A new topology optimization framework for stiffness design of beam structures based on the transformable triangular mesh algorithm

This paper presents an explicit topology optimization method based on the so called Transformable Triangular Mesh (TTM) approach. It improves a general weakness of the traditional explicit approaches in the sense that the genus of initial geometry no longer affects the design result. In the proposed method, we first triangulate the initial geometry and organize it with the halfedge data structure. Then we employ the Laplacian energy controlled mesh deformation algorithm to realize smooth transition from the initial TTM. Furthermore, three geometrical mesh processing techniques (mesh subdivision, mesh split, and mesh refinement) are adopted to realize surface genus change. Respectively, the mesh subdivision is beneficial for the increase of mesh control hot points to obtain more degree of freedoms, the mesh split is able to rip connected triangles such that holes can be generated both inside a mesh and on the border, and the mesh refinement unifies the sizes and shapes of each triangle in the mesh such that no large distortion and self-intersection exist. To enhance the computational efficiency, we realize the above algorithm parallelly using CUDA. Finally, some benchmark examples (a cantilever beam, an MBB beam, and a cantilever beam with a fixed hole) are used to validate the algorithm. By comparing with state-of-the-art algorithms, our method proves to be reliable, accurate, and advanced.