-YPrincipal stressesS:1, 2, 3

-YStress intensityS:INT



PLANE82

RODefinitionName

YYElastic strainsEPEL:X, Y, Z, XY



YYAverage thermal strainsEPTH:X, Y, Z, XY


22Average plastic strainsEPPL:X, Y, XY, Z

2-Equivalent plastic strain [4]EPPL:EQV

22Average creep strainsEPCR:X, Y, XY, Z

2-Equivalent creep strain [4]EPCR:EQV


22Equivalent plastic strainNL:EPEQ


22Equivalent stress on stress-strain curveNL:SEPL


11Face labelFACE

11Surface elastic strains (parallel, perpendicular, Z orhoop)

EPEL(PAR, PER, Z)


11Surface stresses (parallel, perpendicular, Z or hoop)S(PAR, PER, Z)




1. Surface output (if KEYOPT(6) is 1, 2 or 4)

2. Nonlinear solution (if the element has a nonlinear material)



Table 2 PLANE82 Miscellaneous Element Output


-1EPPL, EPEQ, SRAT, SEPL, HPRES, EP-CR, EPSW

Nonlinear Integration Pt. Solution

-2TEMP, SINT, SEQV, EPEL, SIntegration Point Stress Solution

-3TEMP, S, SINT, SEQVNodal Stress Solution

1. Output at each integration point, if the element has a nonlinear material and KEYOPT(6) = 3


3. Output at each vertex node, if KEYOPT(5) = 2



PLANE82

Note

For axisymmetric solutions, the X, Y, XY, and Z stress and strain outputs correspond to theradial, axial, in-plane shear, and hoop stresses and strains.

Table 3: PLANE82 Item and Sequence Numbers (p. 176) lists output available through the ETABLE commandusing the Sequence Number method. See Creating an Element Table in the Basic Analysis Guide andThe Item and Sequence Number Table in this manual for more information. The following notation isused in Table 3: PLANE82 Item and Sequence Numbers (p. 176):

Name

output quantity as defined in the Table 1: PLANE82 Element Output Definitions (p. 174)

Item


E


I,J,...,P


Table 3 PLANE82 Item and Sequence Numbers


Quant-

ity

Name

PONMLKJIEItem

------12-SMISCP1

-----34--SMISCP2

----56---SMISCP3

----8--7-SMISCP4

----161161-NMISCS:1

----171272-NMISCS:2

----181383-NMISCS:3

----191494-NMISCS:INT

----2015105-NMISCS:EQV

2827262524232221-NMISCFLUEN

--------29NMISCTHICK


PLANE82 Assumptions and Restrictions

• The area of the element must be positive.

• The element must lie in a global X-Y plane as shown in Figure 1 (p. 171) and the Y-axis must be the axisof symmetry for axisymmetric analyses. An axisymmetric structure should be modeled in the +X quadrants.


PLANE82

• A face with a removed midside node implies that the displacement varies linearly, rather than parabol-ically, along that face. See Quadratic Elements (Midside Nodes) in the Modeling and Meshing Guide formore information about the use of midside nodes.

PLANE82 Product Restrictions


ANSYS Professional







PLANE82


SOLID92

3-D 10-Node Tetrahedral Structural Solid



Although this legacy element is available for use in your analysis, ANSYS recommends using a current-tech-nology element such as SOLID187.

SOLID92 has a quadratic displacement behavior and is well suited to model irregular meshes (such asproduced from various CAD/CAM systems).

The element is defined by ten nodes having three degrees of freedom at each node: translations in thenodal x, y, and z directions. The element also has plasticity, creep, swelling, stress stiffening, large de-flection, and large strain capabilities.


Y

Z

X

1

23

4

L

PR

Q

K

N

J

MI

O

SOLID92 Input Data

The geometry, node locations, and the coordinate system for this element are shown in Figure 1 (p. 179).

Beside the nodes, the element input data includes the orthotropic material properties. Orthotropicmaterial directions correspond to the element coordinate directions. The element coordinate systemorientation is as described in Coordinate Systems.

Element loads are described in Nodal Loading. Pressures may be input as surface loads on the elementfaces as shown by the circled numbers on Figure 1 (p. 179). Positive pressures act into the element.Temperatures and fluences may be input as element body loads at the nodes. The node I temperatureT(I) defaults to TUNIF. If all other temperatures are unspecified, they default to T(I). If all corner nodetemperatures are specified, each midside node temperature defaults to the average temperature of itsadjacent corner nodes. For any other input temperature pattern, unspecified temperatures default toTUNIF. Similar defaults occurs for fluence except that zero is used instead of TUNIF.



You cannot set initial state conditions (INISTATE) using this element. You can set initial state conditionsusing current-technology elements only (such as LINK180,SHELL181). To continue using initial stateconditions in future versions of ANSYS, consider using a current element technology. For more inform-ation, see Legacy vs. Current Element Technologies in the Element Reference. For more informationabout setting initial state values, see the INISTATE command documentation and Initial State Loadingin the Basic Analysis Guide.





Nodes

I, J, K, L, M, N, O, P, Q, R

Degrees of Freedom

UX, UY, UZ

Real Constants

None

Material Properties

EX, EY, EZ, ALPX, ALPY, ALPZ (or CTEX, CTEY, CTEZ or THSX, THSY, THSZ), PRXY, PRYZ, PRXZ (or NUXY,NUYZ, NUXZ), DENS, GXY, GYZ, GXZ, BETD, ALPD

Surface Loads

Pressures --

face 1 (J-I-K), face 2 (I-J-L), face 3 (J-K-L), face 4 (K-I-L)

Body Loads

Temperatures --

T(I), T(J), T(K), T(L), T(M), T(N), T(O), T(P), T(Q), T(R)

Fluences --

FL(I), FL(J), FL(K), FL(L), FL(M), FL(N), FL(O), FL(P), FL(Q), FL(R)

Special Features

Plasticity (BISO, MISO, BKIN, MKIN, KINH, DP, ANISO)Creep (CREEP, RATE)Swelling (SWELL)Elasticity (MELAS)Other material (USER)Stress stiffeningLarge deflectionLarge strainBirth and deathAdaptive descent



SOLID92

KEYOPT(5)


0 --


1 --

Integration point printout

2 --


KEYOPT(6)


0 --


4 --

Surface printout for faces with nonzero pressure

SOLID92 Output Data




Several items are illustrated in Figure 2 (p. 181). The element stress directions are parallel to the elementcoordinate system. The surface stress outputs are in the surface coordinate system and are availablefor any face (KEYOPT(6)). The coordinate system for face J-I-K is shown in Figure 2 (p. 181). The othersurface coordinate systems follow similar orientations as indicated by the pressure face node description.Surface stress printout is valid only if the conditions described in Element Solution are met. A generaldescription of solution output is given in Solution Output. See the Basic Analysis Guide for ways to viewresults.


Y

Z

X

L

PR

Q

K

N

J

M

I

O

Surface Coordinate System

yx

Y

Z

X




SOLID92



available.


RODefinitionName

YYElement NumberEL

YYCorner nodes - I, J, K, LNODES


YYVolumeVOLU:


YYPressures P1 at nodes J, I, K; P2 at I, J, L; P3 at J, K,L; P4 at K, I, L

PRES

YYTemperatures T(I), T(J), T(K), T(L)TEMP

YYFluences FL(I), FL(J), FL(K), FL(L), FL(M), FL(N), FL(O),FL(P), FL(Q), FL(R)

FLUEN






YYPrincipal elastic strainsEPEL:1, 2, 3

-YEquivalent elastic strains [4]EPEL:EQV

11Thermal strainsEPTH:X, Y, Z, XY, YZ,XZ

11Equivalent thermal strains [4]EPTH:EQV

11Plastic strainsEPPL:X, Y, Z, XY, YZ,XZ

11Equivalent plastic strains [4]EPPL:EQV

11Creep strainsEPCR:X, Y, Z, XY, YZ,XZ

11Equivalent creep strains [4]EPCR:EQV




11Equivalent stress from stress-strain curveNL:SEPL



SOLID92

RODefinitionName

22Face labelFACE

-2Nodes on this faceTRI

22Face areaAREA

22Face average temperatureTEMP

22Surface elastic strainsEPEL(X, Y, XY)

22Surface pressurePRES

22Surface stressesS(X, Y, XY)





1. Nonlinear solution (output if the element has a nonlinear material)

2. Surface output (if KEYOPT(6) = 4 and a nonzero pressure face)





-1TEMP, SINT, SEQV, EPEL, S, EPPL,EPCR, EPSW, EPEQ, SRAT, SEPL,HPRES

Integration Point Stress Solution

-2LOCATION, TEMP, SINT, SEQV, SNodal Stress Solution


2. Output at each vertex node, if KEYOPT(5) = 2


and The Item and Sequence Number Table in this manual for more information. The following notationis used in Table 3: SOLID92 Item and Sequence Numbers (p. 184):

Name

output quantity as defined in the Table 1: SOLID92 Element Output Definitions (p. 182)

Item




SOLID92

I,J,...,R

sequence number for data at nodes I,J,...,R



Quantity

NameM,...,RLKJIItem

--312SMISCP1

-6-54SMISCP2

-987-SMISCP3

-1210-11SMISCP4

-161161NMISCS:1

-171272NMISCS:2

-181383NMISCS:3

-191494NMISCS:INT

-2015105NMISCS:EQV

See Surface Solution in this manual for the item and sequence numbers for surface output for theETABLE command.


• The element must not have a zero volume. Elements may be numbered either as shown in Figure

1 (p. 179) or may have node L below the I-J-K plane.

