1. Chapter 14 設計最佳化 Design Optimization

2. 2/33 Contents 14.1 何謂設計最佳化 ? What is Design Optimization? 14.2ANSYS 設計最佳化 Design Optimization with ANSYS 14.3 實例 : 兩端固定樑的形狀最佳化 Example: Shape Optimization of a Fixed-ends Beam 14.4 實例 : 三角平板之最佳設計 Example: Design of a Triangular Plate 14.5 其它最佳化工具 Other Optimization Tools

3. 3/33 第 14.1 節 何謂設計最佳化 ? What is Design Optimization?

4. 4/33 14.1.1 Mathematical Model

5. 5/33 14.1.2 Optimization Variables Design variables State variables Objective function

6. 6/33 14.1.3 Design Space and Design Sets Design space Design set Feasible design Optimal design Best design

7. 7/33 第 14.2 節 ANSYS 設計最佳化 Design Optimization with ANSYS

8. 8/33 14.2.1 A Design Optimization Procedure Using ANSYS Organize ANSYS procedure into two files: Optimization file—describes optimization variables, and trigger the optimization runs. Analysis file—constructs, analyses, and post-processes the model.

9. 9/33 14.2.2 Typical Commands in an Optimization File 01 02 03 04 05 06 07 08 09 10 11 12 13 /CLEAR! Clear model database...! Initialize design variables /INPUT,...! Execute analysis file once /OPT! Enter optimization phase OPCLEAR! Clear optimization database OPVAR,...! Declare design variables OPVAR,...! Declare state variables OPVAR,...! Declare objective function OPTYPE,...! Select optimization method OPANL,...! Specify analysis file name OPEXE! Execute optimization run OPLIST,...! Summarize the results...! Further examining results

10. 10/33 14.2.3 Typical Commands in an Analysis File 01 02 03 04 05 06 07 08 09 10 11 12 /PREP7...! Build the model using the ! parameterized design variables FINISH /SOLUTION...! Apply loads and solve FINISH /POST1! or /POST26 *GET,...! Retrieve values for state variables *GET,...! Retrieve value for objective function... FINISH

11. 11/33 14.2.4 ANSYS Optimization Algorithms Two built-in algorithms in ANSYS: First order method Subproblem approximation method (Zero order method)

12. 12/33 第 14.3 節 實例 : 兩端固定樑的形狀最佳化 Example: Shape Optimization of a Fixed-end Beam

13. 13/33 14.3.1 Problem Description 6 m F = 100,000 N p =15,000 N/m h b = 100 mm

14. 14/33 14.3.2 Modeling Consideration L 1.5 m C H1 H2 H3

15. 15/33 14.3.3 ANSYS Procedure Optimization File 01 02 03 04 05 06 07 08 09 10 11 12 13 FINISH /CLEAR /TITLE, Design of Beam (SI) H1 = 0.4 H2 = 0.4 H3 = 0.4 /INPUT, BEAM, TXT /OPT OPCLR OPVAR, H1, DV, 0.1, 0.8 14 15 16 17 18 19 20 21 22 23 24 25 26 OPVAR, H2, DV, 0.1, 0.8 OPVAR, H3, DV, 0.1, 0.8 OPVAR, SMAX, SV, -100E6, 100E6 OPVAR, SMIN, SV, -100E6, 100E6 OPVAR, TVOLUME, OBJ,,, 0.0001 OPTYPE, SUBP OPANL, BEAM, TXT OPEXE OPLIST, ALL PLVAROPT, TVOLUME PLVAROPT, SMAX, SMIN PLVAROPT, H1, H2, H3

