Pontificia Universidad Católica de Chile Pontificia Universidad Católica de Chile
Allaire G. and Gutiérrez S. (2007)

Optimal design in small amplitude homogenization. http://dx.doi.org/10.1051/m2an:2007026

Revista : Esaim-Mathematical Modelling and Numerical Analysis-Modelisation Mathematique et Analyse Numerique
Volumen : 41
Número : 3
Páginas : 543-574
Tipo de publicación : ISI Ir a publicación


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.