• An edge with a removed midside node implies that the displacement varies linearly, rather than para-bolically, along that edge. See Quadratic Elements (Midside Nodes) in the Modeling and Meshing Guide

for information about the use of midside nodes.



ANSYS Professional




SOLID92

SOLID95

3-D 20-Node Structural Solid



Although this legacy element is available for use in your analysis, ANSYS recommends using a current-tech-nology element such as SOLID186 (KEYOPT(2) = 1, or KEYOPT(2) = 0 for nonlinear analyses).

SOLID95 is a higher-order version of the 3-D 8-node solid element SOLID45. It can tolerate irregularshapes without as much loss of accuracy. SOLID95 elements have compatible displacement shapes andare well suited to model curved boundaries.

The element is defined by 20 nodes having three degrees of freedom per node: translations in thenodal x, y, and z directions. The element may have any spatial orientation. SOLID95 has plasticity, creep,stress stiffening, large deflection, and large strain capabilities. Various printout options are also available.


5

6

2 3

P

X

M

4

1

Y

I

QJ

T

L

W

O

A

K

R

S

Z

BU

N

etrahedral ption

,,,,,V,,

,

,,

yramid ption

,,,,,V,,

rism ption

,,

,

,,

V

V

SOLID95 Input Data

The geometry, node locations, and the coordinate system for this element are shown in Figure 1 (p. 185).A prism-shaped element may be formed by defining the same node numbers for nodes K, L, and S;



nodes A and B; and nodes O, P, and W. A tetrahedral-shaped element and a pyramid-shaped elementmay also be formed as shown in Figure 1 (p. 185). A similar, but 10-node tetrahedron, element is SOLID187.

Besides the nodes, the element input data includes the orthotropic material properties. Orthotropicmaterial directions correspond to the element coordinate directions. The element coordinate systemorientation is as described in Coordinate Systems.

Element loads are described in Nodal Loading. Pressures may be input as surface loads on the elementfaces as shown by the circled numbers on Figure 1 (p. 185). Positive pressures act into the element.Temperatures may be input as element body loads at the nodes. The node I temperature T(I) defaultsto TUNIF. If all other temperatures are unspecified, they default to T(I). If all corner node temperaturesare specified, each midside node temperature defaults to the average temperature of its adjacent cornernodes. For any other input temperature pattern, unspecified temperatures default to TUNIF.

A lumped mass matrix formulation, which may be useful for certain analyses, may be obtained withLUMPM. While the consistent matrix gives good results for most applications, the lumped matrix maygive better results with reduced analyses using Guyan reduction. The KEYOPT(5) and (6) parametersprovide various element printout options (see Element Solution).

You cannot set initial state conditions (INISTATE) using this element. You can set initial state conditionsusing current-technology elements only (such as LINK180,SHELL181). To continue using initial stateconditions in future releases, consider using a current element technology. For more information, seeLegacy vs. Current Element Technologies in the Element Reference. For more information about settinginitial state values, see the INISTATE command documentation and Initial State Loading in the Basic

Analysis Guide.

You can include the effects of pressure load stiffness using SOLCONTROL,,,INCP. If an unsymmetricmatrix is needed for pressure load stiffness effects, use NROPT,UNSYM.



Nodes

I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X, Y, Z, A, B

Degrees of Freedom

UX, UY, UZ

Real Constants

None

Material Properties

EX, EY, EZ, ALPX, ALPY, ALPZ (or CTEX, CTEY, CTEZ or THSX, THSY, THSZ), PRXY, PRYZ, PRXZ (or NUXY,NUYZ, NUXZ), DENS, GXY, GYZ, GXZ, BETD, ALPD

Surface Loads

Pressures --

face 1 (J-I-L-K), face 2 (I-J-N-M), face 3 (J-K-O-N),face 4 (K-L-P-O), face 5 (L-I-M-P), face 6 (M-N-O-P)


SOLID95

Body Loads

Temperatures --

T(I), T(J), ..., T(Z), T(A), T(B)

Special Features

Plasticity (BISO, MISO, BKIN, MKIN, KINH, DP, ANISO)Creep (CREEP, RATE)Swelling (SWELL)Elasticity (MELAS)Other material (USER)Stress stiffeningLarge deflectionLarge strainBirth and deathAdaptive descent


KEYOPT(5)


0 --


1 --


2 --


KEYOPT(6)


0 --


1 --

Surface printout for face I-J-N-M

2 --

Surface printout for face I-J-N-M and face K-L-P-O (Surface printout valid for linear materials only)

3 --

Nonlinear printout at each integration point

4 --

Surface printout for faces with nonzero pressure

KEYOPT(11)

Integration rule:

0 --

No reduced integration (default)

1 --

2 x 2 x 2 reduced integration option for brick shape



SOLID95

See Failure Criteria in the Mechanical APDL Theory Reference for an explanation of the three predefinedfailure criteria. For a complete discussion of failure criteria, please refer to Failure Criteria.

SOLID95 Output Data





The element stress directions are parallel to the element coordinate system. The surface stress outputsare in the surface coordinate systems and are available for any face (KEYOPT(6)). The coordinate systemsfor faces I-J-N-M and K-L-P-O are shown in Figure 2 (p. 188). The other surface coordinate systems followsimilar orientations as indicated by the pressure face node description. Surface printout is valid only ifthe conditions described in Element Solution are met. The SXY component is the in-plane shear stresson that face. A general description of solution output is given in Solution Output. See the Basic Analysis

Guide for ways to view results.


5

6

23

P

X

M

4

1

Y

I

QJ

T

L

W

O

A

K

R

S

Z

B

U N

V

y

x

Surface Coordinate Sstem

x

y




SOLID95


available.


RODefinitionName

YYElement number and nameEL

YYNodes - I, J, K, L, M, N, O, PCORNER NODES


YYVolumeVOLU:


YYPressures P1 at nodes J, I, L, K; P2 at I, J, N, M; P3at J, K, O, N; P4 at K, L, P, O; P5 at L, I, M, P; P6 atM, N, O, P

PRES

YYTemperatures T(I), T(J), ..., T(Z), T(A), T(B)TEMP







YYEquivalent elastic strain [4]EPEL:EQV

11Average thermal strainsEPTH:X, Y, Z, XY, YZ,XZ

11Equivalent thermal strain [4]EPTH:EQV

11Average plastic strainsEPPL:X, Y, Z, XY, YZ,XZ

11Equivalent plastic strain [4]EPPL:EQV

11Average creep strainsEPCR:X, Y, Z, XY, YZ,XZ

11Equivalent creep strain [4]EPCR:EQV




11Average equivalent stress from stress-strain curveNL:SEPL


22Face labelFACE

22Face areaAREA

22Face average temperatureTEMP

22Surface elastic strainsEPEL(X, Y, XY)



SOLID95

RODefinitionName

22Surface pressurePRES

22Surface stresses (X-axis parallel to line defined byfirst two nodes which define the face)

S(X, Y, XY)





1. Nonlinear solution (output only if the element has a nonlinear material)

2. Surface output (if KEYOPT(6) is 1, 2, or 4)

3. Available only at centroid as a *GET item




-1EPPL, EPEQ, SRAT, SEPL, HPRES, EP-CR

Nonlinear Integration Pt. Solution

-2TEMP, S, SINT, SEQV, EPELIntegration Point Stress Solution

-3TEMP, S, SINT, SEQV, EPELNodal Stress Solution

1. Output at each integration point, if the element has a nonlinear material and KEYOPT(6) = 3


3. Output at each node, if KEYOPT(5) = 2


and The Item and Sequence Number Table in this manual for more information. The following notationis used in Table 3: SOLID95 Item and Sequence Numbers (p. 190):

Name

output quantity as defined in Table 1: SOLID95 Element Output Definitions (p. 189)

Item


I,J,...,P




Quant-

ity

Name

PONMLKJIItem

----3412SMISCP1


SOLID95


Quant-

ity

Name

PONMLKJIItem

--78--65SMISCP2

-1112--109-SMISCP3

1516--1413--SMISCP4

20--1917--18SMISCP5

24232221----SMISCP6

36312621161161NMISCS:1

37322722171272NMISCS:2

38332823181383NMISCS:3

39342924191494NMISCS:INT

403530252015105NMISCS:EQV

Note

N refers to the failure criterion number: N = 1 for the first failure criterion, N = 2 for thesecond failure criterion, and so on.

See Surface Solution in this manual for the item and sequence numbers for surface output for theETABLE command.


• The element must not have a zero volume.

• The element may not be twisted such that the element has two separate volumes. This occurs mostfrequently when the element is not numbered properly.

• Elements may be numbered either as shown in Figure 1 (p. 185) or may have the planes IJKL and MNOPinterchanged.

• An edge with a removed midside node implies that the displacement varies linearly, rather than para-bolically, along that edge. See Quadratic Elements (Midside Nodes) in the Modeling and Meshing Guide

for more information on the use of midside nodes.

• Degeneration to the form of pyramid should be used with caution. The element sizes, when degenerated,should be small in order to minimize the stress gradients. Pyramid elements are best used as filler ele-ments or in meshing transition zones.



ANSYS Professional





SOLID95


Legacy Theory

Following is archived theory information for legacy capabilities.

Chapter 1: Archived Theory Element Library

Following is archived theory information for legacy elements.

