2021 年 87 巻 896 号 p. 20-00412
This paper provides a vector-valued level set-based topology optimization method for multiple materials. The proposed method is characterized by a perfectly symmetric representation of multi-material by a vector valued level set function, which lowers the dependence of initial configuration in the optimization calculation. 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 the regularization parameter. First, a topology optimization problem is formulated based on the representation by the perfectly symmetric vector-valued level set function, and the method to regularize the optimization problem is generalized for multi-material topology optimization. Next, we construct an optimization algorithm in which the level set function is updated by the reaction-diffusion equation. Finally, two- and three-dimensional numerical examples are shown to confirm the validity and utility of the proposed topology optimization method.
