Optimal topologies of structures: homogenization, pseudo‐elastic approximation and the bubble‐method

Abstract

Presents a pseudo‐elastic approach to topological optimization. In comparison with the well‐known homogenization method for topological optimization it is not based on a micro‐cellular structure, but approximates the elastic properties directly. A characteristic difficulty of these methods is the birth of new inner boundaries: thinning out the material can be interpreted as reducing the density of a composite micro‐structure, but eventually this process can result in a bubble with zero‐density. Therefore, the bubble‐method is a valuable asset to topological optimization, which helps to overcome this difficulty.