122 - Understanding Adaptivity Methods

8/14/2019 122 - Understanding Adaptivity Methods

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ConvergenceUnderstandingAdaptivityMethodsLecture

UnderstandingAdaptivityMethods.mp3

Understanding Adaptivity Methods

Adaptivity refers to how Mechanica changes the polynomial order of

each mesh element edge during an analysis.

Adaptivity Single-Pass Adaptive

o First pass: P = 3 Local stress errors estimated New P levels for all edges necessary

o Second Pass = Last Pass

Multi-Pass Adaptiveo First pass: P = 1o Second Pass

P =2 Results compared; % change calculated for each edge P Level +1 where necessary

oRepeat until converged


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Stress Results

P Level ResultsLectureNotes

Adaptivity


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When using the GEA (Geometric Element Analysis) method, a structure is broken downinto geometric elements that follow/map to the structures geometry. After thestructure is meshed, each edge of the geometric element model is associated with apolynomial order. The polynomial order can vary from one up to nine and is used todescribe the deformation of each edge of the geometric element mesh. There are twomethods Mechanica can use to elevate these polynomials in order to converge on thesolution: Multi-Pass Adaptive (MPA) and Single-Pass Adaptive (SPA). The figure on theleft side of this slide shows the resultant von Mises Stress of a Mechanica analysis,while the figure on the right shows the polynomial order of each element edge used in

the analysis.

Single-Pass Adaptive

Single-Pass Adaptive (SPA) refers to the method that Mechanica uses to obtainsolution convergence.

When you run an analysis using the SPA convergence, Mechanica solves the problemat polynomial order three and estimates local stress errors. These errors aredetermined by the difference between stress values computed using two differentmethods (super-converged stress and single element stress results). Next, apercentage is defined for each element and compared to a target internal errorestimator. This target error estimator percentage is set internally and has beendetermined experimentally. Based on the ratio between the actual and target stresserror, the number of degrees of freedom needed to accurately solve for the stress canbe determined. The polynomial order is then increased to the level required to solvethe number of degrees of freedom. The final RMS stress error reported in the summaryfile is calculated by sampling the local error estimates (the same as those used toupdate the polynomials).

The method of improving stress accuracy and estimating stress error isbased on the work by Zinkiewicz & Zhu (The Superconvergent PatchRecovery and A Posteriori Error Estimates. Part 1: The RecoveryTechnique, International Journal for Numerical Methods in Engineering,Vol. 33, p. 1331(1992)).

Multi-Pass Adaptive

If the error estimates from the Single-Pass Adaptive (SPA) convergence tolerance are

not acceptable, switch to the Multi-Pass Adaptive (MPA) convergence strategy for thesubsequent design studies.

In the case of MPA analysis, Mechanica performs calculations and increases thepolynomial order for each element edge until the convergence criteria is satisfied.

In Pass 1, the analysis is performed with all edges at p-level 1 (linear shapefunction). The results for different measures (default or customized) are stored.

In Pass 2, the analysis is performed with all the edges at p-level 2. The results


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are compared to the previous pass and a convergence check is now performedon edges and elements. Edges from previous and current results, which vary bymore than the user-defined percentage convergence, are upgraded to p-level 3.Elements for which previous and current results variation are below or equal tothe user-defined convergence are maintained at the same p-level.

The P-Pass algorithm is repeated until convergence percentage is satisfied for allspecified quantities or the maximum p-level is reached.

UnderstandingAdaptivityMethodsDemonstrationUnderstandingAdaptivityMethods_demo.mp4

UnderstandingAdaptivityMethodsProcedureProcedure: Understanding Adaptivity Methods

ScenarioIn this procedure, you will create a Single-Pass Adaptive and a Multi-Pass Adaptive static

analysis on a simple model and review the analysis summary results.

Convergence Plate.prt

Task 1.Open the Mechanica application and define a static analysis that uses theSingle-Pass Adaptive convergence option.

In this procedure we are going to define Single-Pass Adaptive (SPA) and

Multi-Pass Adaptive (MPA) convergence criterion for Static Analyses of a

simple bracket model. The loads, constraints, and materials are already

defined in the model.

1. Click Applications > Mechanica.

Note PLATE.PRT is fully constrained (selected in the image for clarity) and

loaded along the Y-axis with 100 lbf.


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2. Click Mechanica Analyses/Studies from the Main toolbar.

