1. red cedar TECHNOLOGY 1 Introduction to Automated Design Optimization ME 475

2. red cedar TECHNOLOGY 2 Analysis versus Design Analysis Given: system properties and loading conditions Find: responses of the system Design Given: loading conditions and targets for response Find: system properties that satisfy those targets ME 475

3. red cedar TECHNOLOGY 3 Design Complexity Design Time and Cost ME 475

4. red cedar TECHNOLOGY 4 Typical Design Process Initial Design Concept Specific Design Candidate Build Analysis Model(s) Execute the Analyses Design Requirements Met? Final Design Yes No Modify Design (Intuition) Time Money Intellectual Capital HEEDS $ ME 475

5. red cedar TECHNOLOGY 5 A General Optimization Solution Automotive Civil Infrastructure Biomedical Aerospace ME 475

6. red cedar TECHNOLOGY 6 Automated Design Optimization Create Parameterized Baseline Model Create HEEDS Design Model Execute HEEDS Optimization Plan Design Study Basic Procedure: ME 475

7. red cedar TECHNOLOGY 7 Automated Design Optimization Identify: Objective(s) Constraints Design Variables Analysis Methods Note: These definitions affect subsequent steps Create Parameterized Baseline Model Create HEEDS Design Model Execute HEEDS Optimization Plan Design Study ME 475

8. red cedar TECHNOLOGY Automated Design Optimization 8 Input File(s) Execute Solver(s) Output File(s) Validate Model Create CAD/CAE Models for a Representative Design Create Parameterized Baseline Model Create HEEDS Design Model Execute HEEDS Optimization Plan Design Study ME 475

9. red cedar TECHNOLOGY Automated Design Optimization 9 Define Input Files and Output Files Define Design Variables and Responses Define Objectives, Constraints, and Search Method Tag Variables in Input Files and Responses in Output Files Define Batch Execution Commands for Solvers Create Parameterized Baseline Model Create HEEDS Design Model Execute HEEDS Optimization Plan Design Study ME 475

10. red cedar TECHNOLOGY Automated Design Optimization Create Parameterized Baseline Model Create HEEDS Design Model Execute HEEDS Optimization Plan Design StudyModify Variables in Input File Execute Solver in Batch Mode Extract Results from Output File Optimized Design(s) Yes New Design (HEEDS) No Converged? ME 475

11. red cedar TECHNOLOGY CAE Portals “When” “What” “Where” ME 475

12. red cedar TECHNOLOGY 12 Tangible Benefits* Crash rails:100% increase in energy absorbed 20% reduction in mass Composite wing:80% increase in buckling load 15% increase in stiffness Bumper:20% reduction in mass with equivalent performance Coronary stent:50% reduction in strain * Percentages relative to best designs found by experienced engineers ME 475

13. red cedar TECHNOLOGY 13 Return on Investment Reduced Design Costs Time, labor, prototypes, tooling Reinvest savings in future innovation projects Reduced Warranty Costs Higher quality designs Greater customer satisfaction Increased Competitive Advantage Innovative designs Faster to market Savings on material, manufacturing, mass, etc. ME 475

14. red cedar TECHNOLOGY 14  Suggests material placement or layout based on load path efficiency  Maximizes stiffness  Conceptual design tool  Uses Abaqus Standard FEA solver Topology Optimization ME 475

15. red cedar TECHNOLOGY 15 When to Use Topology Optimization Early in the design cycle to find shape concepts To suggest regions for mass reduction ME 475

16. red cedar TECHNOLOGY 16 Design of Experiments Determine how variables affect the response of a particular design  Design sensitivities Build models relating the response to the variables  Surrogate models, response surface models B A ME 475

17. red cedar TECHNOLOGY 17 When to Use Design of Experiments Following optimization To identify parameters that cause greatest variation in your design ME 475

18. red cedar TECHNOLOGY 18 Parameter Optimization Minimize (or maximize):F(x 1,x 2,…,x n ) such that:G i (x 1,x 2,…,x n ) < 0, i=1,2,…,p H j (x 1,x 2,…,x n ) = 0, j=1,2,…,q where:(x 1,x 2,…,x n ) are the n design variables F(x 1,x 2,…,x n ) is the objective (performance) function G i (x 1,x 2,…,x n ) are the p inequality constraints H j (x 1,x 2,…,x n ) are the q equality constraints ME 475

