Crashworthiness Design using Topology Optimization

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


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)


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


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]


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


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


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


Traditional material parameterization:Static-elastic problems

Traditional material parameterization:Static-elastic problems

linear problems (perfectly elastic material)Density Approach


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


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


y

xz

Example problem: pole testExample problem: pole test

21 21 21 elements*

*~40 minutes/FEA (DYNA) evaluation


Static-elastic results (OptiStruct)Static-elastic results (OptiStruct)

Raw topology Interpreted topology

(40 iterations)


Dynamic-plastic results (HCA)Dynamic-plastic results (HCA)


(37 iterations)


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


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


Thank you


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


Case #1Case #1


Mf=0.3

No base angle (=0°), no top plate

(77 iterations)


Plastic strain distribution (case #1)Plastic strain distribution (case #1)


Case #2Case #2


Mf=0.3

base angle (=25°), no top plate

(26 iterations)


Case #2 – IED distributionCase #2 – IED distribution

Final topologyInitial design domain(x=0.3) (26 iterations)

Documents

Crashworthiness Design using Topology Optimization