3. Click File > New Static....

4. Type SPAin the Name field.

5. Verify that the load and constraint sets already defined in the model are selected,as shown.

6. If required, select the Convergencetab and select Single-Pass Adaptivefrom

the Method drop-down list.

7. Click OKto complete the definition and close the dialog box.


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Task 2.Run the SPA Static Analysis and review the results.

1. Click Start Run in the Analyses and Design Studies dialog box, then click Yes.

2. Click Display Study Status in the Analyses and Design Studies dialog box.

3. When the run in is complete, review the Study Status dialog box and note theMaximum Edge Orderfor Pass 1 and Pass 2.


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4. In the Run Status dialog box, also note the RMS Stress Error Estimates.

5. Click Closeto close the Run Status dialog box. Click Closeto close the Diagnosticsdialog box.


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Task 3.Define another static analysis, this time using the Multi-Pass Adaptiveconvergence option.

1. If necessary, click Mechanica Analyses/Studies from the Main toolbar to openthe Analyses and Design Studies dialog box.


3. Type MPAin the Name field.

4. Verify that the load and constraint sets already defined in the model are selected,

as shown.

5. If necessary, select the Convergencetab. Select Multi-Pass Adaptivefrom theMethod drop-down list.

6. In the Polynomial Order area set the Minimum to 1and the Maximum to 9.

7. Type 1in the Percent Convergencefield.


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8. Define the convergence to be on max_stress_vm (a predefined measure). In the

Converge On area of the dialog box select the Measuresradio button. Click List

Measures and select max_stress_vmfrom the list of predefined measures.Click OKto select the Measure and close the dialog box.

9. Click OKto complete the definition and close the dialog box.

Task 4.Run the MPA Static Analysis, review the results, save the model, and erase itfrom memory.

1. Click Start Run > Yesin the Analyses and Design Studies dialog box.

2. Click Display Study Status in the Analyses and Design Studies dialog box.

3. When the run in is complete, review the Run Status dialog box and note theMaximum Edge Orderfor Pass 1 through Pass 7.

4. In the Run Status dialog box, also note the convergence percentage error for the

max_stress_vm measure. You should find that it is .4% (which is less than the 1%you specified).

5. Click Close > Close > Closeto close the open dialog boxes.

6. Return to the Standard Pro/ENGINEER mode by clicking Applications > Standard.

7. Click Save from the main toolbar and click OKto save the model.

8. Click File > Erase > Current > Yesto erase the model from memory.


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This completes the procedure.

UnderstandingAdaptivityMethodsExerciseExercise: Comparing SPA and MPA Convergence

Objectives

After successfully completing this exercise, you will be able to:

Monitor and interpret results for a Single-Pass Adaptive and (by comparison) aMulti-Pass Adaptive analysis for the same Mechanica model.

Understand analysis summary reports and relate them to the Mechanica adaptivitymethods.

ScenarioIn this exercise we will examine the max Von Mises stress results developed in a turbine

subjected to 600 rpm rotational velocity. The turbine is comprised of AL6061 and isconstrained along the shaft location; it enables for radial expansion, but not for twisting oraxial deformations. You will evaluate the max Von Mises stress with the help of a Static

Analysis. All the loads, constraints, materials, and other simulation features are already

defined in the model.


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The purpose of this exercise is to examine how productive you can be if you run the Static

Analysis using a Single-Pass versus a Multi-Pass Adaptive convergence method. You willinvestigate which method to use and determine how many errors occur when using either

one of the two methods.

SPAvsMPA impeller.prt

Task 1.Open Mechanica and investigate the model.

1. Click Applications > Mechanica.

2. Investigate the model, materials, loads, and constraints.

The load is defined as a Centrifugal load. Also, note that 1 rpm = (2*pi

rad)/(60 sec), which is roughly 0.105 rad/sec.

The constraints are defined with respect to a Cylindrical Coordinate System

(thus, defining the constraints in an R, , Z domain instead of using the

default Cartesian coordinate system).

Task 2.Mesh the Model Using the AutoGEM Tools.

1. Click Create from the main toolbar. Use the default setting and click Createto

mesh the model.


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Because the model is a thick solid piece, it is a good candidate for Solid

elements.

2. When the mesh is complete, note the total number of Solid elements created in the

model (roughly 6200 elements).

3. Click Close > Close > Close > Noto close the open dialog boxes without savingthe mesh.

Task 3.Define a Single-Pass Adaptive Static Analysis.

