crashworthiness design using topology optimization
DESCRIPTION
Crashworthiness Design using Topology Optimization. University of Notre Dame Department of Aerospace and Mechanical Engineering Neal Patel 20 th Graduate Student Conference 19 October 2006. Outline. Problem description Topology optimization Hybrid Cellular Automaton (HCA) method - PowerPoint PPT PresentationTRANSCRIPT
Crashworthiness Design using Topology Optimization
Crashworthiness Design using Topology Optimization
University of Notre DameDepartment of Aerospace and Mechanical
Engineering
Neal Patel20th Graduate Student Conference
19 October 2006
19 October 2006 20th Graduate Student Conference 2/17
OutlineOutline
• Problem description
• Topology optimization
• Hybrid Cellular Automaton (HCA) method
• Material parameterization for nonlinear dynamic problems
• Example and results
19 October 2006 20th Graduate Student Conference 3/17
Vehicle crashworthiness designVehicle crashworthiness design
• Design of structures subject to crushing loads
• Typically the objective to design structures that maximize energy absorption while retaining stiffness
• Simulations of designs typically take hours to days to execute
• Usually optimized by sampling designs and building a meta model (approximated model)
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Topology optimizationTopology optimization
• Optimization process systematically eliminates and re-distributes material throughout the domain to obtain an optimal structure
• Uses the finite element method for structural analysis
• This research utilizes continuum-based topology optimization to generate designs – Cellular automata computing & control theory are used
to distribute material within a discretized design domain
F
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Material parameterization:Traditional elastic-based topology optimization
Material parameterization:Traditional elastic-based topology optimization
is mapped to the global stiffness in the
finite element model each iteration
Density Approach(isotropic)
Solid Isotropic Material w/Penalization (SIMP)
[Bendsøe, 1989]
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Commercial topology optimizationCommercial topology optimization
• Use elastic-static material assumptions
• Well-known schemes are gradient-based– Optimality Criteria (OC) methods– Method of Moving Asymptotes (MMA)– SLP/SQP
• Disadvantages of gradient-based optimizers– Can be time-consuming due to large number of design
variables (numerical finite-differencing)– Complex problems require approximations (analytical
expressions)
We developed the non-gradient HCA method
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Proposed hybrid cellular automaton (HCA) algorithm
Proposed hybrid cellular automaton (HCA) algorithm
Dynamic Analysis
noConvergence test|x(k+1) – x(k)|<
yes
Initial design
Update material distribution
using HCA ruleΔx = f(U,U*)
xk+1) = x(k)+Δx
U(x(k))
Final design
xk+1)
(k+1) = x(k+1)0
E(k+1) = x(k+1)E0
Eh(k+1) = x(k+1)Eh0
Y(k+1) = x(k+1) Y0
(0) = x(0)0 E(0) = x(0)E0
Eh(0) = x(0)Eh0
Y(0) = x(0) Y0
2/3
2/3
newly developed material model
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New HCA targetNew HCA target
• In traditional elastic-static problem, to design for stiffness, material is distributed based on the strain energy (Ue) generated during loading
• For non-conservative problems, we use internal energy (U) which includes both elastic strain energy and plastic work during loading
target (S) internal energy density
target (S) strain energy density
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Traditional material parameterization:Static-elastic problems
Traditional material parameterization:Static-elastic problems
linear problems (perfectly elastic material)Density Approach
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New material parameterization:Nonlinear dynamic problems
New material parameterization:Nonlinear dynamic problems
nonlinear problems (elastic-plastic)
piecewise linear model of the
stress-strain curve
E
Eh
Y
mapping density
to the mass matrix
dynamics problems
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Evolution of structure using HCAEvolution of structure using HCA
displacement ( )re
act
ion f
orc
e (
)
absorbed energy
localbehavior
globalbehavior
strain ( )
loading
unloading
recoverableenergy ( )
plastic work ( )
stre
ss
(
)
local
global
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y
xz
Example problem: pole testExample problem: pole test
21 21 21 elements*
*~40 minutes/FEA (DYNA) evaluation
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Static-elastic results (OptiStruct)Static-elastic results (OptiStruct)
Raw topology Interpreted topology
(40 iterations)
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Dynamic-plastic results (HCA)Dynamic-plastic results (HCA)
Raw topology Interpreted topology
(37 iterations)
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Comparison summaryComparison summary
pe
IED
OptiStruct topology TCO topology2,486,100 J
1,095,800 J
0.695
0.315
max IED=2,486,100 J max IED=1,095,800 J
max pe=0.659 max pe=0.315
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ConclusionsConclusions
• HCA is an efficient non-gradient methodology for generating concept designs for structures subject to collisions
• Demonstrates basic results for a simple problem
• Use of information from previous iterations leads to better convergence
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Thank you
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Honda knee bolster problemHonda knee bolster problem
55 mm
215 mm
125 mm
=25°
• Design domain composed of 36 x 21 x 9 brick elements
• Kneeform has a constant velocity of -833 mm/s
• Aluminum 6060-T6 material
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Case #1Case #1
Raw topology Interpreted topology
Mf=0.3
No base angle (=0°), no top plate
(77 iterations)
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Plastic strain distribution (case #1)Plastic strain distribution (case #1)
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Case #2Case #2
Raw topology Interpreted topology
Mf=0.3
base angle (=25°), no top plate
(26 iterations)
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Case #2 – IED distributionCase #2 – IED distribution
Final topologyInitial design domain(x=0.3) (26 iterations)