engleski

Variant of optimality criteria method for multiple state optimal design problems

In optimal design problems the goal is, for a given domain, two (or more) materials and its proportions, to nd rearrangement of these materials within the body that optimises its properties with respect to some optimality criteria. We consider mixtures of two isotropic materials in context of stationary di usion equation. 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 converging 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.

stationary diffusion equation, optimal design, optimality criteria method

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