16. 16/33 14.3.3 ANSYS Procedure Analysis File (1/2) 01 02 03 04 05 06 07 08 09 10 11 12 13 14 /PREP7 ET, 1, PLANE42,,, 3 R, 1, 0.1 MP, EX, 1, 200E9 MP, NUXY, 1, 0.3 MP, DENS, 1, 7800 K, 1, 0, 0 K, 2, 1.5, 0 K, 3, 3.0, 0 K, 4, 0, -H1 K, 5, 1.5, -H2 K, 6, 3.0, -H3 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 L, 1, 2 L, 2, 3 L, 1, 4 L, 3, 6 SPLINE, 4, 5, 6,,,,,,, 1, 0, 0 A, 1, 2, 5, 4 A, 2, 3, 6, 5 ESIZE, 0.1 MSHAPE, 0, 2D MSHKEY, 1 AMESH, ALL EPLOT FINISH

17. 17/33 14.3.3 ANSYS Procedure Analysis File (2/2) 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 /SOLU NSEL, S, LOC, X, 0 D, ALL, ALL NSEL, S, LOC, X, 3 DSYM, SYMM, X NSEL, S, LOC, Y, 0 SF, ALL, PRES, 15000 NSEL, R, LOC, X, 3 F, ALL, FY, -50000 NSEL, ALL ACEL,, 9.81 SOLVE FINISH 48 49 50 51 52 53 54 55 56 57 /POST1 ETABLE, VOLUME, VOLU SSUM *GET,TVOLUME,SSUM,,ITEM,VOLUME ETABLE, STRESS, S, X ESORT, ETAB, STRESS *GET, SMAX, SORT,, MAX *GET, SMIN, SORT,, MIN FINISH

18. 18/33 14.3.3 ANSYS Procedure The Optimization Design 23 24 25 26 OPLIST, ALL PLVAROPT, TVOLUME PLVAROPT, SMAX, SMIN PLVAROPT, H1, H2, H3 (FEASIBLE) SMAX (SV) 0.94292E+08 SMIN (SV) -0.92123E+08 H1 (DV) 0.25608 H2 (DV) 0.10153 H3 (DV) 0.18085 TVOLUME (OBJ) 0.43822E-01

19. 19/33 14.3.3 ANSYS Procedure Optimization History 23 24 25 26 OPLIST, ALL PLVAROPT, TVOLUME PLVAROPT, SMAX, SMIN PLVAROPT, H1, H2, H3

20. 20/33 第 14.4 節 實例 : 三角平板之最佳設計 Example: Design of a Triangular Plate

21. 21/33 14.4.1 Problem Description 200 T1 40 30 o R = FIL INRAD 30 o Dimension: mm

22. 22/33 14.4.2 Modeling Consideration 1/6 model is used, due to the symmetry of the geometry and loading.

23. 23/33 14.4.3 ANSYS Procedure Optimization File (1/2) 01 02 03 04 05 06 07 08 09 10 11 12 13 14 15 16 17 18 19 FINISH /CLEAR /TITLE, Optimal Design of a hexagonal plate ! UNITS: N-mm-s T1 = 30 ! Thickness FIL = 10 ! Fillet radius /INPUT, TRIPLATE, TXT /OPT OPCLR OPANL, TRIPLATE, TXT OPVAR, T1, DV, 20, 40 ! DVs: Thickness OPVAR, FIL, DV, 5, 15 ! Fillet radius OPVAR, SMAX, SV,, 150 ! SV: Max equ. Stress OPVAR, VTOT, OBJ,,, 1 ! OBJ: Total volume

24. 24/33 14.4.3 ANSYS Procedure Optimization File (2/2) 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 OPKEEP, ON ! Save best design OPTYPE, SUBP OPEXE OPLIST, ALL PLVAROPT, T1, FIL PLVAROPT, SMAX PLVAROPT, VTOT FINISH ! Plot the best design /POST1 RESUME,, BDB FILE,, BRST SET PLNSOL, S, EQV