1.1. BEAM4 - 3-D Elastic Beam

J

I

z, w

x, u

y, v

Y

XZ

xθ

Integration PointsShape FunctionsMatrix or Vector

NoneEquation 12–15, Equation 12–16, Equa-tion 12–17, and Equation 12–18

Stiffness and Mass Matrices

NoneEquation 12–7 and Equation 12–8Stress Stiffness and DampingMatrices

NoneEquation 12–15, Equation 12–16, and Equa-tion 12–17

Pressure Load Vector andTemperatures

DistributionLoad Type

Bilinear across cross-section, linear along lengthElement Temperature

Constant across cross-section, linear along lengthNodal Temperature

Linear along lengthPressure

1.1.1. Stiffness and Mass Matrices

The order of degrees of freedom (DOFs) is shown in Figure 1.1 (p. 196).



Figure 1.1 Order of Degrees of Freedom

I

J

1

23

4

56

7

89

10

1112

The stiffness matrix in element coordinates is (Przemieniecki):

(1–1)

z

y

y y

z zℓ =

−

−

−

Smmetric

zz z

y y

y y

z z

z

y

−

−

−

− y y

z z−

where:

A = cross-section area (input as AREA on R command)E = Young's modulus (input as EX on MP command)L = element lengthG = shear modulus (input as GXY on MP command)

x x

x x

= ==

≠

osonal on of naf

f

Ix = input torsional moment of inertia (input as IXX on RMORE command)

Jx = polar moment of inertia = Iy + Iz



az = a(Iz,φy)

ay = a(Iy,φz)

bz = b(Iz,φy)

⋮

fz = f(Iz,φy)

fy = f(Iy,φz)

φφ

=+3

φφ

=+2

φφφ

=++

φφφ

=−+

φyz

zs

=

φ

=

Ii = moment of inertia about direction i (input as Iii on R command)

i

i

= =hear area normal to drecton

= ff (pu SHEAR )MO

The consistent mass matrix (LUMPM,OFF) in element coordinates LUMPM,OFF is (Yokoyama):

(1–2)

x

ℓ =

−

!"

x

x

−

−

−

where:



BEAM4 - 3-D Elastic Beam

Mt = (ρA+m)L(1-εin)

ρ = density (input as DENS on MP command)m = added mass per unit length (input as ADDMAS on RMORE command)

εin = prestrain (input as ISTRN on RMORE command)Az = A(rz,φy)

Ay = A(ry,φz)

Bz = B(rz,φy)

⋮

Fz = F(rz,φy)

Fy = F(ry,φz)

φφ φ

φ=

+ + +

+

2 2

2

φφ φ

φ=

+ + −

+

φ

φ φ φ

φ=

+ + + −

+

φ

φ φ φ

φ=

+ + − −

+

φ

φ φ φ φ

=

+ + + + +

+

φφ

φ

φ φ φ φ

=

+ + + + −

+

φφ

yyy= = radius of gration

zzz= =

The mass matrix (LUMPM,ON) in element coordinates is:



(1–3)t

ℓ =

Symmeric

1.1.2. Gyroscopic Damping Matrix

The element gyroscopic damping matrix is the same as for PIPE16.

1.1.3. Pressure and Temperature Load Vector

The pressure and temperature load vector are computed in a manner similar to that of BEAM3.

1.1.4. Local to Global Conversion

The element coordinates are related to the global coordinates by:

(1–4)Rℓ =

where:

ℓ = vo of dsplans n ln Casan oodnas

u = vector of displacements in global Cartesian coordinates

=

[T] is defined by:

(1–5)= − − − +

− −

1 2 1 2 2

1 2 3 1 3 1 2 3 1 3 3 2

1 2 3 1 33 1 2 3 1 3 3 2− −

where:




xyxy

xy

1

2 1

=

−>

0.0 <

if

if

=−

S3 = sin (θ)

=

−>

<

=

C3 = cos (θ)

X1, etc. = x coordinate of node 1, etc.

Lxy = projection of length onto X-Y plane

d = .0001 Lθ = user-selected adjustment angle (input as THETA on R command)

If a third node is given, θ is not used. Rather C3 and S3 are defined using:

V1 = vector from origin to node 1



V4 = unit vector parallel to global Z axis, unless element is almost parallel to Z axis, in which

case it is parallel to the X axis.

Then,

(1–6)5 3 = − = vector between nodes I and K

(1–7)6 = − = lg lm X

(1–8)7 4= ×

(1–9)8 = ×

and



(1–10)37 8

7 8

=⋅

(1–11)6 9

6 9

=⋅ ×

The x and • refer to vector cross and dot products, respectively. Thus, the element stiffness matrix inglobal coordinates becomes:

(1–12)e RT

R= ℓ

(1–13)

= ℓ

(1–14)

= ℓ

(1–15) = ℓ

( ℓ is defined in Large Strain).

1.1.5. Stress Calculations

The centroidal stress at end i is:

(1–16)σi

dir x i= ,

where:

σ

= cntoal stss (output as SDI)

Fx,i = axial force (output as FX)

The bending stresses are




(1–17)σz i

bnd y i z

y,

,=

(1–18)σ

=

where:

σ

= eg stress elemet x recto o the elemet

+ se of the eam at e (output as SBZ)

σ

= ! "# "# $ %&

- ' * ! .# . / 010 . 23Y4

My,i = moment about the element y axis at end i

Mz,i = moment about the element z axis at end i

tz = thickness of beam in element z direction (input as TKZ on R command)

ty = thickness of beam in element y direction (input as TKY on R command)

The maximum and minimum stresses are:

(1–19)σ σ σ σ5 5

657

8 5

9:6

; 5

9:6<=>

? ?= + +

(1–20)σ σ σ σ@ @

A@C

D @

EFA

G @

EFAH@F

I I= − −

The presumption has been made that the cross-section is a rectangle, so that the maximum and min-imum stresses of the cross-section occur at the corners. If the cross-section is of some other form, suchas an ellipse, the user must replace Equation 1–19 (p. 202) and Equation 1–20 (p. 202) with other moreappropriate expressions.

For long members, subjected to distributed loading (such as acceleration or pressure), it is possible thatthe peak stresses occur not at one end or the other, but somewhere in between. If this is of concern,the user should either use more elements or compute the interior stresses outside of the program.



1.2. CONTAC12 - 2-D Point-to-Point Contact

Nodes may be coincident

I

J

θ

s

n

X or radial

Y or axial


NoneNone (nodes may be coincident)Stiffness Matrix


None - average used for material property evaluationElement Temperature

None - average used for material property evaluationNodal Temperature

1.2.1. Element Matrices

CONTAC12 may have one of three conditions if the elastic Coulomb friction option (KEYOPT(1) = 0) isused: closed and stuck, closed and sliding, or open. The following matrices are derived assuming thatθ is input as 0.0.

1. Closed and stuck. This occurs if:

(1–21)µ n s>

where:

µ = coefficient of friction (input as MU on TB command with Lab = FRIC or MP command)Fn = normal force across gap

Fs = sliding force parallel to gap

The normal force is:

(1–22) J I= − −, , ∆

where:

kn = normal stiffness (input as KN on R command

un,I = displacement of node I in normal direction



CONTAC12 - 2-D Point-to-Point Contact

un,J = displacement of node J in normal direction

∆ = interferenceinput as INTF on command if KEYOPT(4) = 0

=

R

- d if KEYOPT(4) = 1

d = distance between nodes

The sliding force is:

(1–23) J = − −, ,

where:

ks = sticking stiffness (input as KS on R command)

us,I = displacement of node I in sliding direction

us,J = displacement of node J in sliding direction

uo = distance that nodes I and J have slid with respect to each other

The resulting element stiffness matrix (in element coordinates) is:

(1–24)

ℓ =

−

−

−

−

and the Newton-Raphson load vector (in element coordinates) is:

(1–25)

ℓ =−

−

2. Closed and sliding. This occurs if:

(1–26)µ =

In this case, the element stiffness matrix (in element coordinates) is:



(1–27)n n

n n

ℓ =−

−

and the Newton-Raphson load vector is the same as in Equation 1–25 (p. 204). If the unsymmetricoption is chosen (NROPT,UNSYM), then the stiffness matrix includes the coupling between thenormal and sliding directions; which for STAT = 2 is:

(1–28)

ℓ =

−

−

−

−

µ µ

µ µ

3. Open - When there is no contact between nodes I and J. There is no stiffness matrix or load vector.

Figure 1.2 (p. 205) shows the force-deflection relationships for this element. It may be seen in these figuresthat the element is nonlinear and therefore needs to be solved iteratively. Further, since energy lost inthe slider cannot be recovered, the load needs to be applied gradually.

Figure 1.2 Force-Deflection Relations for Standard Case

Fn

1

kn

(µ ) − (µ ) − δn nJ I

Fs

Fnm | |

Fnm | |-

1ks

FnFor <0, and noreversed loading

(µ ) − (µ ) s sJ I

1.2.2. Orientation of the Element

The element is normally oriented based on θ (input as THETA on R command). If KEYOPT(2) = 1, however,θ is not used. Rather, the first iteration has θ equal to zero, and all subsequent iterations have the ori-entation of the element based on the displacements of the previous iteration. In no case does the elementuse its nodal coordinates.

1.2.3. Rigid Coulomb Friction

If the user knows that a gap element will be in sliding status for the life of the problem, and that therelative displacement of the two nodes will be monotonically increasing, the rigid Coulomb frictionoption (KEYOPT(1) = 1) can be used to avoid convergence problems. This option removes the stiffness




in the sliding direction, as shown in Figure 1.3 (p. 206). It should be noted that if the relative displacementdoes not increase monotonically, the convergence characteristics of KEYOPT(1) = 1 will be worse thanfor KEYOPT(1) = 0.

