1111 新しい境界追跡型レベルセットトポロジー最適化法の構築

Abstract

This paper proposes a new level-set based topology optimization method incorporating a boundary tracking mesh generation method and non-linear programming. Since the mesh generation method provides a mesh conforming to the structural boundary at every optimization iteration, grayscale elements are completely eliminated during optimization. On the other hand, non-linear programming is widely used for efficiently updating the design variables in conventional topology optimization techniques such as homogenization and density based topology optimization. By incorporating these methods, we configure a new topology optimization method for virtually realizing completely grayscale-free, efficient topology optimization. In this paper, we first develop the mathematical formulation for obtaining sensitivity information on level-set based topology optimization problems and then implement a boundary tracking type level-set topology optimization method with the sequential linear programming (SLP) for designing compliant mechanisms. Further, we apply it to a numerical example for confirming the advantages of the proposed method and framework. Even with SLP, which is a most simple scheme of non-linear programming, the result demonstrate the relevance and promise of the proposed framework as a new class of grayscale-free topology optimization.