Multidomain Topology Optimization for Structural and Material Designs

[+] Author and Article Information
Zheng-Dong Ma

Department of Mechanical Engineering,  University of Michigan, 2250 G. G. Brown Building, Ann Arbor, MI 48109-2125mazd@umich.edu

Noboru Kikuchi

Department of Mechanical Engineering,  University of Michigan, 2250 G. G. Brown Building, Ann Arbor, MI 48109-2125kikuchi@umich.edu

Christophe Pierre

 U.S. Army Tank-Automotive and Armaments Command, Warren, MI 48347-5000pierre@umich.edu

Basavaraju Raju

 U.S. Army Tank-Automotive and Armaments Command, Warren, MI 48347-5000

J. Appl. Mech 73(4), 565-573 (Oct 05, 2005) (9 pages) doi:10.1115/1.2164511 History: Received June 02, 2004; Revised October 05, 2005

A multidomain topology optimization technique (MDTO) is developed, which extends the standard topology optimization method to the realm of more realistic engineering design problems. The new technique enables the effective design of a complex engineering structure by allowing the designer to control the material distribution among the subdomains during the optimal design process, to use multiple materials or composite materials in the various subdomains of the structure, and to follow a desired pattern or tendency for the material distribution. A new algorithm of Sequential Approximate Optimization (SAO) is proposed for the multidomain topology optimization, which is an enhancement and a generalization of previous SAO algorithms (including Optimality Criteria and Convex Linearization methods, etc.). An advanced substructuring method using quasi-static modes is also introduced to condense the nodal variables associated with the multidomain topology optimization problem, especially for the nondesign subdomains. The effectiveness of the new MDTO approach is demonstrated for various design problems, including one of “structure-fixture simultaneous design,” one of “functionally graded material design,” and one of “crush energy management.” These case studies demonstrate the potential significance of the new capability developed for a wide range of engineering design problems.

Copyright © 2006 by American Society of Mechanical Engineers
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Figure 1

Basic concept of the homogenization-based topology optimization method

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Figure 2

A multidomain topology optimization problem

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Figure 3

A structure-fixture simultaneous design problem

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Figure 4

Design 1 (7:7): optimized eigenfrequency=4.37

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Figure 5

Design 2 (11:3): optimized eigenfrequency=5.01

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Figure 6

Example FGM with a top layer made of stiff tiles, four supporting layers with graded densities, and a soft skin. The graded densities for the four supporting layers are, from the top layer to the bottom layer, 45%, 36%, 27%, and 18%, respectively.

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Figure 7

Optimal design for the FGM example: (a) optimum layout; (b) finalized design

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Figure 8

Design problem for crush energy management

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Figure 9

Optimized design for the crush energy management problem; (a) optimum layout; (b) finalized design

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Figure 10

Virtual crash test of the prototype: deformed structure is shown at (a) t=0.01s, (b) t=0.02s, (c) t=0.04s. (a) Snapshot 1: first buckling occurs in Design Domain 4 (t=0.01s). (b) Snapshot 2: second buckling occurs in Design Domain 2 (t=0.02s). (c) Snapshot 3: third buckling occurs in Design Domain 3 (t=0.04s)

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Figure 11

Virtual crash test of a homogenous beam without holes

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Figure 12

Comparison of crash forces for the optimized design and the nominal design




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