1. Blast Mitigation Solutions via FEM-Based Design Optimization Rajeev Jain Funded by: US Army Research Office Research Team: ASU, PSU

2. Presentation Outline Background Literature Survey FE Model Design Optimization Final Results Compute Time Reduction Future Work and Conclusions

3. Background The IED detonated directly under the vehicle; however, the blast was pushed outward instead of directly straight up due to the vehicle's “V” –shaped undercarriage.

4. Presentation Outline Background Literature Survey FE Model Design Optimization Final Results Compute Time Reduction Future Work and Conclusions

5. Literature Review Zhu et al, 2009 Rathbun et al, 2008

6. Literature Review

7. Presentation Outline Background Literature Survey FE Model Design Optimization Final Results Compute Time Reduction Future Work and Conclusions

8. FE Model Blast Side Finite element model was able to mimic the experimental ARO results

9. Flat Panel Response

11. 16x16x4 mesh chosen for this study

13. ‘Hexcel’ Website Data

15. Presentation Outline Background Literature Survey FE Model Design Optimization Final Results Compute Time Reduction Future Work and Conclusions

16. Optimization Problem Formulation Find G(x) minimize subject to εj≤ εmax for each element j M ≤ Mmax t tmin xLx xU det Jj(x) ≥ 0 for each element j zLz zU (geometric envelope)

17. Geometric Constraint Small Envelope Large Envelope

18. Shape Optimization Technique Galileo Galilei Book – ‘Dialogues Concerning Two New Sciences’ Belegundu and Rajan, 1988 + =

20. Reading velocity field data from the design file

21. Bounds on design variables, plastic strain limits

22. Input related to optimizer

23. LS-DYNA is run only if mesh is not distorted

24. Objective function

25. ‘nodout’- ASCII file from DYNA

26. Constraint evaluation

27. ‘elout’ – elemental data No Gener-ation Limit? Write results to output file Visualize the optimal shape Yes Best member selection

28. Sin 3-DV – Symmetric Basis Shapes m = n = 1 q1 f (1,1) top surface, q2 f (1,1) bottom surface q3  thickness basis shape Shape change obtained using only 1st basis shape Shape change obtained using only 2nd basis shape Shape change obtained using only 3rd basis shape

29. Sin 9-DV (m = n = 2) q1 f (1,1), q2 f (1,2), q3 f (2,1), q4 f (2,2) f (2,1) basis shape f (2,2) basis shape For a population size of 90 and 45 generation assuming an average simulation time of 10 min Total compute time = 90x45x10 ~ 29 days !!

30. Cubic Bezier (9-DV) Cubic Bezier Patch Control Point Displaced 3D Implementation of Cubic Bezier 4 design for top surface + 4 design variables for bottom surface + 1 thickness design variable = 9-DV

31. Local Point Load (LPL 11-DV) Timoshenko and Gere, 1961 Schematic diagram of a rectangular plate

32. Sinusoidal Sandwich (Sandwich Sin 5-DV) Bottom face plate thickness design variable Sandwich thickness design variable Bottom face plate sinusoidal shape design variable 3 Thickness design variable for top face plate, sandwich and bottom face plate + 2 sinusoidal shape design variable for top and bottom face plate = 5-DV

33. DO Problem Formulation Find Minimize subject to εj≤ 0.15for each element j M ≤ 1890 kg t 0.005 m xL  x  xU det Jj(x) ≥ 0 for each element j zL z  zU (geometric envelope)

34. Presentation Outline Background Literature Survey FE Model Design Optimization Final Results Compute Time Reduction Future Work and Conclusions

35. Large Envelope – Final Shapes Sin 9-DV Sin 3-DV LPL CB Sandwich

36. Large Envelope Results

37. Smearing of Plastic Strain Optimized design LE case Baselinedesign Maximum at the center

38. Final Shapes Small Envelope Sin 9-DV Sin 3-DV CB LPL A unanimous double bulge

39. Small Envelope Results

40. Comparison VSE and SE Final shapes using 3-DV Sin SE and VSE case

41. Special case – Very Small Envelope (VSE)

42. Final Shape – Sin 3-DV Spring Model 3-DV SE Baseline 3-DV LE

43. Result for Plate Supported on Springs Allowable mass for this problem is set to 155 kg Sin 3-DV velocity fields are used for shape change

44. Sensitivity Analysis (SA)

45. SA - Results

46. Presentation Outline Background Literature Survey FE Model Design Optimization Final Results Compute Time Reduction Future Work and Conclusions

47. Compute Time Reduction Separate optimization problem for bounds of shape design variables. DE ideally suited for parallel implementation, Coarse grained parallelization has been implemented

48. LU Bounds of Shape Design Variables Optimization Formulation Find: LU Bounds of Shape Design Variables Maximize: Envelope available Subject to: 1. No mesh distortion 2. Envelope constraints being satisfied For a typical 9-DV problem 1. Using random design variable Total compute time = 72 hrs 2. Using optimized bounds Total compute time is 56 hrs and a better optimal design

49. Parallel Execution of FE Analysis

50. Parallelization Typical Example using 4 processors and 8 population Send All Then Receive (SATR) Approach Load Balancing (LB) Approach Typical scenario with LB Scheme Speedup = 16/6 = 2.67 > 1.78 Typical scenario with SATR approach Speedup = 16/9 = 1.78

51. LB approach- Iteration time of each processor 3DV Sin Case # No. of processors = 4

52. Speedup comparison Population = 3 Iterations = 10 Population = 100 Iterations = 30

53. Load Balancing Higher Population (LBHP) Population More trial vectors are generated Better utilization of idle time predicted. This new member is checked and replaced if inferior members are found in the population

54. LBHP

55. Presentation Outline Background Literature Survey FE Model Design Optimization Final Results Compute Time Reduction Future Work and Conclusions

56. Conclusions A generic FEM based optimization technique Huge improvement over baseline flat plate Developed different shape optimization schemes Sandwich panel design optimization Sequential and parallel implementation with significant speedup

57. Future Work New materials (composites?) Local shape change and automatic meshing Different blast loading conditions Multi-objective optimization formulation

58. Thank you Suggestions'? …… Questions?