Tyler E. Bruns

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.

TOPOLOGY OPTIMIZATION OF GEOMETRICALLY NONLINEAR STRUCTURES AND COMPLIANT MECHANISMS

Topology optimization of structures has become an area of rapidly increasing interest to researchers during the past decade. Most structural topology optimization problems assume a linear elastic response. This assumption is not valid for systems undergoing large deformation. The structural analysis here accommodates geometric and material nonlinearities, and its impact on the topology optimization is investigated. A well-posed regularized topology optimization problem is developed by introducing a Gaussian-weigh ted density measure. Topology results based on the linear and nonlinear elastic formulations are compared. The formulation of the structural design problem is then extended to design compliant mechanisms undergoing large displacements.