Topic 21 A Demonstrative Computer Session Using … · A Demonstrative Computer Session Using ... ADINA Verification Manual, and ADINA Theory and Modeling ... "Studies of Finite Element

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Topic 21

A DemonstrativeComputer SessionUsing ADINALinear Analysis

• Use of the computer program ADINA for finite elementanalysis, discussion of data preparation, programsolution, and display of results

• Capabilities of ADINA

• Computer laboratory demonstration-Part I

• Linear analysis of a plate with a hole for the stressconcentration factor

• Data input preparation and mesh generation

• Solution of the model

• Study and evaluation of results using plots of stresses,stress jumps, and pressure bands

Appendix

The use of the ADINA program is described and sample solutions aregiven in

Bathe, K. J., "Finite Elements in CAD - and ADINA," NuclearEngineering and Design, to appear.

ADINA, ADINAT, ADINA-IN, and ADINA-PLOT Users Manuals,ADINA Verification Manual, and ADINA Theory and Modeling Guide,ADINA Engineering, Inc., Watertown, MA 02172, U.S.A.

Proceeding~ of the ADINA Conferences, (Bathe, K. J., ed.)Computers & Structures

13, 5-6, 198117, 5-6, 198321, 1-2, 1985

21-2 Computer Session Using ADINA - Linear Analysis

References: The use of pressure band plots to evaluate meshes is discussed in (continued) Sussman, T., and K. J. Bathe, "Studies of Finite Element Procedures

Stress Band Plots and the Evaluation of Finite Element Meshes," Engineering Computations, to appear.

A FINITE ELEMENTANALYSIS - LINEAR

SOLUTION• We have presented a considerable

amount of theory and example solution results in the lectures.

• The objective in the next two lectures is to show how an actual finiteelement analysis is performed on thecomputer.

• We cannot discuss in detail all theaspects of the analysis, but shallsummarize and demonstrate on thecomputer the major steps of theanalysis, and concentrate on

- possible difficulties- possible pitfalls- general recommendations

Topic Twenty-one 21-3

Transparency21-1

Transparency21-2


Transparency21-3 We will use as the example problem

the plate with a hole already considered earlier, and perform linear andnonlinear analyses

elastic analysis to obtain thestress concentration factorelasto-plastic analysis to estimatethe limit loadan analysis to investigate the effectof a shaft in the plate hole

Plate with hole: Schematic drawing

Transparency21-4

1 E = 207000 MPaj-----:.---+777Jjrim~ v = 0.3

thickness = 0.01 m

plane stressconditions

:-:~~~t'"We consider thisquarter of the---+ plate and

use symmetryconditions

0.01m-+-_.J

0.1m

I. 0.1m,I

• The first step for a finite elementanalysis is to select a computer program. We use the ADINA system.

ADINA-IN to prepare, generatethe finite elementdata

ADINA to solve the finiteelement model

ADINA-PLOT to display numeri-cally or graphicallythe solution results

Schematically:

graphics..>display

terminal

User work-station

Topic 1\venty-one 21-5

Transparency21-5

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Transparency21-7

I I generatedUser - ADINA-IN - ADINA

input file

• User types into terminal ADINA-INcommands interactively or for batchmode processing. User checks inputand generated data on graphicsdisplay terminal.

Transparency21-8

• ADINA-IN generates the input datafor ADINA.

• The input data is checked internallyin ADINA-IN for errors and consistency and is displayed as perrequest by the user.

• The degree of freedom numbers aregenerated (for a minimum bandwidth).

--I ADINA

Topic 1\ventyo()ne 21-7

Transparency21-9

• User runs ADINA to calculate theresponse of the finite elementmodel. ADINA writes the model dataand calculated results on an outputfile and stores the model data andcalculated results on the portholefile.

ADINA-PLOT I~

User _--;1display outputdata, numericallyor graphically

Transparency21-10

• User runs ADINA-PLOT to accessthe output data and display selectedresults; displacements, stresses,mode shapes, maxima, ...


Transparency21-11

Transparency21-12

A brief overview of ADINA

• Static and dynamic solutions

• Linear and nonlinear analysis

• Small and very large finite elementmodels can be solved.

The formulations, finite elements andnumerical procedures used in the program have largely been discussed inthis course.

DISPLACEMENTASSUMPTIONS

• Infinitesimally small displacements

• Large displacements/large rotationsbut small strains

• Large deformations/large strains

MATERIAL MODELSIsotropic Linear Elastic

Orthotropic Linear Elastic

Isotropic Thermo-Elastic

Curve Description Model for Analysisof Geological Materials

Concrete Model

MATERIAL MODELS

Isothermal Plasticity Models

Thermo-Elastic-Plastic and CreepModels

Nonlinear Elastic, IncompressibleModels

User-Supplied Models


Transparency21-13

Transparency21-14


Transparency21-15 z

ONE-DIMENSIONALELEMENT

I......-.-! RING ELEMENT

x

r-------.... v

Truss and Cable Element(2,3, or 4 nodes)

Transparency21-16

z

v

Two-Dimensional Solid Element(variable number of nodes)

z

x

y

z

)(

Three-Dimensional Solid Element(variable number of nodes I

y

Two-Node Beam Element

Topic 1\ventY'one 21-11

Transparency21-17

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Transparency21-19

z

/

r----V

x

Isoparametric Beam Element(2,3,4 nodes)

Transparency21-20

z

AT EACH NODE 6 BEAMDEGREES OF FREEDOMPLUS OVALIZATION

~-----v DEGREES OF FREEDOMx

Pipe Element with Ovalization

16 Node Element

}-,x

4 Node Element

ELEMENTS ARE USED WITH5 OR 6 DEGREES OFFREEDOM PER NODE


Transparency21-21

Plate and Shell Elements

A SUMMARY OF IMPORTANTOBSERVATIONS

• We need to check the finite elementdata input carefully

prior to the actual responsesolution run, andafter the response solution hasbeen obtained by studyingwhether the desired boundaryconditions are satisfied, whetherthe displacement and stresssolution is reasonable (for thedesired analysis).

