A Level Set Method-based Topology Optimization Method Using the Discretization-based Sensitivity with Respect to the Signed Distance Function

Abstract

This paper discusses a new level set method-based topology optimization method using the discretization-based sensitivity with respect to the signed distance function. First, the basic concepts of structural optimization based on the level set method is briefly discussed, and the minimum compliance problem is formulated based on the level set method. Next, a level set function updating scheme using the discretization-based sensitivity with respect to the signed distance function is constructed. In this scheme, the normal velocity is determined by the discretization-based sensitivities of the mean compliance and the perimeter. By updating the level set function using the discretization-based sensitivities of the mean compliance and the perimeter, simple and appropriate optimal configurations can be obtained. Finally, several numerical examples are provided to confirm the validity of the proposed method.