1. Exploring the Design Domain Chapter Four

2. Training Manual January 30, 2001 Inventory #001449 4-2 Exploring the Design Domain A. Overview Exploring the design domain simply means experimenting with different designs. It is easy to explore the design domain once you have built a parametric model and an analysis file. Analysis File Explore the Design Domain Optimize the Design Initial Design Parametric Model & Loading Solution Parametric Results

3. Training Manual January 30, 2001 Inventory #001449 4-3 The ANSYS optimizer provides several tools to explore the design domain. Exploring the Design Domain...Overview Single Loop Random Sweep Gradient Factorial

4. Training Manual January 30, 2001 Inventory #001449 4-4 Exploring the Design Domain...Overview These tools are also a good way to generate a set of initial designs for the Subproblem optimizer. (Subproblem generates N+2 random sets on its own if they are not provided.)

5. Training Manual January 30, 2001 Inventory #001449 4-5 Exploring the Design Domain...Overview Single Loop Tool Performs one loop through the analysis file. Useful for what-if scenarios such as “What if I eliminate the diagonal members of this truss bridge (set their cross- sectional area to a very small value)?” H1 H2 A1, A2, A3

6. Training Manual January 30, 2001 Inventory #001449 4-6 Exploring the Design Domain...Overview Random Tool Generates random designs by assigning random values to the design variables. Useful for starting a subsequent design optimization session with a few “good” designs.

7. Training Manual January 30, 2001 Inventory #001449 4-7 Exploring the Design Domain...Overview Sweep Tool Sweeps through the entire range of design variable values for each DV. Useful for global sensitivity studies - how a given design responds over the entire range of values of a given DV. An existing set must be specified to sweep through. DV1 DV2 Reference Design

8. Training Manual January 30, 2001 Inventory #001449 4-8 Exploring the Design Domain...Overview Gradient Tool Generates designs in the neighborhood of a reference design by changing each DV by a small amount. Useful for local sensitivity studies - how a given design responds to small perturbations in DVs. This tool is applied automatically at the end of a Subproblem optimization run to see if the optimum design is perhaps still perched on a hillside. Obj DV

9. Training Manual January 30, 2001 Inventory #001449 4-9 Exploring the Design Domain...Overview Factorial Tool A statistical tool that samples all extreme points in the design domain, i.e, the minimum and maximum of each DV. Useful for understanding not only the effect of each DV on the design but also the effect of two-variable and three- variable interactions. Also known as design of experiments (since factorial methods are widely used in the interpretation of experimental results). Design Space

10. Training Manual January 30, 2001 Inventory #001449 4-10 Exploring the Design Domain B. Procedure Once the analysis file is created, the same general sequence of steps applies to all the optimization tools: 1.Establish the initial design (DV, SV and OBJ values) 2.Enter the optimizer and identify the analysis file 3.Identify optimization variables 4.Run the optimization tool 5.Review results

11. Training Manual January 30, 2001 Inventory #001449 4-11 Exploring the Design Domain...Procedure To illustrate the steps, we will use a half-symmetry model of the truss bridge example. Objective is to minimize the total volume, subject to: –Maximum vertical deflection < 1.0 in –Maximum member stress < 10,000 psi Loading: –P1 = 20 lb/in –Gravity, g = 386 in/s 2 Design variables: –A1, A2, A3, H1, H2 H1 H2 A1, A2, A3 P1

12. Training Manual January 30, 2001 Inventory #001449 4-12 Exploring the Design Domain...Procedure Step 1. Establish the Initial Design The analysis file contains the initial design - the design with initial values for DVs. To establish the initial design: –First clear the database (or exit and re-enter ANSYS). –Then use Utility Menu > File > Read Input from… –Or the /INPUT command: /input,trussbr,inp

13. Training Manual January 30, 2001 Inventory #001449 4-13 Exploring the Design Domain...Procedure Step 2. Enter optimizer and identify analysis file This step simply tells the optimizer the name of the analysis file. Use: –Main Menu > Design Opt > -Analysis File- Assign… –Or the OPANL command: /opt opanl,trussbr,inp

14. Training Manual January 30, 2001 Inventory #001449 4-14 Exploring the Design Domain...Procedure Step 3. Identify optimization variables This step designates the appropriate parameters as DVs, SVs, and OBJ. Use: –the Design Opt menus shown on the right... –or the OPVAR command: opvar,a1,dv,1,10 opvar,uymax,sv,-1.0 opvar,totvol,obj etc.

