複数材料を用いた熱構造連成問題に対するトポロジー最適化

Abstract

Maximization of structural stiffness and thermal diffusivity is crucial in designs of mechanical products such as internal combustion engines that operate under extreme mechanical and thermal loads. However, meeting such requirements at a high level is difficult because current product design methods typically only deal with a single material. To further increase product performances, an optimal design method especially adapted for use with multi-materials is required. To this end, this paper presents a topology optimization method for a coupled thermal and structural problem incorporating two materials and a void phase. For the topology optimization method, we apply the Multi-Material Level Set (MM-LS) topology description model, which uses a total of n level set functions to represent n materials, plus the void phase. A reaction-diffusion equation is solved to update the distribution of the level set functions, which enables specification of the degree of geometric complexity of the optimal configuration. The proposed method is applied in several numerical examples to demonstrate its validity.