Transparency21-22


Transparency21-23

Transparency21-24

• We need to carefully evaluate andinterpret the calculated response

study in detail the calculated displacements and stresses alongcertain lines, study stress jumps

stress averaging, stress smoothing should only be done after theabove careful evaluation

Data for Construction of64 Element Mesh:

100 MPa

E = 207,000 MPav = 0.3Plane stressthickness = 0.01 m

Finite element mesh to be generatedusing ADINA-IN:

• Mesh contains 64 elements,288 nodes.


Transparency21-25

eight-nodeisoparametricelement

DemonstrationPhotograph

21-1Finite Element Research

Group Laboratorycomputer configuration


ADINADemonstration

21-1Input data

Transparency21-26

(Repeat 21-25)

QUARTER PLATE WITH HOLE - 64 ELEMENTS2261001110 1 0 1 1 1.0000000

C... MASTER CONTROL99999 0 0 1 0 0 50 30.C••* 3 LOAD CONTROL

o 4 0 0 0 0 0 0C*.* 4 MASS AND DAMPING CONTROL

o 0 0 0 .0 .0C••* 5 EIGENVALUE SOLUTION CONTROL

o 0 0 0 0 0C... 6 TIME INTEGRATION METHOD CONTROL

o 20.500000000.25000000 0 0C••* 7 INCREMENTAL SOLUTION CONTROL

1 1 210 15.001000000.010000000.05C.*. 8 PRINT-OUT CONTROL

11111 0




Stress vector output: Example


Transparency21-27

integrationpoint ~

/ maximum principal stress,/----' (tensile)

minimum principal stress(compressive)

The length of the line is proportionalto the magnitude of the stress.

TIME 1.000 DMAX ,300

ADINADemonstration

21-2Deformed meshplot


Plate with hole: Schematic drawing

Transparency21-28

0.1m

0.01 m--+----./

0.1m.1

E = 207000 MPav =0.3

thickness = 0.01 m

We consider thisquarter of theplate anduse symmetryconditions

plane stressconditions

Transparency21-29

(Repeat 21-25)



~eight-node

isoparametricelement

s-- stress computed at closestintegration point

Stress point numbers and integrationpoint numbers for element 57

2 integrationpoint

6 3X

2X

3 1 6 5x 5 X4 X

7x

987 X Xx4

P 8stress point

Behavior of stresses near the stressconcentration:

radius(J of s- stress computed at nodal point

hole

length of element


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distance z = 0


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Maximum principal stress calculation:

_ {1yy + {1zz + !({1yy - {1ZZ)2 + 2{11 - 2 -V. 4 {1yz

Transparency21-33

(Repeat 21-30)

Stress point numbers and integrationpoint numbers for element 57

integrationpoint

2

62X

5X

8 9X x

8

3

4--_~t-------1

.:5stress POint

RESULTANT • SMAX ARITHMETIC EXPRESSION.


lTVV+TZZI ITWO+SllRT IITVV-TZZ) * lTVV-TZZ) IFDUR+TVZHVZ I

EXTREME ELEMENT RESULTS PER ELEMENT GROUP FOR WHOLE MODEL

TVV • VV-STRESSTZZ • ZZ-STRESSTVZ • VZ-STRESSTWO • 2.1Il1ll1ll00FOUR • 4.1Il1ll1ll1ll1ll

INTERVAL TSTART- 1.1Il1ll1ll1ll TEND= 1. 0000 SCANNED FOR ABSOLUTE MAXIMUM

ADINADemonstration

21-3Close-up ofcalculations

ELEMENT BROUP NO. 1 (2-D SOLID) LISTED RESULTS ARE MEASURED INGLOBAL COORD I NATE SYSTEM

RESULTANT SMAX ELEMENT POINT TIME STEP

Ill. 34~ISIE+1Il3 ~7 4 Ill. 1IIlIIlIllIllE+1Il1



Transparency21-34

(Repeat 21-25)



Transparency21-35

(Repeat 2-33)

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(Repeat 2-35)

• To be confident that the stressdiscontinuities are small everywhere,we should plot stress jumps along eachline in the mesh.

• An alternative way of presentingstress discontinuities is by means ofa pressure band plot:- Plot bands of constant pressure

where

pressure = - (Txx + ; yy + Tzz)

Sixty-four element mesh: Pressure bandplot

H~5 MPa 5 MPa

A SUMMARY OF IMPORTANTOBSERVATIONS

• We need to check the finite elementdata input carefully

- prior to the actual responsesolution run, and

- after the response solution hasbeen obtained by studyingwhether the desired boundaryconditions are satisfied, whetherthe displacement and stresssolution is reasonable (for thedesired analysis).


ADINADemonstration

21-4Close-up of

pressure bands

. Transparency21-37

(Repeat 21-221


Transparency21·38

(Repeat 21-23) • We need to carefully evaluate andinterpret the calculated response

study in detail the calculated displacements and stresses alongcertain lines, study stress jumps

stress averaging, stress smoothing should only be done after theabove careful evaluation

MIT OpenCourseWare http://ocw.mit.edu

Resource: Finite Element Procedures for Solids and Structures Klaus-Jürgen Bathe

The following may not correspond to a particular course on MIT OpenCourseWare, but has been provided by the author as an individual learning resource.

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Topic 21 A Demonstrative Computer Session Using … · A Demonstrative Computer Session Using ... ADINA Verification Manual, and ADINA Theory and Modeling ... "Studies of Finite Element