Figure 1.3 Force-Deflection Relations for Rigid Coulomb Option

Fn

1

kn

(µ ) − (µ ) − δn nJ I

Fs

Fnm | |

Fnm | |-

FnFor <0, and noreversed loading

(µ ) − (µ ) s sJ I

1.3. PIPE16 - Elastic Straight Pipe

I

z,w

y,v

x,u

θ

JY

XZ

x


NoneEquation 12–15,Equation 12–16,Equation 12–17,and Equation 12–18

Stiffness and MassMatrices

NoneEquation 12–16 and Equation 12–17Stress Stiffness andDamping Matrices


Pressure and ThermalLoad Vectors


Linear thru thickness or across diameter, and along lengthElement Temperature


Internal and External: constant along length and around circumfer-ence. Lateral: constant along length

Pressure



1.3.1. Assumptions and Restrictions

The element is assumed to be a thin-walled pipe except as noted. The corrosion allowance is used onlyin the stress evaluation, not in the matrix formulation.

1.3.2. Stiffness Matrix

The element stiffness matrix of PIPE16 is similar to that of a 3-D elastic beam, except that

(1–29)w

o i= = − =π 2 2

ppe all crss-sectnal area

(1–30)y z If

= = = − =π 4 4

bdg mm

(1–31) = − =π

and,

(1–32) = = h

where:

π = 3.141592653Do = outside diameter (input as OD on R command)

Di = inside diameter = Do - 2tw

tw = wall thickness (input as TKWALL on R command)

=

!" " = 0.0

!" " > 0.0

f = flexibility factor (input as FLEX on R command)

Further, the axial stiffness of the element is defined as

(1–33)

#

ℓ =

$% k & '('

$% k ) '('

where:

ℓ = *x+*, /1+3356// 73 6,68651

E = Young's modulus (input as EX on MP command)L = element length



PIPE16 - Elastic Straight Pipe

k = alternate axial pipe stiffness (input as STIFF on RMORE command)

1.3.3. Mass Matrix

The element mass matrix of PIPE16 is the same as for a 3-D elastic beam, except total mass of the elementis assumed to be:

(1–34)e ew

flfl

inin= + +ρ ρ

where:

me = total mass of element

==

>

=

ρ

pp a mass

mw = alternate pipe wall mass (input as MWALL on RMORE command)

ρ = pipe wall density (input as DENS on MP command)ρfl = internal fluid density (input as DENSFL on R command)

=

π 2

ρin = insulation density (input as DENSIN on RMORE command)

o o

=

− =

>

=+

π

uut cr-ct r

Do+ = Do + 2tin

tin = insulation thickness (input as TKIN on RMORE command)

= alternate representation of the surface area of the outside of the pipe element (input asAREAIN on RMORE command)

Also, the bending moments of inertia (Equation 1–30 (p. 207)) are used without the Cf term.

1.3.4. Gyroscopic Damping Matrix

The element gyroscopic damping matrix is:



(1–35)e =

−

−

− −

−

Ωρ

Antisymmtric

−

−

−

− −

−

−

where:

Ω = rotation frequency about the positive x axis (input as SPIN on RMORE command)

=+

2

2 2φ

=− −

+

φ

φ

=+ +

+

φ φ

φ

=− + −

+

φ φ

φ

=

φ =

G = shear modulus (input as GXY on MP command)

As = shear area ( = Aw/2.0)

1.3.5. Load Vector

The element pressure load vector is

(1–36)ℓ⋮

=

1

1

where:




F1 = FA + FP

F7 = -FA + FP

Aw

xpr= ε

ε = aial stain due to essue load, defined belo

=

1

KEYOPT(5) = 0

KEYOPT(5) =

2 82= =

3 93= =

F4 = F10 = 0.0

= − =

6

= − =

P1 = parallel pressure component in element coordinate system (force/unit length)

P2, P3 = transverse pressure components in element coordinate system (force/unit length)

=

.

v h !g" #$

h !% h "m !& h

&'c h '*'+ !

& & #y - +/ - !& -

47:;-<>?@ B

47:;-<>?@ B

C D

The transverse pressures are assumed to act on the centerline, and not on the inner or outer surfaces.The transverse pressures in the element coordinate system are computed by

(1–37)

X

F

Z

G

H

I

=

where:

[T] = conversion matrixPX = transverse pressure acting in global Cartesian X direction) (input using face 2 on SFE

command)



PY = transverse pressure acting in global Cartesian Y direction) (input using face 3 on SFE

command)PZ = transverse pressure acting in global Cartesian Z direction) (input using face 4 on SFE

command)

εxpr

, the unrestrained axial strain caused by internal and external pressure effects, is needed to computethe pressure part of the element load vector (see Figure 1.4 (p. 211)).

Figure 1.4 Thermal and Pressure Effects

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y

z

I

T

TT

T90

T180

P

P

out

inavg

int

out

ε

is computed using thick wall (Lame') effects:

(1–38)ε ν

Ei i o o

o i

= −−

−

2 2

2 2

where:

=

f KYOPT(8) = 0

f KYOPT(8) = 1

ν = Poisson's ratio (input as PRXY or NUXY on MP command)Pi = internal pressure (input using face 1 on SFE command)

Po = external pressure (input using face 5 on SFE command)

An element thermal load vector is computed also, based on thick wall effects.




1.3.6. Stress Calculation

The output stresses, computed at the outside surface and illustrated in Figure 1.5 (p. 213) and Figure

1.6 (p. 213), are calculated from the following definitions:

(1–39)σdirx E

w=

+

(1–40)σ σbenb o

=

(1–41)σt =

(1–42)σh

=− +

−

2 2 2

2 2

(1–43)σℓfs

=

where:

σdir = direct stress (output as SDIR)

Fx = axial force

=

−

π KYOPT(8) = 0

KYOPT(8) = 1

= −π

do = 2 ro

c= −

tc = corrosion allowance (input as TKCORR on RMORE command)

σbend = bending stress (output as SBEND)

Cσ = stress intensification factor, defined in Table 1.1: Stress Intensification Factors (p. 213)

y z= = +g mm

= −π 4 4

σtor = torsional shear stress (output as ST)

Mx = torsional moment



J = 2Irσh = hoop pressure stress at the outside surface of the pipe (output as SH)

i

=

te = tw - tc

σℓf = lateral force shear stress (output as SSF)

s y z= = +hear orce2 2

Average values of Pi and Po are reported as first and fifth items of the output quantities ELEMENT

PRESSURES. The outside surface is chosen as the bending stresses usually dominate over pressure inducedstresses.

Figure 1.5 Elastic Pipe Direct Stress Output

J

σbend

σdir

Figure 1.6 Elastic Pipe Shear Stress Output

M

F

J

x

s

hσtor

σ dirσ , bendσ

Stress intensification factors are given in Table 1.1: Stress Intensification Factors (p. 213).

Table 1.1 Stress Intensification Factors

CσKEYOPT(2)

at node Jat node I




Jσ,Iσ0

1.0Tσ

1

σ1.02

σσ3

Any entry in Table 1.1: Stress Intensification Factors (p. 213) either input as or computed to be less than1.0 is set to 1.0. The entries are:

σ = stress intensification factor of end I of straight pipe (input as SIFI on R command)

σ = stress intensification factor of end J of straight pipe (input as SIFJ on R command)

w

i o

σ =

+

=2 3

" " stess ntensfcatn factr (ASME(40))

σth (output as STH), which is in the postprocessing file, represents the stress due to the thermal gradient

thru the thickness. If the temperatures are given as nodal temperatures, σth = 0.0. But, if the temperatures

are input as element temperatures,

(1–44)σα

υh = −−

−

where:

To = temperature at outside surface

Ta = temperature midway thru wall

Equation 1–44 (p. 214) is derived as a special case of Equation 2–8, Equation 2–9 and Equation 2–11 withy as the hoop coordinate (h) and z as the radial coordinate (r). Specifically, these equations

1. are specialized to an isotropic material

2. are premultiplied by [D] and -1

3. have all motions set to zero, hence εx = εh = εr = γxh = γhr = γxr = 0.0

4. have σr = τhr = τxr = 0.0 since r = Ro is a free surface.

This results in:



(1–45)

σ

σ

σ

ν

υ

νν

ν ν

xt

h

t

xh

t

=

−−

−−

−−

−−

−

2 2

2 2

α

α

∆

∆

or

(1–46)σ σαν

σ

= = −

−=

∆

and

(1–47)σ

=

Finally, the axial and shear stresses are combined with:

(1–48)σ σ σ σ dir bend = + +

(1–49)σ σ σ o f= + ℓ

where:

A, B = sine and cosine functions at the appropriate angleσx = axial stress on outside surface (output as SAXL)

σxh = hoop stress on outside surface (output as SXH)

The maximum and minimum principal stresses, as well as the stress intensity and the equivalent stress,are based on the stresses at two extreme points on opposite sides of the bending axis, as shown in

Figure 1.7 (p. 216). If shear stresses due to lateral forces σℓ are greater than the bending stresses, thetwo points of maximum shearing stresses due to those forces are reported instead. The stresses arecalculated from the typical Mohr's circle approach in Figure 1.8 (p. 216).

The equivalent stress for Point 1 is based on the three principal stresses which are designated by smallcircles in Figure 1.8 (p. 216). Note that one of the small circles is at the origin. This represents the radialstress on the outside of the pipe, which is equal to zero (unless Po ≠ 0.0). Similarly, the points marked

with an X represent the principal stresses associated with Point 2, and a second equivalent stress isderived from them.

Next, the program selects the largest of the four maximum principal stresses (σ1, output as S1MX), the

smallest of the four minimum principal stresses (σ3, output as S3MN), the largest of the four stress in-

tensities (σI, output as SINTMX), and the largest of the four equivalent stresses (σe, output as SEQVMX).

