A Level Set Method With a Bounded Diffusion for Structural Topology Optimization

Abstract

In level-set-based topology optimization methods, the spatial gradients of the level set field need to be controlled to avoid excessive flatness or steepness at the structural interfaces. One of the most commonly utilized methods is to generalize the traditional Hamilton−Jacobi equation by adding a diffusion term to control the level set function to remain close to a signed distance function near the structural boundaries. This study proposed a new diffusion term and built it into the Hamilton-Jacobi equation. This diffusion term serves two main purposes: (I) maintaining the level set function close to a signed distance function near the structural boundaries, thus avoiding periodic re-initialization, and (II) making the diffusive rate function to be a bounded function so that a relatively large time-step can be used to speed up the evolution of the level set function. A two-phase optimization algorithm is proposed to ensure the stability of the optimization process. The validity of the proposed method is numerically examined on several benchmark design problems in structural topology optimization.