Engineering

Ecology

Network topology

Biology

Applied mathematics

Operating system

Computer science

Mathematical optimization

Homogenization (climate)

Finite element method

Mathematics

Topology optimization

Combinatorics

Structural engineering

Topology (electrical circuits)

Biodiversity

Computer Methods in Applied Mechanics and Engineering

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, i~otropic 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.

Generating optimal topologies in structural design using a homogenization method