Finally, these are also compared (and replaced as necessary) to the values at the right positions around




the circumference at each end. These four values are then printed out and put on the postprocessingfile.

Figure 1.7 Stress Point Locations

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z

y

Point 1

Point 2

α

Figure 1.8 Mohr Circles

For point 1

For point 2

σ

τ

σx

σx

σxh

σxh

σ3

σh

σ1

Three additional items are put on the postdata file for use with certain code checking. These are:



(1–50)σprc i o

w

=

(1–51)σMI

XI YI ZI

= + +2 2 2

(1–52)σJ

J J J

= + +

where:

σ = se al h stess (utut as SPR)

σ

= bndng nd !! "#$

σ%&

' = *+,-./0 1,34.35 *67,** /6 ,34 8 9:;6+;6 /* <=8>

MXI = moment about the x axis at node I, etc.

1.4. PIPE18 - Elastic Curved Pipe

I

J

x

Y

XZ


NoneNo shape functions are explicitly used. Rather aflexibility matrix similar to that developed by Chenis inverted and used.

Stiffness Matrix

NoneNo shape functions are used. Rather a lumpedmass matrix using only translational degrees offreedom is used.

Mass Matrix


Thermal and PressureLoad Vector


Linear thru thickness or across diameter, and along lengthElement Temperature


Internal and External: constant along length and around the circum-ference Lateral: varies trigonometrically along length (see below)

Pressure



PIPE18 - Elastic Curved Pipe

1.4.1. Other Applicable Sections

PIPE16 - Elastic Straight Pipe (p. 206) covers some of the applicable stress calculations.


The geometry in the plane of the element is given in Figure 1.9 (p. 218).

Figure 1.9 Plane Element

θR

The stiffness matrix is developed based on an approach similar to that of Chen. The flexibility of oneend with respect to the other is:

(1–53)=

11 13 15

22 24 26

31 33 35

42 44 46

51 533 55

62 64 66

where:

fi

w

= − +

+ +

++

θθ θ θ θ θ θ

νw

θ θ θ−

= − = − +

+ +

θ

θθ

θ θν

= = −θ θ



fo

22

3

3

=+

−

+ + + −

++

νθ θ

ν θ θ θ

θ νw

4 4

= = + + −ν θ θ θ

6 6

= − = + − + + +

ν θ

θθ ν

i

= −

+

+ +

θθ θ

θθ θ

+

ν

5 5

= − = −θ

= + + + + −ν θ θ ν θ

= − = + +ν θ θ

= θ

= + + − + −ν θ θ ν θ

and where:

R = radius of curvature (input as RADCUR on R command) (see Figure 1.9 (p. 218))θ = included angle of element (see Figure 1.9 (p. 218))E = Young's modulus (input as EX on MP command)ν = Poisson's ratio (input as PRXY or NUXY on MP command)

= = −mment nerta crss-sectnπ

! "= = −#$%# &' ($&))*)%(+,&.

π / /

Do = outside diameter (input as OD on R command)

Di = Do - 2t = inside diameter

t = wall thickness (input as TKWALL on R command)




fi

fi fi

fi

=

′ ′ > 0.0

whchever s greater

′′ = 0.0 and KEYOPT(3) = 0

(ASME lexblty actor, ASME Coode(40))

whchever s greater

+

ffi

′ = 0.0 and KEYOPT(3) = 1

(ASME lexblty actor, ASME Code(40))

= 0.0 and KEYOPT(3) = 2

(K

+

+

′fi

aarman lexblty actor)

′ = -p pu FLXI R

=

=−

!

" # "

# "

=− − >

− ≤

$ %&

%&

Pi = internal pressure (input on SFE command)

Po = external pressure (input on SFE command)

' =

≥

<

*

+

/

+

′ =′ ′ >

′ =

5656 56

57 56

′ =89 :;<>:?>@BDGH ?BHJNQNBN<U V:;<@;< DW Z[\] :G ^:_`jk`q __DGz

The user should not use the KEYOPT(3) = 1 option if:

(1–54)θ| <

where:

θc = included angle of the complete elbow, not just the included angle for this element (θ)

Next, the 6 x 6 stiffness matrix is derived from the flexibility matrix by inversion:



(1–55)o = −1

The full 12 x 12 stiffness matrix (in element coordinates) is derived by expanding the 6 x 6 matrix derivedabove and transforming to the global coordinate system.

1.4.3. Mass Matrix

The element mass matrix is a diagonal (lumped) matrix with each translation term being defined as:

(1–56)te=

where:

mt = mass at each node in each translation direction

me= (ρAw + ρflAfl + ρinAin)Rθ = total mass of element

ρ = pipe wall density (input as DENS on MP command)ρfl = internal fluid density (input as DENSFL on RMORE command)

fli=

π 2

ρin = insulation density (input as DENSIN on RMORE command)

n = − =+π

sua crss-sc ara

Do+ = Do + 2 tin

tin = insulation thickness (input as TKIN on RMORE command)

1.4.4. Load Vector

The load vector in element coordinates due to thermal and pressure effects is:

(1–57), ,h p

x p

ℓ ℓ ℓ+ = +ε

where:

εx = strain caused by thermal as well as internal and external pressure effects (see Equa-

tion 1–38 (p. 211) )[Ke] = element stiffness matrix in global coordinates

T= ⋮

ℓ

= m d v d v

ℓ is computed based on the transverse pressures acting in the global Cartesian directions (input

using face 2, 3, and 4 on SFE command) and curved beam formulas from Roark. Table 18, reference no.




(loading) 3, 4, and 5 and 5c was used for in-plane effects and Table 19, reference no. (end restraint) 4ewas used for out-of-plane effects. As a radial load varying trigonometrically along the length of theelement was not one of the available cases given in Roark, an integration of a point radial load wasdone, using Loading 5c.

1.4.5. Stress Calculations

In the stress pass, the stress evaluation is similar to that for PIPE16 - Elastic Straight Pipe (p. 206). The wallthickness is diminished by the corrosion allowance, if present. The bending stress components aremultiplied by stress intensification factors (Cσ). The “intensified” stresses are used in the principal and

combined stress calculations. The factors are:

(1–58)I

o

σ, =

if SF < 1.0

stress intensificatin factr at end

(input as SF n cmmand) if SF > 1.0R

(1–59)J

σ =

(1–60) =

2 3wh !h"v"# $ g#"%&"# 'A*ME C+-"'4/55

where:

66

7 8

=+ 9

te = t - tc

do = Do - 2 tc (where tc = corrosion allowances, input as TKCORR on the R command)

1.5. PLANE42 - 2-D Structural Solid

K

J

I

t

L

s

X,R,u

Y,v



Integration PointsShape FunctionsGeometryMatrix or Vector

2 x 2

Equation 12–118 and Equa-tion 12–119 and, if modified extra

Quad

Stiffness Matrix

shapes are included (KEYOPT(2)≠ 1) and element has 4 uniquenodes, Equation 12–130 andEquation 12–131

3 if axisymmetric1 if plane

Equation 12–98 and Equa-tion 12–99

Triangle

Same as stiffnessmatrix


QuadMass and Stress StiffnessMatrices Equation 12–98 and Equa-

tion 12–99Triangle

2Same as mass matrix, specialized to facePressure Load Vector


Bilinear across element, constant thru thickness or around circumfer-ence

Element Temperature

Same as element temperature distributionNodal Temperature

Linear along each facePressure

References: Wilson, Taylor


"Structures" describes the derivation of structural element matrices and load vectors as well as stressevaluations.

1.6. SOLID45 - 3-D Structural Solid

J

K

O

P

M

IL

r

N

s

t

Z,w

Y,v

X,u



SOLID45 - 3-D Structural Solid


2 x 2 x 2 if KEYOPT(2) = 01 if KEYOPT(2) = 1

Equation 12–221, Equation 12–222, andEquation 12–223 or, if modified extrashape functions are included (KEYOPT(1)Stiffness Matrix and

Thermal Load Vector = 0) and element has 8 unique nodes,Equation 12–236, Equation 12–237, andEquation 12–238

Same as stiffness matrixEquation 12–221, Equation 12–222, andEquation 12–223

Mass and Stress StiffnessMatrices

2 x 2Equation 12–68 and Equa-tion 12–69

Quad

Pressure Load Vector

3Equation 12–49 and Equa-tion 12–50

Triangle


Trilinear thru elementElement Temperature

Trilinear thru elementNodal Temperature

Bilinear across each facePressure

Reference: Wilson, Taylor et al.


"Structures" describes the derivation of structural element matrices and load vectors as well as stressevaluations. Uniform reduced integration technique (Flanagan and Belytschko) can be chosen by usingKEYOPT(2) = 1.

1.7. CONTAC52 - 3-D Point-to-Point Contact

xy

z

I

J

Y

XZ


NoneNoneNormal DirectionStiffness Matrix

NoneNoneSliding Direction


None - average used for material property evaluationElement Temperature




None - average used for material property evaluationNodal Temperature


CONTAC12 - 2-D Point-to-Point Contact (p. 203) has many aspects also valid for CONTAC52, includingnormal and sliding force determinations, rigid Coulomb friction (KEYOPT(1) = 1), and the force-deflectionrelationship shown in Figure 1.2 (p. 205).

1.7.2. Element Matrices

CONTAC52 may have one of three conditions: closed and stuck, closed and sliding, or open.

