Velocity Field Level Set Method Incorporating Topological Derivatives for Topology Optimization

Abstract The velocity field level set method constructs the velocity field by velocity design variables and basis functions, and thus facilitates the use of general optimizers while still retaining the level set-based implicit topological representation. This paper incorporates the topological derivative concept into the velocity field level set method to enable automatic nucleation of interior holes. In each design iteration, a specified volume fraction of new holes is inserted at locations with smaller values of topological derivatives. Thus, the method provides a way to directly change the structural topology during the boundary evolution using the velocity field based on the shape sensitivity. Compared with the original velocity field level set method, the current implementation can further accelerate the topological and shape evolution during the optimization process. More importantly, the capability of hole nucleation eliminates the need of prescribing initial holes and thus alleviates the dependency of the optimized design on the initial design. Several numerical examples in both 2D and 3D design domains are presented to demonstrate the validity and efficiency of the proposed method.