A generative design method for structural topology optimization via transformable triangular mesh (TTM) algorithm

Abstract

This article presents a way of optimizing the conduction topology for heat-generating structures by means of transformable triangular mesh (TTM) algorithm which is implemented in an explicit and geometrical way. Unlike the traditional optimization approaches, the proposed method capitalizes on the use of a special morphing algorithm to generate optimal topologies from a genus zero surface. In this method, the initial geometry is firstly converted into triangular mesh and stored as a half-edge data structure. Then, the mesh operations (i.e., subdivision, split, and refinement) are employed to activate the geometry to move, split, and deform upon the underlying finite element mesh so that the conduction topology can be achieved by optimizing the positions and orientations of the triangular grids. The unique feature of the mesh operation is the split, which makes the geometries have different number of faces, edges, vertices as the initial one, and therefore different genus number between these geometries. This method renders the optimization process more flexibility. Finally, some examples with verification results are presented to demonstrate that TTM algorithm is capable of proposing solutions having almost the same cooling effectiveness with less computing resources compared with the commonly used density approaches.