Structural topology and shape optimization using a level set method with distance-suppression scheme

In level set methods for structural topology and shape optimization, the level set function gradients at the design interface need to be controlled in order to ensure stability of the optimization process. One popular way to do this is to enforce the level set function to be a signed distance function by periodically using initialization schemes, which is commonly known as re-initialization. However, such re-initialization schemes are time-consuming, as additional partial differential equations need to be solved in every iteration step. Furthermore, the use of re-initialization brings some undesirable problems; for example, it may move the zero level set away from the expected position. This paper presents a level set method with distance-suppression scheme for structural topology and shape optimization. An energy functional is introduced into the level set equation to maintain the level set function to close to a signed distance function near the structural boundaries, meanwhile forcing the level set function to be a constant at locations far away from the structural boundaries. As a result, the present method not only can avoid the need for re-initialization but also can simplify the setting of the initial level set function. The validity of the proposed method is tested on the mean compliance minimization problem and the compliant mechanisms synthesis problem. Different aspects of the proposed method are demonstrated on a number of benchmarks from the literature of structural optimization.