Topology Optimization with Level Set Method Incorporating Topological Derivative

Topology optimization is at the highest level in the field of structural optimization. The introduction of the level set methods into this field has demonstrated several attractive advantages. However, a significant limit of the level set methods in topology optimization is that it can not create new holes in the design domain. Topological derivative approach is a relatively new procedure to overcome this problem. It can indicate the appropriate location to create new holes such that the strong dependency of the optimal topology on the initial design can be alleviated. In this paper, we investigated the use of topological derivative in combination with the level set methods for topology optimization of solid structures. By comparing the topological derivative value with the penalized volume constraint function value, we can determine whether and where the holes should be nucleated. In this paper we also developed an approach to evolving the level set function by replacing the gradient item by a Delta function in the standard Hamilton-Jacobi equation. We found that this handling can create new holes in the solid domain, grow a structure from an empty domain, and improve the convergence rate of the optimization process. We also discussed some issues in the implementation of our new approach. The success of our approach is demonstrated by several numerical examples. 2. Keywords: level set method, topology optimization, topological derivative The level set models are topologically flexible, and can split and merge as necessary in the course of deformation without the need for re-parametrization. Because of these advantages, level set methods are becoming a powerful mathematical tool to deal with shap