Journal
ESAIM-MATHEMATICAL MODELLING AND NUMERICAL ANALYSIS-MODELISATION MATHEMATIQUE ET ANALYSE NUMERIQUE
Volume 41, Issue 3, Pages 543-574Publisher
EDP SCIENCES S A
DOI: 10.1051/m2an:2007026
Keywords
optimal design; H-measures; homogenization
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This paper is concerned with optimal design problems with a special assumption on the coefficients of the state equation. Namely we assume that the variations of these coefficients have a small amplitude. Then, making an asymptotic expansion up to second order with respect to the aspect ratio of the coefficients allows us to greatly simplify the optimal design 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 the optimal microstructures are always simple laminates.
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