Hierarchical Optimization of the Structure and the Material Used in its Manufacture

Abstract

This work addresses the problem of hierarchical topology optimization of structures and its applicability. Assuming that the structure is made of a locally periodic material, and based on the premises of topology optimization of structures, hierarchical topology optimization has the purpose of simultaneously optimize the lay-out of the structure and the material microstructure i.e. its characteristic unit cell. Here the problem is formulated as a structural compliance minimization (stiffness maximization) problem subjected, not only to a global volume upper bound constraint, but also to local material constraints that will guarantee appropriate features for fabrication or requirements in specific applications. The inclusion of (local) material microstructure constraints is critical if one seeks the identification of practical materials designs for instance in the design of bone substitutes (bone grafts). To demonstrate the model developed and its applicability, several examples ranging from structural engineering to biomechanical applications will be presented and discussed.