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Generating optimal topologies in structural design using a homogenization method. (English) Zbl 0671.73065
Summary: Optimal shape design of structural elements based on boundary variations results in final designs that are topologically equivalent to the initial choice of design, and general, stable computational schemes for this approach often require some kind of remeshing of the finite element approximation of the analysis problem. This paper presents a methodology for optimal shape design where both these drawbacks can be avoided. The method is related to modern production techniques and consists of computing the optimal distribution in space of an anisotropic material that is constructed by introducing an infimum of periodically distributed small holes in a given homogeneous, isotropic material, with the requirement that the resulting structure can carry the given loads as well as satisfy other design requirements. The computation of effective material properties for the anisotropic material is carried out using the method of homogenization. Computational results are presented and compared with results obtained by boundary variations.

MSC:
74P99 Optimization problems in solid mechanics
74E05 Inhomogeneity in solid mechanics
65K10 Numerical optimization and variational techniques
74E30 Composite and mixture properties
49M99 Numerical methods in optimal control
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