19. red cedar TECHNOLOGY 19 Parameter Optimization Objective: Search the performance design landscape to find the highest peak or lowest valley within the feasible range Typically don’t know the nature of surface before search begins Search algorithm choice depends on type of design landscape Local searches may yield only incremental improvement Number of parameters may be large ME 475

20. red cedar TECHNOLOGY 20 Selecting an Optimization Method Design Space depends on: Number, type and range of variables and responses Objectives and constraints  Gradient-Based  Simplex  Simulated Annealing  Response Surface  Genetic Algorithm  Evolutionary Strategy  Etc. ME 475

21. red cedar TECHNOLOGY 21  Adaptive  Each “method” adapts itself to the design space  Master controller determines the contribution of each “method” to the search process  Efficiently learns about design space and effectively searches even very complicated spaces  Hybrid  Blend of “methods” used simultaneously, not sequentially  Aspects of evolutionary methods, simulated annealing, response surface methods, gradient methods, and more  Takes advantage of best attributes of each approach  Global and local search performed together SHERPA Search Algorithm  Both single and multi-objective capabilities ME 475

22. red cedar TECHNOLOGY 22 Find the cross-sectional shape of a cantilevered I-beam with a tip load (4 design vars) Design variables: H, h1, b1, b2 Objective: Minimize mass Constraints: Stress, Deflection SHERPA Benchmark Example ME 475

23. red cedar TECHNOLOGY 23 Effectiveness and Efficiency of Search (Goal = 1) Find the cross-sectional shape of a cantilevered I-beam with a tip load (4 design vars) SHERPA Benchmark Example ME 475

24. red cedar TECHNOLOGY 24 Advantages of SHERPA  Efficient  Requires fewer evaluations than other methods for many problems  Rapid set up – no tuning parameters  Solution the first time more often, instead of iterating to identify the best method or the best tuning parameters  Robust  Better solutions more often than other methods for broad classes of problems  Global and local optimization at the same time  Easy to Use  Only one parameter – number of allowable evaluations  Need not be an expert in optimization theory ME 475

25. red cedar TECHNOLOGY 25 Nonlinear Optimization Problems Usually involve nonlinear or transient analysis Gradients not accurate, not available, or expensive Multi-modal and or noisy design landscape Moderate to large CPU time per evaluation In other words, most engineering problems ME 475

26. red cedar TECHNOLOGY 26 Example: Hydroformed Lower Rail Crush zone ME 475

27. red cedar TECHNOLOGY 27 Shape Design Variables rigid wall lumped mass arrows indicate directions of offset crush zone x z y cross-section 67 design variables: 66 control points and one gage thickness ME 475

28. red cedar TECHNOLOGY 28 Optimization Statement Identify the rail shape and thickness Maximize energy absorbed in crush zone Subject to constraints on: Peak force Mass Manufacturability ME 475

29. red cedar TECHNOLOGY 29 Optimized Design ME 475

30. red cedar TECHNOLOGY 30 Validation ME 475

31. red cedar TECHNOLOGY 31 Lower Rail Benefits Compared to 6 month manual search: Peak force reduction by 30% Energy absorption increased by 100% Weight reduction by 20% Overall crash response resulted in equivalent of FIVE STAR rating ME 475

32. red cedar TECHNOLOGY 32 Side Impact Roof Crush Mass improvement in safety cage: 30 kg (about 23%) Future Gen Passenger Compartment ME 475

33. red cedar TECHNOLOGY 33 Magnetic Circuit 6.0 mm N N S S Displacement Rack Cover Magnets Hall-effect Device Holder Sensor – Magnetic Flux Linearity ME 475

34. red cedar TECHNOLOGY 34 Compared to previous best design found: Linearity of response ~ 7 times better Volume reduced by 50% Setup & solution time was 4 days, instead of 2-3 weeks Sensor – Magnetic Flux Linearity ME 475

35. red cedar TECHNOLOGY 35 Front Suspension Picture taken from MSC/ADAMS Manual ME 475

36. red cedar TECHNOLOGY 36 Problem Statement Determine the optimum location of the front suspension hard points to produce the desired bump steer and camber gain. ME 475

