engleski

Variant of optimality criteria method for multiple state optimal design problems

In optimal design problems the goal is to find the best arrangement of given materials within the body which optimizes its properties with respect to some optimality criteria. We consider mixtures of two isotropic materials in context of stationary diffusion equation and deal with multiple state optimal design problems, where one can have several different regimes effecting on the observed body. The performance of the mixture is measured by an objective function which is an integral functional. It is well known that these problems do not admit classical solution, therefore we use relaxation by homogenization method. We rewrite optimality conditions for relaxed problem in order to apply optimality criteria method to multiple state problems in two and three dimensions. This problem was considered by Vrdoljak (2010), but optimality criteria method didn’t give con- verging sequence of designs for some energy minimization problems. We present another variant of optimality criteria method that can be applied to those problems as well.

optimal design, homogenization, optimality criteria method

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