Topology optimization of non-linear elastic structures and compliant mechanisms

Abstract

A linear elastic response is assumed in most structural topology optimization problems. While this assumption is valid for a wide variety of problems, it is not valid for structures undergoing large displacements. The elastic structural analysis used here accommodates geometric and material non-linearities. The material density field is filtered to enforce a length scale on the field variation and is penalized to remove less effective intermediate densities. The filtering scheme is embedded in the structural analysis to resolve the non-existent solution to the solid-void topology problem. In this way, we know precisely what optimization problem is being solved. The structural topology optimization formulation is also used to design compliant mechanisms.