Optimal design with small contrast

Grégoire Allaire; Sergio Gutiérrez

doi:10.1007/1-4020-4752-5_14

Optimal design with small contrast

Grégoire Allaire, Sergio Gutiérrez

Ecole polytechnique

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

Abstract

This paper is concerned with optimal design problems where we assume that the coefficients in the state equation have small contrast. Making an asymptotic expansion up to second order with respect to the contrast greatly simplifies the optimization problem. By using the notion of H-measures we are able to prove general existence theorems for small amplitude optimal design and to provide simple and efficient numerical algorithms for their computation. A key feature of this type of problems is that optimal microstructures are always simple laminates.

Original language	English
Title of host publication	IUTAM Symposium on Topological Design Optimization of Structures, Machines and Materials
Subtitle of host publication	Status and Perspectives
Publisher	Springer Verlag
Pages	137-146
Number of pages	10
ISBN (Print)	1402047290, 9781402047299
DOIs	https://doi.org/10.1007/1-4020-4752-5_14
Publication status	Published - 1 Jan 2006
Event	IUTAM Symposium on Topological Design Optimization of Structures, Machines and Materials: Status and Perspectives - Rungstedgaard, Denmark Duration: 26 Oct 2005 → 29 Oct 2005

Publication series

Name	Solid Mechanics and its Applications
Volume	137
ISSN (Print)	1875-3507

Conference

Conference	IUTAM Symposium on Topological Design Optimization of Structures, Machines and Materials: Status and Perspectives
Country/Territory	Denmark
City	Rungstedgaard
Period	26/10/05 → 29/10/05

Keywords

H-measures
Homogenization
Optimal design

Access to Document

10.1007/1-4020-4752-5_14

Cite this

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title = "Optimal design with small contrast",

abstract = "This paper is concerned with optimal design problems where we assume that the coefficients in the state equation have small contrast. Making an asymptotic expansion up to second order with respect to the contrast greatly simplifies the optimization problem. By using the notion of H-measures we are able to prove general existence theorems for small amplitude optimal design and to provide simple and efficient numerical algorithms for their computation. A key feature of this type of problems is that optimal microstructures are always simple laminates.",

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Allaire, G & Gutiérrez, S 2006, Optimal design with small contrast. in IUTAM Symposium on Topological Design Optimization of Structures, Machines and Materials: Status and Perspectives. Solid Mechanics and its Applications, vol. 137, Springer Verlag, pp. 137-146, IUTAM Symposium on Topological Design Optimization of Structures, Machines and Materials: Status and Perspectives, Rungstedgaard, Denmark, 26/10/05. https://doi.org/10.1007/1-4020-4752-5_14

Optimal design with small contrast. / Allaire, Grégoire; Gutiérrez, Sergio.
IUTAM Symposium on Topological Design Optimization of Structures, Machines and Materials: Status and Perspectives. Springer Verlag, 2006. p. 137-146 (Solid Mechanics and its Applications; Vol. 137).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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Optimal design with small contrast

Abstract

Publication series

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Keywords

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