If the element is closed and stuck, the element stiffness matrix (in element coordinates) is:

(1–61)

n n

s s

s s

n n

s s

s

ℓ =

−

−

−

−

−

−ss

where:

kn = normal stiffness (input as KN on R command)

ks = sticking stiffness (input as KS on R command)

The Newton-Raphson load vector is:

(1–62)r

y

z

y

z

ℓ =−

−

−

where:

Fn = normal force across gap (from previous iteration)

Fs = sticking force across gap (from previous iteration)

If the element is closed and sliding in both directions, the element stiffness matrix (in element coordin-ates) is:




(1–63)

n n

n nℓ =

−

−

and the Newton-Raphson load vector is the same as in Equation 1–62 (p. 225). For details on the unsym-metric option (NROPT,UNSYM), see CONTAC12 - 2-D Point-to-Point Contact (p. 203)

If the element is open, there is no stiffness matrix or load vector.

1.7.3. Orientation of Element

For both small and large deformation analysis, the orientation of the element is unchanged. The elementis oriented so that the normal force is in line with the original position of the two nodes.

1.8. PIPE59 - Immersed Pipe or Cable

I

z,w

y,v

x,u

J

Z

Y

R

X

θ

Integration

Points

Shape FunctionsOptionsMatrix or Vector

NoneEquation 12–15, Equa-tion 12–16, Equa-

Pipe Option (KEYOPT(1) ≠1)

Stiffness Matrix; andThermal, Pressure, andHydrostatic Load Vectors tion 12–17, and Equa-

tion 12–18

NoneEquation 12–6, Equa-tion 12–7, and Equa-tion 12–8

Cable Option (KEYOPT(1)= 1)

NoneEquation 12–16 andEquation 12–17

Pipe Option (KEYOPT(1) ≠1)

Stress Stiffness Matrix



Integration

Points

Shape FunctionsOptionsMatrix or Vector

NoneEquation 12–7 and Equa-tion 12–8

Cable Option (KEYOPT(1)= 1)


Pipe Option (KEYOPT(1) ≠1) with consistent massmatrix (KEYOPT(2) = 0)

Mass Matrix


Cable Option (KEYOPT(1)= 1) or reduced massmatrix (KEYOPT(2) = 1)

2Same as stiffness matrixHydrodynamic Load Vec-tor


Linear thru thickness or across diameter, and along lengthElement Temperature*

Constant across cross-section, linear along lengthNodal Temperature*

Linearly varying (in Z direction) internal and external pressure causedby hydrostatic effects. Exponentially varying external overpressure(in Z direction) caused by hydrodynamic effects

Pressure

Note

* Immersed elements with no internal diameter assume the temperatures of the water.

1.8.1. Overview of the Element

PIPE59 is similar to PIPE16. The principal differences are that the mass matrix includes the:

1. Outside mass of the fluid (“added mass”) (acts only normal to the axis of the element),

2. Internal structural components (pipe option only), and the load vector includes:

a. Hydrostatic effects

b. Hydrodynamic effects

1.8.2. Location of the Element

The origin for any problem containing PIPE59 must be at the free surface (mean sea level). Further, theZ axis is always the vertical axis, pointing away from the center of the earth.

The element may be located in the fluid, above the fluid, or in both regimes simultaneously. There is

a tolerance of only

e

below the mud line, for which

(1–64) o i= +

where:



PIPE59 - Immersed Pipe or Cable

ti = thickness of external insulation (input as TKIN on RMORE command)

Do = outside diameter of pipe/cable (input as DO on R command)

The mud line is located at distance d below the origin (input as DEPTH with TB,WATER (water motiontable)). This condition is checked with:

(1–65)e> − +

← no rror mssag

(1–66)≤ − +

← ftl

where Z(N) is the vertical location of node N. If it is desired to generate a structure below the mud line,one can set up a second material property for those elements using a greater d and deleting hydro-dynamic effects. Alternatively, a second element type such as PIPE288 can be used.

If the problem is a large deflection problem, greater tolerances apply for second and subsequent itera-tions:

(1–67)> − + ←

(1–68)− + ≥ > ← wi

(1–69)− ≥ ← !""#

where Z(N) is the present vertical location of node N. In other words, the element is allowed to sinkinto the mud for 10 diameters before generating a warning message. If a node sinks into the mud adistance equal to the water depth, the run is terminated. If the element is supposed to lie on the oceanfloor, gap elements must be provided.


The element stiffness matrix for the pipe option (KEYOPT(1) ≠ 1) is the same as for a 3-D elastic beam,except that:

[ ]( , ) [ ]( , ) [ ]( , ) [ ]( , ) [ ]( , ) [K K K K T K$ℓ ℓ ℓ ℓ ℓ4 1 1 4 10 7 7 10 7 4= = = = =%&d KK K K T$ℓ ℓ ℓ]( ' ) [ ]( ' ) [ ]( ' )4 7 10 1 110= = = −

where:

* =

+- .EYOP/235 = 68 3 29:;<>;?> @p:+@< -@? :@?quA

b;B;<cA> c;bBA @? p+pA5

+- .EYOP/235 = C 2:D+9: :A<:+@<* F G

H H−@p:+@< -@? <@<I:@?quA

b;B;<cA> c;bBA @? p+pA5



GT = twist-tension stiffness constant, which is a function of the helical winding of the armoring

(input as TWISTEN on RMORE command, may be negative)Di = inside diameter of pipe = Do - 2 tw

tw = wall thickness (input as TWALL on R command)

L = element length

oi

= − =π 2 2

crss-sectnal area

= − =π

mm f 4 4

J = 2I

1.8.4. Mass Matrix

The element mass matrix for the pipe option (KEYOPT(1) ≠ 1) and KEYOPT(2) = 0) is the same as for a

3-D elastic beam, except that ℓ (1,1), ℓ (7,7), ℓ (1,7), and ℓ (7,1), as well as M(4,4), M(10,10),M(4,10), and M(10,4), are multiplied by the factor (Ma /Mt).

where:

Mt = (mw + mint + mins + madd) L = mass/unit length for motion normal to axis of element

Ma = (mw + mint + mins) L= mass/unit length for motion parallel to axis of element

w

= − − ε ρ π

ρ = density of the pipe wall (input as DENS on MP command)

εin = initial strain (input as ISTR on RMORE command)mint = mass/unit length of the internal fluid and additional hardware (input as CENMPL on RMORE

command)

= − − ε ρπ

ρi = density of external insulation (input as DENSIN on RMORE command)

dd I = − ε ρπ

CI = coefficient of added mass of the external fluid (input as CI on RMORE command)

ρw = fluid density (input as DENSW with TB,WATER)

1.8.5. Load Vector

The element load vector consists of two parts:

1. Distributed force per unit length to account for hydrostatic (buoyancy) effects (F/Lb) as well as axial

nodal forces due to internal pressure and temperature effects Fx.

2. Distributed force per unit length to account for hydrodynamic effects (current and waves) (F/Ld).

The hydrostatic and hydrodynamic effects work with the original diameter and length, i.e., initial strainand large deflection effects are not considered.




1.8.6. Hydrostatic Effects

Hydrostatic effects may affect the outside and the inside of the pipe. Pressure on the outside crushesthe pipe and buoyant forces on the outside tend to raise the pipe to the water surface. Pressure on theinside tends to stabilize the pipe cross-section.

The buoyant force for a totally submerged element acting in the positive z direction is:

(1–70)b b w e= ρπ 2

where: F/Lb = vector of loads per unit length due to buoyancy

Cb = coefficient of buoyancy (input as CB on RMORE command)

g = acceleration vector

Also, an adjustment for the added mass term is made.

The crushing pressure at a node is:

(1–71)os

oa= − +ρ

where:

= crushing pressure due to hydrostatic effectsg = acceleration due to gravityz = vertical coordinate of the node

= input external pressure (input on SFE command)

The internal (bursting) pressure is:

(1–72)i f i

= − − +ρ

where:

Pi = internal pressure

ρo = internal fluid density (input as DENSO on R command)

Sfo = z coordinate of free surface of fluid (input as FSO on R command)

= input internal pressure (input as SFE command)

To ensure that the problem is physically possible as input, a check is made at the element midpoint tosee if the cross-section collapses under the hydrostatic effects. The cross-section is assumed to be unstableif:



(1–73)os

iw

o

− >−

2

3

ν

where:

E = Young's modulus (input as EX on MP command)ν = Poisson's ratio (input as PRXY or NUXY on MP command)

The axial force correction term (Fx) is computed as

(1–74)x x= ε

where εx, the axial strain (see Equation 2–12) is:

(1–75)ε α σ ν σ σ h r= + − +∆

where:

α = coefficient of thermal expansion (input as ALPX on MP command)∆T = Ta - TREF

Ta = average element temperature

TREF = reference temperature (input on TREF command)

σx = axial stress, computed below

σh = hoop stress, computed below

σr = radial stress, computed below

The axial stress is:

(1–76)σ

=

−

−

f KEYOPT(8) = 0

f KEYOPT(8) = 1

and using the Lamé stress distribution,




(1–77)σhi i o o

i oi o

o i

=− + −

−

2 22 2

2

2 2

(1–78)σr

=− − −

−

where:

s

d= +

= hydrodynamic pressure, described belowD = diameter being studied

Pi and Po are taken as average values along each element. Combining Equation 1–75 (p. 231) thru Equa-

tion 1–78 (p. 232).

(1–79)ε αν

xE

= +− −

−∆

Note:

=

f KYOPT(8) = 0

f KYOPT(8) = 1

Note that if the cross-section is solid (Di = 0.), Equation 1–77 (p. 232) reduces to:

(1–80)ε αν

= −−

∆

1.8.7. Hydrodynamic Effects

See Hydrodynamic Loads in the Element Tools section of this document for information about thissubject.

1.8.8. Stress Output

The below two equations are specialized either to end I or to end J.

