パラメータ曲面のレベルセットに基づく新しいトポロジー最適化とその応用

抄録

In this paper, we review an implementation of topology optimisation method based on the level-set method and present its applications. The topology optimisation presented here follows Amstutz’ method which evolves the level-set function by the spherical linear interpolation of the topological derivative and the level-set function itself. In our implementation, the level-set function is discretised in space by a parametric surface such as B- and T-splines, which enables us to represent shapes with smooth boundaries with a few design variables. Moreover, this allows us to control the geometric complexity of the shape by adjusting the number of control points on the parameter surface. In addition to the basic benchmark problem of finding the optimal shape of a linear elastic body that minimizes the work by a given external force work, applications to the optimal design of optical cloaking devices, acoustic lenses, etc are presented.