Homogeneous optimum material based model for concurrent optimization of thermoelastic structures and materials

Abstract

This paper presents an optimization technique for structures composed of uniform cellular materials in macro scale. The optimization aims at to obtain optimal configurations of macro scale structures and microstructures of material under certain mechanical and thermal loads with specific base material volume. A concurrent topology optimization method is proposed for structures and materials to minimize compliance of thermoelastic structures. In this method macro and micro densities are introduced as the design variables for structure and material microstructure independently. Penalization approaches are adopted at both scales to ensure clear topologies, i.e. SIMP (Solid Isotropic Material Penalization) in micro-scale and PAMP (Porous Anisotropic Material Penalization) in macro-scale. Optimizations in two scales are integrated into one system with homogenization theory and the distribution of base material between two scales can be decided automatically by the optimization model. Microstructure of materials is assumed to be uniform at macro scale to reduce manufacturing cost. The proposed method and computational model are validated by some numerical experiments. The effects of temperature differential, volume of base material, numerical parameters on the optimal results are also discussed. At last, for cases in which both mechanical and thermal loads are applied, the configuration of cellular material can help to reduce the system compliance.