The stress output for the pipe format (KEYOPT(1) ≠ 1), is similar to PIPE16. The average axial stress is:



(1–81)σxn E=+

where:

σx = average axial stress (output as SAXL)

Fn = axial element reaction force (output as FX, adjusted for sign)

i i o o=

−

π 2 2f KYOPT(8) = 0

f KYOPT(8) = 1

Pi = internal pressure (output as the first term of ELEMENT PRESSURES)

Po = external pressure = s

d+ (output as the fifth term of the ELEMENT PRESSURES)

and the hoop stress is:

(1–82)σh

=− +

−

where:

σh = hoop stress at the outside surface of the pipe (output as SH)

Equation 1–82 (p. 233) is a specialization of Equation 1–77 (p. 232). The outside surface is chosen as thebending stresses usually dominate over pressure induced stresses.

All stress results are given at the nodes of the element. However, the hydrodynamic pressure had beencomputed only at the two integration points. These two values are then used to compute hydrodynamicpressures at the two nodes of the element by extrapolation.

For the stress output for the cable format (KEYOPT(1) = 1 with Di = 0.0), the stress is given with and

without the external pressure applied:

(1–83)σI = +ℓ

(1–84)σe =ℓ

(1–85)a = σ

where:

σxI = axial stress (output as SAXL)




Eo=

if KYOPT(8) = 0

if KYOPT(8) = 1

σeI = equivalent stress (output as SEQV)

ℓ = axial force on node (output as FX)Fa = axial force in the element (output as FAXL)

1.9. SHELL63 - Elastic Shell

L

K

J

I

y,v

st

z,w

t

x,u

Y

XZ


2 x 2

Equation 12–92 and Equa-tion 12–93 (and, if modified

Membrane / Quad

Stiffness Matrix andThermal Load Vector

extra shape functions areincluded (KEYOPT(3) = 0)and element has 4 uniquenodes, Equation 12–95,Equation 12–96, and Equa-tion 12–97

1Equation 12–65, Equa-tion 12–66, and Equa-tion 12–67

Membrane / Tri-angle

3 (for each triangle)

Four triangles that areoverlaid are used.These

Bendingsubtriangles refer to Equa-tion 12–67

2 x 2Equation 12–68, Equa-tion 12–69, and Equa-tion 12–70

Membrane / Quad

Mass, Foundation Stiff-ness and Stress StiffnessMatrices


Membrane / Tri-angle

3 (for each triangle)Four triangles that areoverlaid are used.These tri-Bendingangles connect nodes IJK,




IJL, KLI, and KLJ. w isdefined as given in Zien-kiewicz

None

One-sixth (one- third fortriangles) of the total pres-

Reduced shellpressure loading

Transverse Pressure LoadVector

sure times the area is ap-(KEYOPT(6) = 0)

plied to each node normal(Load vector ex-cludes moments)

of each subtriangle of theelement

Same as mass matrixSame as mass matrix

Consistent shellpressure loading(KEYOPT(6) = 2)(Load vector in-cludes moments)

2Equation 12–68 and Equa-tion 12–69 specialized tothe edge

Quad

Edge Pressure Load Vec-tor

2Equation 12–49 and Equa-tion 12–50 specialized tothe edge

Triangle


Bilinear in plane of element, linear thru thicknessElement Temperature

Bilinear in plane of element, constant thru thicknessNodal Temperature

Bilinear in plane of element, linear along each edgePressure



1.9.2. Foundation Stiffness

If Kf, the foundation stiffness, is input, the out-of-plane stiffness matrix is augmented by three or four

springs to ground. The number of springs is equal to the number of distinct nodes, and their directionis normal to the plane of the element. The value of each spring is:

(1–86)f if

d

, =∆

where:

Kf,i = normal stiffness at node i

∆ = element areaKf = foundation stiffness (input as EFS on R command)

Nd = number of distinct nodes



SHELL63 - Elastic Shell

The output includes the foundation pressure, computed as:

(1–87)σpf

I J K L= + + +

where:

σp = foundation pressure (output as FOUND, PRESS)

wI, etc. = lateral deflection at node I, etc.

1.9.3. In-Plane Rotational Stiffness

The in-plane rotational (drilling) DOF has no stiffness associated with it, based on the shape functions.A small stiffness is added to prevent a numerical instability following the approach presented by Kanok-Nukulchai for nonwarped elements if KEYOPT(1) = 0. KEYOPT(3) = 2 is used to include the Allman-typerotational DOFs.

1.9.4. Warping

If all four nodes are not defined to be in the same flat plane (or if an initially flat element loses its flatnessdue to large displacements (using NLGEOM,ON)), additional calculations are performed in SHELL63.The purpose of the additional calculations is to convert the matrices and load vectors of the elementfrom the points on the flat plane in which the element is derived to the actual nodes. Physically, thismay be thought of as adding short rigid offsets between the flat plane of the element and the actualnodes. (For the membrane stiffness only case (KEYOPT(1) = 1), the limits given with SHELL41 are used).When these offsets are required, it implies that the element is not flat, but rather it is “warped”. To ac-count for the warping, the following procedure is used: First, the normal to element is computed bytaking the vector cross-product (the common normal) between the vector from node I to node K andthe vector from node J to node L. Then, the check can be made to see if extra calculations are neededto account for warped elements. This check consists of comparing the normal to each of the four elementcorners with the element normal as defined above. The corner normals are computed by taking thevector cross-product of vectors representing the two adjacent edges. All vectors are normalized to 1.0.If any of the three global Cartesian components of each corner normal differs from the equivalentcomponent of the element normal by more than .00001, then the element is considered to be warped.

A warping factor is computed as:

(1–88)φ =

where:

D = component of the vector from the first node to the fourth node parallel to the element normalt = average thickness of the element

If:

φ ≤ 0.1 no warning message is printed.10 ≤ φ ≤ 1.0 a warning message is printed1.0 < φ a message suggesting the use of triangles is printed and the run terminates



To account for the warping, the following matrix is developed to adjust the output matrices and loadvector:

(1–89)=

1

2

3

4

(1–90)i

i

o

i

o

=

where:

= ffset frm average plane at nde

and the DOF are in the usual order of UX, UY, UZ, ROTX, ROTY, and ROTZ. To ensure the location of theaverage plane goes through the middle of the element, the following condition is met:

(1–91)

0

0

+ + + =

1.9.5. Options for Non-Uniform Material

SHELL63 can be adjusted for nonuniform materials, using an approach similar to that of Takemoto andCook . Considering effects in the element x direction only, the loads are related to the displacementby:

(1–92)x x x= ε

(1–93)

yy

= −

−

ν

κ

where:

Tx = force per unit length

t = thickness (input as TK(I), TK(J), TK(K), TK(L) on R command)Ex = Young's modulus in x direction (input as EX on MP command)



SHELL63 - Elastic Shell

Ey = Young's modulus in y direction (input as EY on MP command)

εx = strain of middle fiber in x direction

Mx = moment per unit length

νxy = Poisson's ratio (input as PRXY on MP command)

κx = curvature in x direction

A nonuniform material may be represented with Equation 1–93 as:

(1–94)x r

x

xyy

x

x= −

−

3

2ν

κ

where:

Cr = bending moment multiplier (input as RMI on RMORE command)

The above discussion relates only to the formulation of the stiffness matrix.

Similarly, stresses for uniform materials are determined by:

(1–95)σ ε κtop

= +

(1–96)σ ε κb

= −

where:

σ = diecin sess a fi e

σ = m

For nonuniform materials, the stresses are determined by:

(1–97)σ ε κ !"

= +

(1–98)σ ε κ#$%&

# $ #= −

where:

ct = top bending stress multiplier (input as CTOP, RMORE command)

cb = bottom bending stress multiplier (input as CBOT, RMORE command)



The resultant moments (output as MX, MY, MXY) are determined from the output stresses rather thanfrom Equation 1–94.

1.9.6. Extrapolation of Results to the Nodes

Integration point results can be requested to be copied to the nodes (ERESX,NO command). For thecase of quadrilateral shaped elements, the bending results of each subtriangle are averaged and copiedto the node of the quadrilateral which shares two edges with that subtriangle.

1.10. PLANE82 - 2-D 8-Node Structural Solid

X,R,u

Y,v

I

J

K

L

M

NO

P

s

t



QuadMass, Stiffness and StressStiffness Matrices; andThermal Load Vector 3


Triangle

2 along faceSame as stiffness matrix, specialized to the facePressure Load Vector


Same as shape functions across element, constant thru thickness oraround circumference

Element Temperature

Same as element temperature distributionNodal Temperature

Linear along each facePressure

Reference: Zienkiewicz



1.10.2. Assumptions and Restrictions

A dropped midside node implies that the face is and remains straight.



PLANE82 - 2-D 8-Node Structural Solid

1.11. SOLID92 - 3-D 10-Node Tetrahedral Structural Solid

K

R

L

QO

P

MN

J

I

Y,v

X,uZ,w


4Equation 12–184, Equation 12–185, and Equa-tion 12–186

Stiffness, Mass, and StressStiffness Matrices; andThermal Load Vector

6Equation 12–184, Equation 12–185, and Equa-tion 12–186 specialized to the face



Same as shape functionsElement Temperature

Same as shape functionsNodal Temperature

Linear over each facePressure






1.12. SOLID95 - 3-D 20-Node Structural Solid

L

N

M

P WO

KR

J

YS

U

X

V

Q

I

T Z

BA

r

s

t

Y,v

X,uZ,w

Integration PointsShape FunctionsGeo-

metryMatrix or Vector

14 if KEYOPT(11) = 02 x 2 x 2 if KEYOPT(11) = 1

Equation 12–239 , Equa-tion 12–240, and Equa-tion 12–241

Brick

Stiffness, Mass, andStress StiffnessMatrices; andThermal Load Vector

3 x 3Equation 12–215, Equa-tion 12–216, and Equa-tion 12–217

Wedge

2 x 2 x 2Equation 12–199, Equa-tion 12–200, and Equa-tion 12–201

Pyramid


Tet


Quad


6Equation 12–57 and Equa-tion 12–58

Triangle


Same as shape functions thru elementElement Temperature

Same as shape functions thru elementNodal Temperature

Bilinear across each facePressure



"Structures" describes the derivation of structural element matrices and load vectors as well as stressevaluations. If KEYOPT(3) = 1, the mass matrix is diagonalized as described in Lumped Matrices.



