マルチマテリアル構造の固有振動数の最大化を目的とするトポロジー最適化

抄録

A multi-material structure that is composed of several different material properties is promising for achieving an ideal functionality that can outperform a single material structure. In particular, increasing the value of the fundamental eigenfrequency is important because it can increase dynamic stability. Since the beginning, Topology optimization (TO) to maximize the fundamental eigenfrequency of a single-material structure has been investigated. However, there are few research papers on multi-material topology optimization (MMTO) for the eigenfrequency maximization problem thus far. Therefore, we propose a novel framework for the MMTO of the eigenfrequency problem. From a theoretical standpoint, two key features are addressed: (i) multi-material level set (MMLS) method is developed. In this method, interfaces between different material phases are represented by iso-surfaces of multiple level set functions. Hence, the optimal solutions have a 1/0 binary structure and are free from greyscale elements; (ii) The proposed design methodology uses a reaction-diffusion equation (RDE) to update the level-set functions based on the topological derivative, allowing new holes to form during the optimization process. The effectiveness of our methodology is demonstrated by benchmark test cases.