15. Training Manual January 30, 2001 Inventory #001449 4-15 Exploring the Design Domain...Procedure Step 4. Run the optimization tool Step 5. Review results We will describe these steps for each tool separately since they are unique to each tool.  

16. Training Manual January 30, 2001 Inventory #001449 4-16 Exploring the Design Domain - Procedure C. Single Loop Tool 3Step 1. Establish the initial design 3Step 2. Enter optimizer and identify analysis file 3Step 3. Identify optimization variables Step 4. Run the optimization tool: –Choose Single Loop tool –Specify desired DV values –Initiate the run Step 5. Review results

17. Training Manual January 30, 2001 Inventory #001449 4-17 Exploring the Design Domain - Procedure...Single Loop Tool Choosing Single Loop Tool: Design Opt > Method/Tool… Choose Single Run. Or use the OPTYPE command: optype,run

18. Training Manual January 30, 2001 Inventory #001449 4-18 Exploring the Design Domain - Procedure...Single Loop Tool Specifying Desired DV Values: Use the Name=Value format, in the Input window or in the Scalar Parameters dialog ( Utility Menu > Parameters > Scalar Parameters... ). The values presumably represent a what-if scenario you want to examine. For example, what if the diagonal members of the bridge are eliminated (a3 set a very small value)? a1=10 a2=8 a3=0.01 (very small value) h1=300 h2=400

19. Training Manual January 30, 2001 Inventory #001449 4-19 Exploring the Design Domain - Procedure...Single Loop Tool Initiating the Run: Design Opt > Run… Or use the OPEXE command: opexe This creates a new design set, with new values for the state variables and objective function.

20. Training Manual January 30, 2001 Inventory #001449 4-20 Exploring the Design Domain - Procedure...Single Loop Tool

21. Training Manual January 30, 2001 Inventory #001449 4-21 Exploring the Design Domain - Procedure...Single Loop Tool Step 5. Review Results One way is to simply list the design set and check values of the state variables and objective function: –Design Opt > -Design Sets- List… –Or use the OPLIST command: oplist

22. Training Manual January 30, 2001 Inventory #001449 4-22 Exploring the Design Domain - Procedure...Single Loop Tool –OPLIST for the truss bridge example shows that the design (set number 3) is infeasible because of high compressive stress in the middle (SCMID) and high tensile stress in the left region (STLEFT).

23. Training Manual January 30, 2001 Inventory #001449 4-23 Exploring the Design Domain - Procedure...Single Loop Tool Another way to review results of a single loop run is to use POST1 (the General Postprocessor): –Deformed shape –Stress contours –etc.

24. Training Manual January 30, 2001 Inventory #001449 4-24 Exploring the Design Domain - Procedure...Single Loop Tool ANSYS allows you to run any number of single loops. Each design is given a new set number, and all design sets are stored in the optimization database (jobname.opt by default). You can use OPSEL or Design Opt > -Design Sets- Select/Delete… to keep only the feasible designs. One possible application of the single loop is to run several single loops and use the design sets as a starting point for design optimization.

25. Training Manual January 30, 2001 Inventory #001449 4-25 Exploring the Design Domain - Procedure D. Random Tool Generates designs by assigning random values to DVs. Procedure is as follows: 3Step 1. Establish the initial design 3Step 2. Enter optimizer and identify analysis file 3Step 3. Identify optimization variables Step 4. Run the optimization tool –Specify run-time controls –Choose Random tool –Save the optimization database –Initiate the run Step 5. Review Results

26. Training Manual January 30, 2001 Inventory #001449 4-26 Exploring the Design Domain - Procedure...Random Tool Run-time Controls: Optimization database file name (OPDATA command). Defaults to jobname.opt. How to read the analysis file (OPLOOP). Default is to read from the beginning and to ignore DV parameter definitions. Printout controls (OPPRNT). Default is to suppress details. Save-best-design option (OPKEEP). Allows you to save the best design as it occurs. Default is OFF. Use the commands above or Design Opt > Controls…

27. Training Manual January 30, 2001 Inventory #001449 4-27 Exploring the Design Domain - Procedure...Random Tool Choosing Random Tool: Requires two pieces of information: –Number of random designs to be generated (NITR) –Number of feasible designs after which to stop (NFEAS). Default is to run all NITR iterations. Use OPTYPE and OPRAND commands: optype,random oprand,nitr,nfeas

28. Training Manual January 30, 2001 Inventory #001449 4-28 Exploring the Design Domain - Procedure...Random Tool Or Design Opt > Method/Tool...

