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Research Papers

Crashworthiness Design Using Topology Optimization

[+] Author and Article Information
Neal M. Patel1

Department of Aerospace and Mechanical Engineering, Design Automation Laboratory, University of Notre Dame, Notre Dame, IN 46556npatel@nd.edu

Byung-Soo Kang

Department of Aerospace and Mechanical Engineering, Design Automation Laboratory, University of Notre Dame, Notre Dame, IN 46556bkang1@nd.edu

John E. Renaud1

Department of Aerospace and Mechanical Engineering, Design Automation Laboratory, University of Notre Dame, Notre Dame, IN 46556jrenaud@nd.edu

Andrés Tovar

Department of Mechanical and Mechatronic Engineering, National University of Colombia, Bogotá, Colombiaatovarp@unal.edu.co

1

Corresponding authors.

J. Mech. Des 131(6), 061013 (May 21, 2009) (12 pages) doi:10.1115/1.3116256 History: Received April 10, 2008; Revised January 30, 2009; Published May 21, 2009

Crashworthiness design is an evolving discipline that combines vehicle crash simulation and design synthesis. The goal is to increase passenger safety subject to manufacturing cost constraints. The crashworthiness design process requires modeling of the complex interactions involved in a crash event. Current approaches utilize a parametrized optimization approach that requires response surface approximations of the design space. This is due to the expensive nature of numerical crash simulations and the high nonlinearity and noisiness in the design space. These methodologies usually require a significant effort to determine an initial design concept. In this paper, a heuristic approach to continuum-based topology optimization is developed for crashworthiness design. The methodology utilizes the cellular automata paradigm to generate three-dimensional design concepts. Furthermore, a constraint on maximum displacement is implemented to maintain a desired performance of the structures synthesized. Example design problems are used to demonstrate that the proposed methodology converges to a final topology in an efficient manner.

Copyright © 2009 by American Society of Mechanical Engineers
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References

Figures

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Figure 1

The stress-strain curve for inelastic material behavior: The area under the curve from the plastic strain during loading is energy dissipated during the plastic deformation. The area due to the elastic component of the strain is the absorbed energy that is recoverable.

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Figure 2

The load-displacement diagram. The area under the load-displacement curve represents energy absorption.

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Figure 3

An illustration of a piecewise linear approximation of the stress-strain curve for a given material. A bilinear model is shown in (a). The multilinear model, shown in (b), better approximates the strain-hardening behavior of the material.

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Figure 4

Typical 3D CA neighborhoods

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Figure 5

Illustration of the HCA method for synthesis of crashworthy designs

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Figure 6

The relationship between maximum displacement of a topology resulting from an impact and the mass of the topology. The topologies are generated for a problem similar to that shown in Fig. 1(v0=40 m/s).

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Figure 7

The initial design domain for Problem 1. The pole impacts the beam given an initial velocity (v0) of 10 m/s.

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Figure 8

The half-span of the final topology generated for the problem in Fig. 7. The actual topology is shown in (a). An interpretation of the topology is shown in (b). The full-span of the topology is shown in (c).

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Figure 9

The mean IED history of the topology synthesis for the structure generated in Problem 1

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Figure 10

The maximum deformation of the final topology during the impact event is 25.0 mm, shown in (a). The force-displacement plot of the dynamic event on the final topology is shown in (b).

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Figure 11

The initial design domain for Problem 2. The pole impacts the beam given an initial velocity of 10 m/s.

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Figure 12

The half-span of the final topology generated for the design problem illustrated in Fig. 1. The actual topology is shown in (a) and an interpretation is shown in (b). The full-span of the topology is shown in (c).

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Figure 13

The mean IED history of the topology synthesis for the structure generated in Problem 2

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Figure 14

The maximum deformation of the final topology during the impact event is 22.9 mm. The force-displacement plot of the dynamic event on the final topology.

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Figure 15

Design domain for the beam design problem. The beam is discretized into 80×20×20 cube elements. A rigid pole impacts the design domain at the midspan with an initial velocity v0=20 m/s. The structure is supported at the ends of the domain (in the yz-plane).

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Figure 16

The final topology generated for the problem in Fig. 7 using a mass constraint Mf=0.2 and no displacement constraint. The raw topology is shown in (a) and an interpretation is shown in (b).

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Figure 17

The evolution of the topology synthesis for the beam design problem with an initial mass distribution of xi(0)=1.0 and a maximum displacement constraint of dmax∗=40.1 mm. The final mass fraction of the structure is Mf=0.2.

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Figure 18

The evolution of the topology synthesis for the beam design problem with an initial mass distribution of xi(0)=0.25 and a maximum displacement constraint of dmax∗=40.1 mm. The final mass fraction of the structure is Mf=0.191.

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Figure 19

The (a) mass (in terms of Mf) and (b) maximum displacement (dmax) histories for the topology synthesis for the short beam design problem, starting from full densities (xi(0)=1.0) and intermediate densities (xi(0)=0.25)

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