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Continuous approximation of material distribution for topology optimization

Continuous approximation of material distribution for topology optimization In this paper, we propose a checkerboard‐free topology optimization method without introducing any additional constraint parameter. This aim is accomplished by the introduction of finite element approximation for continuous material distribution in a fixed design domain. That is, the continuous distribution of microstructures, or equivalently design variables, is realized in the whole design domain in the context of the homogenization design method (HDM), by the discretization with finite element interpolations. By virtue of this continuous FE approximation of design variables, discontinuous distribution like checkerboard patterns disappear without any filtering schemes. We call this proposed method the method of continuous approximation of material distribution (CAMD) to emphasize the continuity imposed on the ‘material field’. Two representative numerical examples are presented to demonstrate the capability and the efficiency of the proposed approach against some classes of numerical instabilities. Copyright © 2004 John Wiley & Sons, Ltd. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png International Journal for Numerical Methods in Engineering Wiley

Continuous approximation of material distribution for topology optimization

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References (27)

Publisher
Wiley
Copyright
Copyright © 2004 John Wiley & Sons, Ltd.
ISSN
0029-5981
eISSN
1097-0207
DOI
10.1002/nme.945
Publisher site
See Article on Publisher Site

Abstract

In this paper, we propose a checkerboard‐free topology optimization method without introducing any additional constraint parameter. This aim is accomplished by the introduction of finite element approximation for continuous material distribution in a fixed design domain. That is, the continuous distribution of microstructures, or equivalently design variables, is realized in the whole design domain in the context of the homogenization design method (HDM), by the discretization with finite element interpolations. By virtue of this continuous FE approximation of design variables, discontinuous distribution like checkerboard patterns disappear without any filtering schemes. We call this proposed method the method of continuous approximation of material distribution (CAMD) to emphasize the continuity imposed on the ‘material field’. Two representative numerical examples are presented to demonstrate the capability and the efficiency of the proposed approach against some classes of numerical instabilities. Copyright © 2004 John Wiley & Sons, Ltd.

Journal

International Journal for Numerical Methods in EngineeringWiley

Published: Apr 14, 2004

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