Abstract

This paper describes an optimization methodology giving simultaneously the optimal spatial material distribution and the optimal material orthotropy distribution in a two-dimensional space. The spatial material distribution is parametrized by a density variable that defines the presence or absence of material. A general orthotropic material is parametrized by the polar invariants of the elasticity tensor. The criterion is the compliance that measures the global structural stiffness. The numerical procedure iterates successively between local minimizations and finite element calculations. Thanks to the polar method, the local minimizations are solved explicitly providing analytical solutions. An optimization of a beam shows the effectiveness of the method in finding concurrently the optimal shape and the optimal material.

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Mathematical Subject Classification 2010

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