37. red cedar TECHNOLOGY 37 Results ME 475

38. red cedar TECHNOLOGY 38 Piston Design for a Diesel Engine Piston pin location is optimized to reduce piston slap in a diesel engine at 1100, 1500, 2000, and 2700 RPM Design Variables: –Piston Pin X location –Piston Pin Y location Design Objectives: –Minimize maximum piston impact with the wall –Minimize total piston impact with the wall throughout the engine cycle. ME 475

39. red cedar TECHNOLOGY 39 Piston Design for a Diesel Engine 110 designs were evaluated for each engine speed (440 runs of CASE) Total computational time was approximately 0.5 days using a 2.4 GHz processor. Optimized pin offset was essentially identical to what was found experimentally on the dynamometer. ME 475

40. red cedar TECHNOLOGY A biaxial stress state suitable for interrogating nonlinear anisotropic properties of membranous soft tissue can be realized using membrane inflation Orthotropic nonlinear elasticity: four material parameters Drexler et al., J. Biomech. 40 (2007), 812-819 Soft Tissue Membrane Inflation Courtesy of Jeffrey Bischoff, Zimmer Inc. ME 475

41. red cedar TECHNOLOGY Optimization Progression 0 50 100 150 Iteration R2 1.6 1.8 2.0 ME 475

42. red cedar TECHNOLOGY 42 Polymer Property Calibration Rate Sensitive Polymer: Neo-Hookean material model with a four-term Prony series Five undetermined coefficients (design variables) ME 475

43. red cedar TECHNOLOGY 43 LOADCASE 1 Expand the stent in the radial direction by 8.23226 mm. LOADCASE 2 Crimp the annealed stent by 2.0 mm. ANNEAL Stent Shape Optimization ME 475

44. red cedar TECHNOLOGY 44 Stent – Subsystem Design Model ME 475

45. red cedar TECHNOLOGY 45 BASELINE DESIGN ( Provided ) FINAL DESIGN ( Found by HEEDS ) Max. Strain = 3.3% Max. Strain = 0.99% Stent – Baseline and Final Designs ME 475

46. red cedar TECHNOLOGY 46 Example: Frame Torsional Stiffness Goal:Maximize torsional stiffness with no increase in mass ME 475

47. red cedar TECHNOLOGY 47 Loading and Optimization Statement Objective: Minimize deflection of unsupported corner Constraints: mass < baseline model max von mises stress < baseline model first 3 modal frequencies > baseline model ME 475

48. red cedar TECHNOLOGY 48 Design Variables 10 shape parameters:5 each for two cross members 7 thickness variables:3 each for two cross members 1 for the longitudinal rails ME 475

49. red cedar TECHNOLOGY 49 Design Results Torsional stiffness increased by 12% height of cross members increased cross member locations moved toward the ends connection plate thicknesses decreased cross member thicknesses increased thickness of the rails remained constant Baseline Design Optimized Design ME 475

50. red cedar TECHNOLOGY 50 Design of a Composite Wing Design variables: –Number of plies –Orientation of plies –Skin, spars, tip Objectives, Constraints: –Minimize mass –Buckling, stiffness, failure constraints Analysis Tool: –Abaqus ME 475

51. red cedar TECHNOLOGY 51 Failure Index Baseline HEEDS: 30% reduction in failure index ME 475

52. red cedar TECHNOLOGY 52 Deflection Baseline HEEDS: 15% reduction in deflection ME 475

53. red cedar TECHNOLOGY 53 Buckling Baseline HEEDS: 80% increase in buckling load ME 475

54. red cedar TECHNOLOGY 54 Design of a Composite Wing Buckling Load increased by 80% Failure index decreased by 30% Bending stiffness increased by 15% Mass increased by 6% ME 475

55. red cedar TECHNOLOGY 55 Rubber Bushing Parametric model: 6 parameters Fixed D1 D2 D4 D5 θ D3 ME 475

56. red cedar TECHNOLOGY 56 Rubber Bushing Target Response Displacement (mm) 10 mm F o r c e (N) Load deflection curve when the bushing is loaded to the left Load –deflection curve while the bushing is loaded to the right ME 475

57. red cedar TECHNOLOGY 57 Rubber Bushing Final Design Final design: ME 475

58. red cedar TECHNOLOGY 58 Rubber Bushing Response ME 475