Department of Civil & Environmental Engineering

Blast Mitigation Solutions via FEM-Based Design Optimization

Rajeev Jain

Funded by: US Army Research Office

Research Team: ASU, PSU

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Presentation Outline

Background

Literature Survey

FE Model

Design Optimization

Final Results

Compute Time Reduction

Future Work and Conclusions

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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.

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Presentation Outline

Background

Literature Survey

FE Model

Design Optimization

Final Results

Compute Time Reduction

Future Work and Conclusions

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Literature Review

Zhu et al, 2009Rathbun et al, 2008

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Literature Review

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Presentation Outline

Background

Literature Survey

FE Model

Design Optimization

Final Results

Compute Time Reduction

Future Work and Conclusions

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FE Model

Finite element model was able to mimic the experimental ARO results

Blast Side

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Flat Panel Response

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Convergence Study

• Simulation time varied between 10 min to 35 min• 16x16x4 mesh chosen for this study• Relative displacement at the first peak is monitored

Displacement w read from nodout file Plastic Strain e read from elout file

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Sandwich Panels

(a)

3.464a

2a2t2t

t

t t

t

(b)

Unit Cell Models

(c)

• Compression Test Validation• ‘Hexcel’ Website Data• Regression Model for a,t and h

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Sandwich Panel Response

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Presentation Outline

Background

Literature Survey

FE Model

Design Optimization

Final Results

Compute Time Reduction

Future Work and Conclusions

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Optimization Problem FormulationFind 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)

22

1 1

n n

relative fixturei i

RMS

w w ww

n n

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Geometric Constraint

Small Envelope Large Envelope

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Shape Optimization Technique

1

G q G( )k

ioriginal i

i

x x

+ =ix

Galileo GalileiBook – ‘Dialogues Concerning Two New Sciences’

Belegundu and Rajan, 1988

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Program Flow and Code

Preliminary operations

for optimization

Generate new population

(initial pop : randomSubsequent pop : DE

strategy)

Run LS-DYNA.

Objective function and

constraint calculation

Best member selection

Gener-ation

Limit?

No

Write results to output file

Visualize the optimal shape

Yes

Generate Velocity field

according to the setup FE model

Generated offline using a matlab code• Reading FE model to store all the nodal data• Reading velocity field data from the design file• Bounds on design variables, plastic strain limits• Input related to optimizer

• LS-DYNA is run only if mesh is not distorted• Objective function • ‘nodout’- ASCII file from DYNA

• Constraint evaluation• ‘elout’ – elemental data

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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

sin( , ) sin n yL L

m xf m n C

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Sin 9-DV• (m = n = 2)• q1 f (1,1), q2 f (1,2), q3 f (2,1), q4 f (2,2)

f (2,2) basis shape f (2,1) 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 !!

Cubic Bezier (9-DV)

,1 1

( ) ( ) ( )n m

n mi j i j

i j

f P B u B v P

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

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Local Point Load (LPL 11-DV)2

1 13

1

1

2

1 coth coth coth

sinh sinh sinh sinh

sinh

m m m mm m

m

m m

m

Pa y yw

D b b b b

y m m xb b a a

m

Schematic diagram of a rectangular plate

Timoshenko and Gere, 1961

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Sinusoidal Sandwich (Sandwich Sin 5-DV)

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

Bottom face plate thickness design variable

Sandwich thickness design variable

Bottom face plate sinusoidal shape design variable

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DO Problem Formulation

( )G x

rw )(x

Find

Minimize subject to εj ≤ 0.15 for 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)

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Presentation Outline

Background

Literature Survey

FE Model

Design Optimization

Final Results

Compute Time Reduction

Future Work and Conclusions

Large Envelope – Final Shapes

Sin 3-DV Sin 9-DV

CB LPL

Sandwich

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Large Envelope ResultsProperty Baseline Sin 3-DV Sin 9-DV CB LPL Sandwich

Total mass of structure (kg) 1872.2 1894.7 1866.5 1892.1 1894.5 1852.0Max. relative displacement (mm) occurs at 1st peak

58.43 7.32 4.36 3.56 8.35 7.2

% improvement in max. relative displacement over baseline design

87.4 92.5 93.9 85.7 87.6

Objective = RMS displacement, mm

20.51 4.33 2.101 1.89 4.57 3.32

% improvement in objective function over baseline design

78.8 89.7 90.8 77.7 83.8

Max. plastic strain 0.127 0.019 0.054 0.067 0.02 0.146% improvement in max. plastic strain over baseline design