25. 25/33 14.4.3 ANSYS Procedure Analysis File (1/6) 01 02 03 04 05 06 07 08 09 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 /PREP7 *AFUN, DEG INRAD = 200*COS(30)-20 ! Inner radius CYL4,-200,0,INRAD,-30,INRAD+T1,30 CYL4,200*COS(60),200*SIN(60),INRAD,-90,INRAD+T1,-150 CYL4,200*COS(60),200*SIN(-60),INRAD,90,INRAD+T1,150 APLOT AADD, ALL ADELE, ALL ! Delete area, keep lines LPLOT ! Fillets on inner slot LSEL,, RADIUS,, INRAD+T1 ! Select inner arcs L1 = LSNEXT(0) L2 = LSNEXT(L1) L3 = LSNEXT(L2) LFILLET, L1, L2, FIL LFILLET, L2, L3, FIL LFILLET, L3, L1, FIL LSEL, ALL LPLOT

26. 26/33 14.4.3 ANSYS Procedure Analysis File (2/6) 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 ! Keep only symmetric portion WPROT,, 90 LSBW, ALL WPROT,,, 60 LSBW, ALL WPCSYS WPSTYLE CSYS, 1 LSEL, U, LOC, Y, 0, 60 LDELE, ALL,,, 1 LSEL, ALL KSLL KSEL, INVE KDELE, ALL ! Delete unnecessary keypoints KSEL, ALL LPLOT

27. 27/33 14.4.3 ANSYS Procedure Analysis File (3/6) 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 ! Create missing lines and combine right edge lines KSEL,, LOC, Y, 0 K1 = KPNEXT(0) K2 = KPNEXT(K1) LSTR, K1, K2 KSEL,, LOC, Y, 60 K1 = KPNEXT(0) K2 = KPNEXT(K1) LSTR, K1, K2 ALLSEL CSYS, 0 LSEL,, LOC, X, 100 LCOMB, ALL ALLSEL LPLOT

28. 28/33 14.4.3 ANSYS Procedure Analysis File (4/6) 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 ! Create the area AL, ALL APLOT ! MESHING ET, 1, PLANE82,,, 3 R, 1, 10 ! Thickness MP, EX, 1, 2.07E5 ! Young's modulus, MPa MP, NUXY, 1, 0.3 SMRTSIZE, 3 AMESH, ALL EPLOT FINISH

29. 29/33 14.4.3 ANSYS Procedure Analysis File (5/6) 80 81 82 83 84 85 86 87 88 89 90 91 92 /SOLU CSYS, 1 LSEL,, LOC, Y, 0 LSEL, A, LOC, Y, 60 DL, ALL,, SYMM ! Symmetry b.c. CSYS, 0 LSEL,, LOC, X, 100 SFL, ALL, PRES, -50 ! Pressure load (MPa) ALLSEL LPLOT SOLVE FINISH

30. 30/33 14.4.3 ANSYS Procedure Analysis File (6/6) 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 /POST1 PLNSOL, S, EQV /DSCALE,, OFF /EXPAND, 6, POLAR, HALF, 0, 60 /REPLOT ! Retrieve maximum equivalent stress and volume NSORT, S, EQV *GET, SMAX, SORT,, MAX ETABLE, EVOL, VOLU SSUM *GET, VTOT, SSUM,, ITEM, EVOL FINISH

31. 31/33 14.4.3 ANSYS Procedure The Optimum Design 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 OPKEEP, ON ! Save best design OPTYPE, SUBP OPEXE OPLIST, ALL PLVAROPT, T1, FIL PLVAROPT, SMAX PLVAROPT, VTOT FINISH ! Plot the best design /POST1 RESUME,, BDB FILE,, BRST SET PLNSOL, S, EQV

32. 32/33 14.4.3 ANSYS Procedure Optimization History 25 26 27 PLVAROPT, T1, FIL PLVAROPT, SMAX PLVAROPT, VTOT

33. 33/33 14.5 Other Optimization Tools Provided by ANSYS Single Iteration Design Tool Random Design Tool Gradient Tool Sweep Tool Factorial Tool