SOLID95 - 3-D 20-Node Structural Solid


Chapter 2: Hydrodynamic Loads on Line Elements

Hydrodynamic effects may occur because the structure moves in a motionless fluid, the structure isfixed but there is fluid motion, or both the structure and fluid are moving. The fluid motion consists oftwo parts: current and wave motions. The current is input by giving the current velocity and direction(input as W(i) and θ(i)) at up to eight different vertical stations (input as Z(i)). (All input quantities referredto in this section not otherwise identified come from the TBDATA commands used with TB,WATER).The velocity and direction are interpolated linearly between stations. The current is assumed to flowhorizontally only.

The information in this section applies to the legacy PIPE59 element.

The following topic is available:2.1.Wave Theory

2.1. Wave Theory

The wave may be input using one of four wave theories in the following table (input as KWAVE viaTB,WATER).

Table 2.1 Wave Theory Table

KWAVE TB,WATER In-

putDescription of Wave Theory

1Small amplitude wave theory, unmodified (Airy wave theory), (Wheeler)

0Small amplitude wave theory, modified with empirical depth decay function,(Wheeler)

2Stokes fifth order wave theory, (Skjelbreia et al.)

3Stream function wave theory, (Dean)

The free surface of the wave is defined by

(2–1)η η βs ii

Ni

i

N

i

w w= ∑ = ∑

= =1 1

where:

ηs = total wave height

= =≠

number of ave componentnumber of ave K 2

5

K 2 =

Kw = wave theory key (input as KWAVE with TB,WATER)

ηi = wave height of component i



i = =surface coeffcent (component heght)nput quantty H(() on the OCTABLE command f K = 0 or 1

derved from

w

oother nput f K = 2

β

πλ τ

φ

πλ τ

=

− +

−

+

φ

π

3

3

4

−

π

π

R = radial distance to point on element from origin in the X-Y plane in the direction of the waveλi = wave length = input as WL(i) if WL(i) > 0.0 and if Kw = 0 or 1 otherwise derived from

Equation 2–2 (p. 244)t = time elapsed (input as TIME on TIME command) (Note that the default value of TIME isusually not desired. If zero is desired, 10-12 can be used).

τ

= = ! " #$%&'* +,, -- ./

-, "

≠ 5

- ./ =

5

φi = phase shift = input as φ(i)

If λi is not input (set to zero) and Kw < 2, λi is computed iteratively from:

(2–2)λ λπλ6 6

7

6

=

89:;

where:

λi = output quantity small amplitude wave length

λτ

π<

> <= =?

@DFGDF IDJMFNFP QRRG SJFRU SJVR lRMWFX

g = acceleration due to gravity (Z direction) (input on ACEL command)d = water depth (input as DEPTH via TB,WATER)

Each component of wave height is checked that it satisfies the “Miche criterion” if Kw ≠3. This is toensure that the wave is not a breaking wave, which the included wave theories do not cover. A breakingwave is one that spills over its crest, normally in shallow water. A warning message is issued if:

(2–3)Y b>

where:



b ii

=

=tanhλ

πλ

heght of reakng wave

When using wave loading, there is an error check to ensure that the input acceleration does not changeafter the first load step, as this would imply a change in the wave behavior between load steps.

For Kw = 0 or 1, the particle velocities at integration points are computed as a function of depth from:

(2–4)R

N

D

r r= ∑ +

=1

πτη

(2–5)Z

rɺ= ∑

=η

where:

r

= radial particle velocity

r

= vertical particle velocityki = 2π/λi

= height of integration point above the ocean floor = d+Z

ɺη = time derivative of ηi

r

= drift velocity (input via TB,WATER)

s

=+

=

=

K 0 (mll mplud y)

K

η(Wl(35))

The particle accelerations are computed by differentiating

r

and

r

with respect to time. Thus:

(2–6)ɺr

ɺ

= ∑

−

=

πτ

η η

(2–7)ɺr

ɺ !

!!

"

! !! !

#= ∑

− −

=$

πτ

πτ

η η τπ

where:



Wave Theory

si s

= +=ɺη

λ η 2

Πf K 0 (mall ampltude wave theory)

ff K 1 (Wheeler(35)) =

Expanding equation 2.29 of the Shore Protection Manual for a multiple component wave, the wavehydrodynamic pressure is:

(2–8)

N

= ∑

=ρ η

πλ

πλ

However, use of this equation leads to nonzero total pressure at the surface at the crest or trough ofthe wave. Thus, Equation 2–8 (p. 246) is modified to be:

(2–9)

= ∑

+

=ρ η

πλ η

πλ

which does result in a total pressure of zero at all points of the free surface. This dynamic pressure,which is calculated at the integration points during the stiffness pass, is extrapolated to the nodes forthe stress pass. The hydrodynamic pressure for Stokes fifth order wave theory is:

(2–10)

= ∑

=ρ η

πλ

πλ

Other aspects of the Stokes fifth order wave theory are discussed by Skjelbreia et al.. The modificationas suggested by Nishimura et al.has been included. The stream function wave theory is described byDean.

If both waves and current are present, the question of wave-current interaction must be dealt with.Three options are made available through Kcr (input as KCRC via TB,WATER):

For Kcr = 0, the current velocity at all points above the mean sea level is simply set equal to Wo, where

Wo is the input current velocity at Z = 0.0. All points below the mean sea level have velocities selected

as though there were no wave.

For Kcr = 1, the current velocity profile is “stretched” or “compressed” to fit the wave. In equation form,

the Z coordinate location of current measurement is adjusted by



(2–11)s

s′ =+

+η

η

where:

Z(j) = Z coordinate location of current measurement (input as Z(j))

′ = adjusted value of Z(j)

For Kcr = 2, the same adjustment as for Kcr = 1 is used, as well as a second change that accounts for

“continuity.” That is,

(2–12)

′ =+ η

where:

W(j) = velocity of current at this location (input as W(j))

′ = adjusted value of W(j)

These three options are shown pictorially in Figure 2.1 (p. 247).

Figure 2.1 Velocity Profiles for Wave-Current Interactions

Horizontal arrows represent

input velocities

Mean Water

Surface

Mud Line

Constant (K = 0)

Stretch (K = 1)

Continuity (K = 2)

Water Surface

Z

Nonlinear Stretch (K = 3)

CR

CR

CR

CR

To compute the relative velocities (ɺn ,

ɺt ), both the fluid particle velocity and the structure velocity

must be available so that one can be subtracted from the other. The fluid particle velocity is computedusing relationships such as Equation 2–4 (p. 245) and Equation 2–5 (p. 245) as well as current effects. Thestructure velocity is available through the Newmark time integration logic (see Transient Analysis).

Finally, a generalized Morison's equation is used to compute a distributed load on the element to accountfor the hydrodynamic effects:



Wave Theory

(2–13)

d D we

n n M w e n

T we

t t

= +

+

ρ ρπ

ρ

2ɺ ɺ ɺ

ɺ ɺ

where:

F/Ld = vector of loads per unit length due to hydrodynamic effects

CD = coefficient of normal drag (see below)

ρw = water density (mass/length3) (input as DENSW on MP command with TB,WATER)

De = outside diameter of the pipe with insulation (length)

ɺ = normal relative particle velocity vector (length/time)

CM = coefficient of inertia (input as CM on the R command)

ɺ = normal particle acceleration vector (length/time2)

CT = coefficient of tangential drag (see below)

ɺ = tangential relative particle velocity vector (length/time)

Two integration points along the length of the element are used to generate the load vector. Integrationpoints below the mud line are simply bypassed. For elements intersecting the free surface, the integrationpoints are distributed along the wet length only.

The coefficients of drag (CD,CT) may be defined in one of two ways:

• As fixed numbers (via both the R and RMORE commands), or

• As functions of Reynolds number.

The dependency on Reynolds number (Re) may be expressed as:

(2–14) =

where:

fD = functional relationship (input on the water motion table as RE, CDy, and CDz via TB,WATER)

= ɺρ

µ

µ = viscosity (input as VISC on MP command)

and

(2–15) =

where:

fT = functional relationship (input on the water motion table as RE and CT via TB,WATER)



= ɺ te wρ

µ

Temperature-dependent quantity may be input as µ, where the temperatures used are those given byinput quantities T(i) of the water motion table.

When the MacCamy-Fuchs corrections are requested to account for diffraction effects, especially forlarge diameter objects with shorter wave lengths, two things occur:

1. The coefficient of inertia is adjusted:

′ =′[ ] ′[ ]

m m

2

1

2

1

2

π

where:

=π

λ

′ = −o

′ = −

J0 = zero order Bessel function of the first kind

J1 = first-order Bessel function of the first kind

Y0 = zero order Bessel function of the second kind

Y1 = first-order Bessel function of the second kind

2. The phase shift is added to φi (before the Wc correction, if used):

ϕ′ ϕi i= +′′

arcan



Wave Theory
