Generalized hole nucleation through BESO for the level set based topology optimization of multi-material structures

When a multi-material structure is optimized by using the level set method, besides the topological changes that are familiar to people (i.e., vanishing of a hole, nucleation of a hole, merging of holes, and breaking apart of a region), another topological change, i.e., the conversion between a pair of materials, is also possible to happen but receives little attention. In this case, a hole is no longer a region of void but becomes occupied by a different solid material. In our present study, such a topological change is called the generalized hole nucleation, and the material conversion scheme of the BESO is integrated into the level set based framework to deal with it. A strategy determining where and when to conduct generalized hole nucleation is presented. In addition, the shape derivatives of the structure's traction free boundary and the interfaces between material regions are carefully analyzed. The results of several numerical examples prove that the proposed method is effective and efficient. (C) 2019 Elsevier B.V. All rights reserved.