85.1 57.4 47.2 84.2 -14.9

Total Z-momentum (kN-sec) 6.25 5.29 4.87 4.95 5.30 5.61% improvement total z-momentum over baseline design

15.3 22.1 20.8 17.9 10.2

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Smearing of Plastic Strain

Baseline design Optimized design LE case

Maximum at the center

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Final Shapes Small Envelope

Sin 3-DV Sin 9-DV

CB LPL

A unanimous double bulge

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Small Envelope ResultsProperty Baseline Sin 3-DV Sin 9-DV CB LPL

Total mass of structure (kg) 1872.2 1894.5 1895.5 1893.9 1895.3

Max. relative displacement (mm) occurs at 1st peak

58.43 7.67 8.07 7.59 8.35

Objective = RMS displacement, mm 20.51 4.48 4.48 3.89 4.49

Max. plastic strain 0.127 0.020 0.023 0.025 0.023

Total Z-momentum (kN-sec) 6.25 5.41 5.31 5.58 5.42

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Comparison VSE and SE

Final shapes using 3-DV Sin SE and VSE case

Special case – Very Small Envelope (VSE)Property Baseline 3-DV SE 3-DV VSE

Total mass of structure (kg) 1872.2 1895.5 1893.1

Max. relative displacement (mm) occurs at 1st peak

58.43 7.67 11.08

% improvement in max. relative displacement over baseline design

86.8 81.1

Objective = RMS displacement, mm 20.51 4.48 5.69

% improvement in objective function over baseline design

78.1 72.2

Max. plastic strain 0.127 0.020 0.026

% improvement in max. plastic strain over baseline design

84.25 79.5

Total Z-momentum (kN-sec) 6.25 5.41 5.45

% improvement in Z-momentum over baseline design

13.4 12.8

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Final Shape – Sin 3-DV Spring Model

3-DV LE

3-DV SE Baseline

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

Property Baseline 3DV SE

3DVLE

Total mass of structure (kg) 152.9 147.01 149.87Max. relative displacement, 86.2 31.3 28.2

% improvement in max. relative displacement over

baseline design

61.1 67.3

Objective = RMS displacement, mm

46.8 23.1 21.8

% improvement in objective function over baseline design

50.1 53.4

Max. plastic strain 0.055 0.126 0.149% improvement in max. plastic

strain over baseline design-129 -171

Total Z-momentum (kN-sec) 4.93 3.7 3.6% improvement in Z-

momentum over baseline design

24.9 27.0

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Sensitivity Analysis (SA)

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SA - Results

Model Baseline flat

Baseline opt.

Run1 flat

Run1 opt.

Run2 flat

Run2 opt.

Run3 flat

Run3 opt.

Run4 flat

Run4 opt.

Max. relative displ., (mm) occurs at 1st

peak58.43 7.67 47.5 35.7 63.7 66.5 52.9 21.7 40.2 42.1

Objective = RMS displ.,

mm20.51 4.48 26.5 24.5 44.1 44.5 18.8 13.6 25.9 24.9

Max. plastic strain 0.127 0.020 0.076 0.026 0.040 0.023 0.092 0.036 0.058 0.052

Total Z-momentum

(kN-sec)6.25 5.41 6.13 5.57 5.27 5.57 6.21 5.51 6.00 5.64

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Presentation Outline

Background

Literature Survey

FE Model

Design Optimization

Final Results

Compute Time Reduction

Future Work and Conclusions

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Compute Time Reduction

1. Separate optimization problem for bounds of shape design variables.

2. DE ideally suited for parallel implementation, Coarse grained parallelization has been implemented

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LU Bounds of Shape Design Variables

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

Optimization Formulation

Find: LU Bounds of Shape Design Variables

Maximize: Envelope available

Subject to:

1. No mesh distortion2. Envelope constraints being satisfied

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Parallel Execution of FE Analysis

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Parallelization

Typical scenario with SATR approach

Typical scenario with LB Scheme

Load Balancing (LB) ApproachSend All Then Receive (SATR) Approach

Speedup = 16/6 = 2.67 > 1.78

Speedup = 16/9 = 1.78

Typical Example using 4 processors and 8 population

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LB approach- Iteration time of each processor

3DV Sin Case # No. of processors = 4

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Speedup comparison

Population = 3Iterations = 10

Population = 100Iterations = 30

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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

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LBHP

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Presentation Outline

Background

Literature Survey

FE Model

Design Optimization

Final Results

Compute Time Reduction

Future Work and Conclusions

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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

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Future Work

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

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Thank you

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