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Article

Design Optimization of Vehicle Structures for Crashworthiness Using Equivalent Mechanism Approximations

[+] Author and Article Information
Karim Hamza

Kazuhiro Saitou

Associate Professorkazu@umich.edu Department of Mechanical Engineering, University of Michigan, Ann Arbor, MI 48109-2125

J. Mech. Des 127(3), 485-492 (Jul 15, 2004) (8 pages) doi:10.1115/1.1862680 History: Received April 23, 2003; Revised July 15, 2004

A new method for crashworthiness optimization of vehicle structures is presented, where an early design exploration is done by the optimization of an “equivalent” mechanism approximating a vehicle structure. An equivalent mechanism is a network of rigid links with lumped mass connected by prismatic and revolute joints with nonlinear springs approximating aggregated behaviors of structural members. A number of finite element (FE) models of the thin-walled beams with typical cross sections and wall thicknesses are analyzed to build a surrogate model that maps a property of nonlinear spring to the corresponding FE model. Using the surrogate model, an equivalent mechanism is optimized for given design objectives by selecting the properties of the nonlinear springs among the values that can be realized by an FE model. After the optimization, the component FE models corresponding to the optimal spring properties are “assembled” into a FE model of an entire structure, which is further modified for final tuning. Two case studies of a vehicle front substructure are presented, which demonstrate the approach can help obtain a better design with far less computational resources than the direct optimization of a FE model.

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Copyright © 2005 by American Society of Mechanical Engineers
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Figure 1

(a) finite element, (b) lumped parameter, and (c) equivalent mechanism models of a vehicle substructure

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Figure 2

Crashworthiness optimization with equivalent mechanism (EM) models: (a) optimization of EM model with FE component database and (b) tuning of the obtained FE model by matching crush mode (CM) with the optimal EM

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Figure 3

Typical deformation resistance curves for (a) box section and (b) hat section

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Figure 7

Deformed shapes by FE models (left) and equivalent mechanism models (right) for (a) test 1, (b) test 2, and (c) test 3

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Figure 6

EM model of the main rail

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Figure 5

Finite element model of a vehicle mid rail

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Figure 4

EM nonlinear spring behavior and main curve parameters

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Figure 12

Summary of the results of case studies

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Figure 10

Vehicle midrail subject to frontal crash: (a) schematic layout, (b) design A exhibiting one crash mode, and (c) design B exhibiting a different crash mode

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Figure 9

Horizontal (x) location of passenger cabin (mass M2) by FE and EM models for (a) test 1, (b) test 2, and (c) test 3

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Figure 8

Horizontal (x) location of engine (mass M1) by FE and EM models for (a) test 1, (b) test 2, and (c) test 3

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Figure 11

Finite element model of a vehicle mid and lower rails

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