2505 双曲線正接関数を用いたレベルセット法に基づく形状最適化(設計と最適化V)

Abstract

The aim of this research is to construct a structural optimization method based on a level set method, the so-called convected level set method. The basic idea of this method is that the level set function is defined as a truncated smooth function obtained using a sinus filter based on a hyperbolic tangent function. The local property of the hyperbolic tangent level set function stabilizes the computation of the advection equation used for evolving the level set function and reduces the computational cost of the reinitialization that maintains the profile of the level set function. Additionally, the low computational cost characteristic enables the use of convective reinitialization, whose basic idea is that the reinitialization is incorporated in the advection equation, avoiding the need for a separate computation. Consequently, the convected level set method can avoid the need for additional computations when conducting reinitialization. The validity of our proposed method is tested with standard structural optimization problems.