固有振動問題を対象としたマルチマテリアルトポロジー最適化

Multi-material structures consisting of several different material properties are promising for achieving ideal functionality over single-material structures. In particular, increasing the value of the fundamental eigenfrequency is important because it can enhance dynamic stability. Since the beginning, topology optimization (TO) for maximization of the fundamental eigenfrequencies of single-material structures has been studied. However, there have been few research papers on multi-material topology optimization (MMTO) for eigenfrequency maximization problems. Therefore, we propose a new framework for MMTO of eigenfrequency problems. In the proposed method, a multi-material level set (MMLS) method is developed, which represents the interfaces between different material phases by isosurfaces of multiple level set functions. The proposed design methodology uses the reaction-diffusion equation (RDE) to update the level set functions based on topological derivatives, allowing the nucleation of new holes during the optimization process. In addition, the eigenfrequency analysis with ersatz material and that without ersatz material using body-fitted mesh are compared and discussed.