Three-dimensional grayscale-free topology optimization using a level-set based r-refinement method

In this paper, we propose a three-dimensional (3D) grayscale-free topology optimization method using a conforming mesh to the structural boundary, which is represented by the level-set method. The conforming mesh is generated in an r-refinement manner; that is, it is generated by moving the nodes of the Eulerian mesh that maintains the level-set function. Although the r-refinement approach for the conforming mesh generation has many benefits from an implementation aspect, it has been considered as a difficult task to stably generate 3D conforming meshes in the r-refinement manner. To resolve this task, we propose a new level-set based r-refinement method. Its main novelty is a procedure for minimizing the number of the collapsed elements whose nodes are moved to the structural boundary in the conforming mesh; in addition, we propose a new procedure for improving the quality of the conforming mesh, which is inspired by Laplacian smoothing. Because of these novelties, the proposed r-refinement method can generate 3D conforming meshes at a satisfactory level, and 3D grayscale-free topology optimization is realized. The usefulness of the proposed 3D grayscale-free topology optimization method is confirmed through several numerical examples.