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### Transcript of 150 - Understanding Optimization Design Studies

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OptimizationStudiesUnderstandingOptimizationDesignStudiesLecture

UnderstandingOptimizationDesignStudies.mp3

Understanding Optimization Design Studies

Optimization Studies adjust design variables to best achieve a

specified goal while satisfying specified design limits.

Components:

Goal Design Limits Design Variables

Optimization versus Feasibility

Algorithm

1. Initial Values2. Local Sensitivities3. Base Analysis4. Repeat until convergence or Max Iterations

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Optimization Model

Maximum Von Mises Stress during an Optimization Design StudyLectureNotes

The Optimization Design Study

An Optimization Design Study adjusts one or more design variables to best achieve aspecified goal or to test feasibility of a design, while respecting specified limits.Mechanica adjusts the model's variables in a series of iterations through which it triesto move closer to the goal while respecting specified limits.

The following components are required in order to define an Optimization Study:

Goal: During the course of an Optimization, you specify a default or user-defined Mechanica measure that you wish to maximize or minimize.

Design Limits: Design Limits can be specified for any default or user-definedmeasures. During the Optimization, Mechanica attempts to find a solution thatdoes not violate any of the design limits while trying to improve the goal. Youcan specify whether a design limit should be greater than, less than, or equalto a specified value.

Design Variables: Similar to a Global Sensitivity Design Study, you select thedesign variables that you want Mechanica to adjust during the study. Therange and initial values for these design variables can be specified as

necessary.

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A good example of an Optimization problem might be trying to minimize the massand material used for a loaded structural member (the Goal) by varying keydimensions such as thicknesses (the Design Variables) while keeping the stress below

acceptable levels to avoid failure (the Design Limits).

Note the following key aspects of the Optimization Design Study:

The Goal and Design Limits are optional, but you must have at least one Goalor one Limit.

If you have not specified a Goal, Mechanica simply searches for the firstfeasible design that satisfies the defined Design Limits.

When defining an Optimization Design Study, you can change the type

to Feasibility and the goal section of the dialog box becomes

unavailable. As such, it becomes an Optimization Design Study without

a goal. As the name suggests, a Feasibility Study determines whether

the design variables can be changed to values such that the model is

feasiblea state defined where none of the design limits are

compromised.

The Optimization Algorithm.

The following steps summarize the procedure deployed by Mechanica when runningand Optimization Design Study:

1. Mechanica starts the optimization by using the initial values specified forDesign Variables.

2. For the initial Design Variable's values, Mechanica runs Local SensitivityStudies in the background and tests the slopes of every Design Variable.

Depending on the outcome of these local sensitivity studies, some of thevariables may or may not contribute dramatically satisfying the limits. As such,some variables values will stay the same during the study (flatter slope localstudy graphs) and some will adjust (steeper slope local study graphs).

3. The base analysis (or analyses) is run at the current Design Variables. Thenecessary measures (used for Design Limits and Goal) are extracted,

evaluated, and investigated against the imposed conditions.

Design Limits have precedence over the Optimization Goal.

4. If the Goal or the maximum number of iterations has not been reached, theprocess repeats starting with Step 1 above.

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Best Practices

Optimization typically requires more iterations as the number of DesignVariables increases. Therefore, use as few Design Variables as possible. LocalSensitivity Studies are helpful in deciding which design variables are important.

The smaller the design space being considered, the shorter the optimizationrun time. Therefore, use the results from the Global Sensitivity Studies tonarrow the range of each design variable being considered and thus limit theoverall design space.

The Optimization takes less time the closer the baseline model is to theoptimum. You might find it useful to review results from Sensitivity Studies toimprove the candidate design prior to optimization.

It if often helpful to start an Optimization from a feasible design state. If youhave trouble getting an solution from an Optimization problem, considerrunning a Feasibility Study first and using the resulting design variable valuesas the starting point for an Optimization.

UnderstandingOptimizationDesignStudiesDemonstrationUnderstandingOptimizationDesignStudies_demo.mp4UnderstandingOptimizationDesignStudiesProcedure

Procedure: Understanding Optimization Design Studies

ScenarioDefine an Optimization Design Study.

Optimization support_bracket.prt

Task 1.Open the Mechanica Application and define an Optimization Design Study.

In this example, you are defining an Optimization Study that will help you

identify the design changes required to find the lightest weight bracket able

to sustain specific von Mises stress values. Notice that some of thesimulation features (material, load, constraints, surface regions, static

analysis) are already defined in the model. Investigate them and identify the

1. Click Applications > Mechanica.

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

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3. Click File > New Optimization Design Study....

4. In the Name field, type SP_BRCK_OPTM.

Because you have only one analysis defined in the model, Mechanica will

automatically select it as the base analysis. The same is true for the single

load set defined in the model.

5. In the Goal area of the dialog box, verify that the drop-down menu is set to

Minimizeand that the measure is set to total_massas shown in the dialog box.

These settings are the Mechanica defaults and just happen to match our

objectives in this procedure.

6. Click Add Row in the Design Limits area of the dialog box.

7. Select max_stress_vmfrom the Measures dialog box and click OK.

8. Verify that the operator is set to

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10. Click Select Dimension in the Optimization Study Definition dialog box.

11. Select the Round 1feature from the model tree and select the 1.5dimensionas shown in the figure.

12. Click Select Dimension in the Optimization Study Definition dialog box.

13. Select the CROSS_SECTIONfeature from the model tree and select the 10dimension as shown in the figure.

14. Type the following variable names and values in the corresponding cells in the

variables section of the dialog box as shown in the figure below.

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15. Click Options...to open the Design Study Options dialog box.

16. Verify that the Optimization Algorithm drop-down menu is set to Automatic.

Based on the computation needs, the Automatic setting enables the software

to change between the SDP and GDP algorithms as necessary.

17. Type 5.0for the Optimization Convergence.

Note that the Optimization Convergence value you set above is for the

Optimization algorithm and not for the multi-pass adaptive-style polynomial

convergence.

18. Verify that the Maximum Iterations is set to 20.

19. Select the Repeat P-Loop Convergenceand Remesh after each shape

updatecheck boxes.

20. The dialog box should appear as shown in the figure. Click Closeto close the

Design Study Options dialog box.

21. Click OKto complete the Optimization Study Definition and close the dialogbox.

1.

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You can actually run the optimization if you have time. It should take about

510 minutes to complete. If you do not have the time to actually run the

Optimization, you can review the results in the Completedirectory, or skip

to Step 4 and end the exercise.

1. Verify that SP_BRCK_OPTMis selected in the Analyses and Design Studies

dialog box and click Start Run > Yesto start the design study.

2. Click Display Study Status once the analysis is started.

3. When the analysis is complete, review the Run Status window. You should beable to make the following observations:

Four iterations of the optimization algorithm were required.

Four base analyses were required. Nine perturbation analyses were required. In order to reduce stress below the design limit, the FILLET dimension grew to 191

and the BRCKT_HEIGHT dimension shrank to 8.

The final von Mises stress finished at 235.79 N/mm2, less than the MaximumDesign Limit of 240 N/mm2(MPa).

4. Close any open dialog boxes.