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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
Department of Civil & Environmental Engineering
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.
Department of Civil & Environmental Engineering
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
Department of Civil & Environmental Engineering
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
Suggestions'? …… Questions?