29. Training Manual January 30, 2001 Inventory #001449 4-29 Exploring the Design Domain - Procedure...Random Tool Saving the Opt Database: Allows you to resume the optimization database in its current state if needed. Specify a file name different from the default name of jobname.opt, since the default name gets updated each iteration. Design Opt > -Opt Database- Save… Or the OPSAVE command: opsave,trussbr,opt0

30. Training Manual January 30, 2001 Inventory #001449 4-30 Exploring the Design Domain - Procedure...Random Tool Initiating the Run: Design Opt > Run… Or use the OPEXE command: opexe Up to NITR designs are generated. NITR is the number of random designs requested on the OPRAND command.

31. Training Manual January 30, 2001 Inventory #001449 4-31 Exploring the Design Domain - Procedure...Random Tool Step 5. Review Results Typically consists of listing the random design sets: –Design Opt > -Design Sets- List… –Or use the OPLIST command: oplist

32. Training Manual January 30, 2001 Inventory #001449 4-32 Exploring the Design Domain - Procedure...Random Tool The Random tool is useful as a precursor to a design optimization session: you can generate random designs, select only the feasible ones, and use them as a starting point for the optimizer. Next, we will see how to use the Sweep tool.

33. Training Manual January 30, 2001 Inventory #001449 4-33 Exploring the Design Domain - Procedure E. Sweep Tool The Sweep tool uses a specified design as a reference point and increments each DV through its entire range while holding the others constant. Gives an idea of the global sensitivity of a response quantity to a design variable.

34. Training Manual January 30, 2001 Inventory #001449 4-34 Exploring the Design Domain - Procedure...Sweep Tool Procedure is as follows: 3Step 1. Establish the initial design 3Step 2. Enter optimizer and identify analysis file 3Step 3. Identify optimization variables Step 4. Run the optimization tool –Specify run-time controls (as before) –Choose Sweep tool –Save the optimization database (as before) –Initiate the run (as before) Step 5. Review Results

35. Training Manual January 30, 2001 Inventory #001449 4-35 Exploring the Design Domain - Procedure...Sweep Tool Choosing Sweep Tool: Requires two pieces of information: –The reference design set number DSET. While each DV is swept, the other DVs are held at values specified by DSET. If only one design exists (such as the initial design), then that design is used as the reference point. –Number of sweeps per DV (NSPS). NSPS = 2 generates two designs per DV - one each at the minimum and maximum values.

36. Training Manual January 30, 2001 Inventory #001449 4-36 Exploring the Design Domain - Procedure...Sweep Tool Use –Design Opt > Method/Tool… –Or OPTYPE and OPSWEEP commands: optype,sweep opsweep,dset,nsps Creates NSPS*N designs, where NSPS is the number of sweep points per design variable and N is the number of design variables.

37. Training Manual January 30, 2001 Inventory #001449 4-37 Exploring the Design Domain - Procedure...Sweep Tool Step 5. Reviewing Results Results from the Sweep tool indicate how each DV affects the design - global sensitivity. –For example, what happens to UYMAX (vertical deflection) if A3 (area of diagonal members) is incremented from MIN to MAX? You can use graphs or tabular listings for this purpose.

38. Training Manual January 30, 2001 Inventory #001449 4-38 Exploring the Design Domain - Procedure...Sweep Tool Graphs: –Design Opt > Tool Results > -Graph- Sweeps... –Or the OPLSW command: oplsw,uymax,a1,a2,a3

39. Training Manual January 30, 2001 Inventory #001449 4-39 Exploring the Design Domain - Procedure...Sweep Tool Tabular listings: –Design Opt > Tool Results > Print... –Or the OPRSW command: oprsw,all –Prints a table of normalized values of response variables versus normalized DV values.

40. Training Manual January 30, 2001 Inventory #001449 4-40 Exploring the Design Domain - Procedure F. Gradient Tool The Gradient tool uses a specified design as a reference point and slightly perturbs each DV to determine local sensitivities. Useful as a follow-on to design optimization, to test the sensitivity of the optimum design to small DV changes.

41. Training Manual January 30, 2001 Inventory #001449 4-41 Exploring the Design Domain - Procedure...Gradient Tool Procedure is as follows: 3Step 1. Establish the initial design 3Step 2. Enter optimizer and identify analysis file 3Step 3. Identify optimization variables Step 4. Run the optimization tool –Specify run-time controls (as before) –Choose Gradient tool –Save the optimization database (as before) –Initiate the run (as before) Step 5. Review Results

42. Training Manual January 30, 2001 Inventory #001449 4-42 Exploring the Design Domain - Procedure...Gradient Tool Choosing Gradient Tool: Requires two pieces of information: –The reference design set number DSET. DV values of this design set are slightly perturbed to measure the gradient. If only one design exists (such as the initial design), then that design is used as the reference point. –Amount of perturbation DELTA, specified as a percent forward difference. Each DV is changed by the amount ± DELTA*(MAX-MIN)/100

43. Training Manual January 30, 2001 Inventory #001449 4-43 Exploring the Design Domain - Procedure...Gradient Tool Use –Design Opt > Method/Tool… –Or OPTYPE and OPGRAD commands: optype,sweep opgrad,dset,delta Creates N designs, where N is the number of design variables.

