材料規定の完全等方性を実現する複数材料に対するレベルセット法に基づくトポロジー最適化

抄録

This paper provides a perfectly isotropic level set based topology optimization method for multiple materials. The problem that the multi material optimal configuration depends on how the parameters are given, due to the asymmetric material representation, is fundamentally solved. Also this paper implements the method to adjust the geometrical complexity of optimal configurations with regularization parameter. First, a topology optimization problem is formulated based on the representation by the vector-valued level set function, and the method of regularizing the optimization problem is generalized for multi-material topology optimization. Next, an optimization algorithm is introduced, and a generalized topological derivertive with regularization and constraints is derived. Finally, an example of design optimization is shown to confirm the validity and utility of the proposed topology optimization method.