1. Click Mechanica Analyses/Studies from the main toolbar.


3. In the Name field, type SPA.

4. Verify that ConstraintSet1and LoadSet1are selected in the Constraints and

Loads areas of the dialog box.

5. Verify the Single-Pass Adaptiveis selected in the Convergence area of the dialogbox.

6. Click OKto complete the Static Analysis Definition.


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Task 4.Run the Single-Pass Adaptive Analysis and Monitor the Summary Report.

1. If necessary, select SPAin the dialog box as shown in the figure. Click Start Run

> Yesto start the analysis.

The analysis will likely take from 5 to 10 minutes to complete.


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2. Click Display Study Status from the Analyses and Design Studies dialog box.

Observe and investigate the progress and completion of the analysis.

Because we did not save the mesh as part of Task 2, the analysis will start

by meshing the model and continue with calculations of equations at Pass 1.

For Pass 1, all element edges are assigned a polynomial level of order 3. The

stress computations are performed and based on the comparison with the

target internal estimator, polynomial order will be increased as necessary for

each edge.


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For Pass 2, the polynomial order, for at least some edges of the existing

elements, has been raised to 7. Final computations conclude with the RMS

error estimates.

The maximum Von Mises stress is reported under the default measures as

max_stress_vm and is equal to .1032 N/mm2.

3. When the analysis is complete and you have reviewed the results, click Closetoclose the Diagnostics dialog box and Closeto close the Run Status window. Leave

the Analyses and Design Studies dialog box open.


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Task 5.Define a Multi-Pass Adaptive Static Analysis.

1. Click Copy from the Analyses and Design Studies dialog box.

2. Right-click Copy_of_SPAand select Edit.

Copying analyses is a recommended procedure if the same loads andconstraints are consistently used for the same model but different

studies/analyses are carried out.

3. Edit the Name field toMPA.

4. Verify that ConstraintSet1and LoadSet1are selected in the Constraints and

Loads areas of the dialog box.

5. Select Multi-Pass Adaptivefrom the Method drop-down menu. Type 9in the

Maximum field. Verify that the Minimum field is set to 1.

6. Type 5in the Percent Convergence dialog box.

7. Select the Measuresradio button and click List Measures .

8. Select max_stress_vmfrom the list of Predefined measures and click OK.

9. The dialog box should appear as shown in the figure. Click OKto complete the

Static Analysis Definition.


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Task 6.Run the MPA analysis.

1. If necessary, select MPAin the dialog box as shown in the figure. Click Start Run

> Yesto start the analysis.

The analysis will likely take between 7.5 and 15 minutes to complete.


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2. Click Display Study Status from the Analyses and Design Studies dialog box.

Observe and investigate the progress and completion of the analysis.

For Pass 1, the polynomial assigned to all the edges of all elements has been

set to 1. Notice Maximum Edge Order at Pass 1. The stress measure

computations are performed.

For Pass 2, all edges have their polynomial order raised to 2. The stress

measure is computed and compared to the values evaluated at Pass 1.


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For Pass 4, note that the convergence has been reached for the

max_stress_vm measure at a polynomial level of 4. The Von Mises stress is

evaluated at .1003 N/mm2.

3. When the analysis is complete and you have reviewed the results, click Closeto

close the Diagnostics dialog box and click Closeto close the Summary window.


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Task 7.Note the following conclusions when comparing SPA and MPA convergencemethods, save the model, and erase it from memory.

1. Investigate and compare the results of both the SPA and MPA analyses to verify thestatements that follow:

From this investigation you can determine that the results are close to each other(1.039 compared to 1.003).

The time it takes to run each analysis can be problematic. As a general rule,analyses using MPA convergence criteria take longer (sometimes much longer) torun than those analyses which are run using SPA convergence criteria.

As a best practice, it is recommended to start an analysis with SPA convergence tonote the overall behavior of the analysis model subjected to your loads andconstraints. You can then decide whether the use of an MPA convergence run iswarranted to obtain the desired accuracy for the measures you are concerned about

for the analysis.

2. Return to the Standard Pro/ENGINEER mode by clicking Applications > Standard.

3. Click Save from the main toolbar and click OKto save the model.

4. Click File > Erase > Current > Yesto erase the model from memory.

This completes the exercise.

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122 - Understanding Adaptivity Methods