44. Training Manual January 30, 2001 Inventory #001449 4-44 Exploring the Design Domain - Procedure...Gradient Tool Step 5. Reviewing Results Results from the Gradient tool indicate how a small change in a DV affects the design - i.e, local sensitivity. –For example, what happens to UYMAX if mid-span height H2 is perturbed by ±1 %? You can use graphs or tabular listings for this purpose. Both outputs are based on a ±1% change in DVs.

45. Training Manual January 30, 2001 Inventory #001449 4-45 Exploring the Design Domain - Procedure...Gradient Tool Graphs: –Design Opt > Tool Results > -Graph- Gradient... –Or the OPLGR command: oplsw,uymax,a1,a2,a3

46. Training Manual January 30, 2001 Inventory #001449 4-46 Exploring the Design Domain - Procedure...Gradient Tool Tabular listings: –Design Opt > Tool Results > Print... –Or the OPRGR command: oprgr,all

47. Training Manual January 30, 2001 Inventory #001449 4-47 Exploring the Design Domain - Procedure G. Factorial Tool This tool samples the extremes of the design domain - the minimum and maximum values of all DVs. Full factorial and fractional factorial runs are available. –Full factorial creates 2 n designs, where n is the number of DVs. –Fractional factorial creates fraction*2 n designs, where fraction may be 1/2, 1/4, 1/8, 1/16, 1/32, or 1/64. –For example, if there are two design variables A and B, a full factorial run would create 4 designs: A min B min A min B max A max B min A max B max

48. Training Manual January 30, 2001 Inventory #001449 4-48 Exploring the Design Domain - Procedure...Factorial Tool Procedure is as follows: 3Step 1. Establish the initial design 3Step 2. Enter optimizer and identify analysis file 3Step 3. Identify optimization variables Step 4. Run the optimization tool –Specify run-time controls (as before) –Choose Factorial tool –Save the optimization database (as before) –Initiate the run (as before) Step 5. Review Results

49. Training Manual January 30, 2001 Inventory #001449 4-49 Exploring the Design Domain - Procedure...Factorial Tool Choosing Factorial Tool: Specify full or fractional factorial: full, 1/2, 1/4, etc. Use –Design Opt > Method/Tool… –Or OPTYPE and OPFACT commands: optype,fact opfact,type Creates Fraction*2**N Design Sets

50. Training Manual January 30, 2001 Inventory #001449 4-50 Exploring the Design Domain - Procedure...Factorial Tool Step 5. Reviewing Results Results from the Factorial tool can be used to review the following: –Main effects, i.e, the overall effect of each DV on the design. –Two-variable interaction effects, i.e, how much the effect of one DV on the design depends on the value of another DV. –Three-variable interaction effects. You can use bar charts or tabular listings for this purpose.

51. Training Manual January 30, 2001 Inventory #001449 4-51 Exploring the Design Domain - Procedure...Factorial Tool Bar Charts: –Design Opt > Tool Results > -Graph- Factorial... –Or the OPLFA command: oplfa,name,effect

52. Training Manual January 30, 2001 Inventory #001449 4-52 Exploring the Design Domain - Procedure...Factorial Tool This bar chart shows the main effects for SCLEFT (maximum compressive stress in the left region of the truss bridge). A1 and H1 (DV numbers 1 and 4) have the most effect, and H2 (DV 5) has virtually no effect on SCLEFT.

53. Training Manual January 30, 2001 Inventory #001449 4-53 Exploring the Design Domain - Procedure...Factorial Tool Two-factor DV interactions for SCLEFT:

54. Training Manual January 30, 2001 Inventory #001449 4-54 Exploring the Design Domain - Procedure...Factorial Tool Tabular listings: –Design Opt > Tool Results > Print... –Or the OPRFA command: oprfa,all

55. Training Manual January 30, 2001 Inventory #001449 4-55 Exploring the Design Domain H. Workshop In this workshop, we will perform Sweep and Gradient studies on the hexagonal steel plate from previous workshop exercises. See your Design Optimization Workshop Supplement for details.