On the treatment of volume constraints in topology optimization by level-set method

Abstract

Among topological optimization methods, Amstutz's method based on spherical linear interpolation of level set functions and topological derivatives is an excellent method with guaranteed convergence. Based on this, the authors showed that it is possible to control the complexity of the optimal design solution by representing the level set function as a spline surface. However, depending on the setting of the free parameters related to the volume constraint, it was found that there were cases where an extremely large number of optimization steps were required before convergence, or where an unreasonably simple design solution was given. Therefore, in this study, we discuss the rational setting method of the relevant parameters