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Optimal design in small amplitude homogenization

Published online by Cambridge University Press:  02 August 2007

Grégoire Allaire  and
Sergio Gutiérrez
Grégoire Allaire
Affiliation:
Centre de Mathématiques Appliquées (UMR 7641), École Polytechnique, 91128 Palaiseau, France. gregoire.allaire@polytechnique.fr
Sergio Gutiérrez
Affiliation:
Centre de Mathématiques Appliquées (UMR 7641), École Polytechnique, 91128 Palaiseau, France. gregoire.allaire@polytechnique.fr : Departamento de Ingeniería Estructural y Geotécnica, Pontificia Universidad Católica de Chile, Santiago Chile, Chile. sgutierr@ing.puc.cl
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Abstract

This paper is concerned with optimal design problems with aspecial assumption on the coefficients of the state equation.Namely we assume that the variations of these coefficientshave a small amplitude. Then, making an asymptotic expansionup to second order with respect to the aspect ratio of thecoefficients allows us to greatly simplify the optimal designproblem. By using the notion of H-measures we are able toprove general existence theorems for small amplitudeoptimal design and to provide simple and efficient numericalalgorithms for their computation. A key feature of thistype of problems is that the optimal microstructures arealways simple laminates.

Keywords

Optimal designH-measureshomogenization.
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 41 , Issue 3 , May 2007 , pp. 543 - 574
Copyright
© EDP Sciences, SMAI, 2007

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