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.

中文翻译：

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基于可变形三角网格（TTM）算法的结构拓扑优化生成设计方法

摘要

本文提出了一种通过可变换的三角形网格（TTM）算法优化热生成结构的传导拓扑的方法，该算法以显式和几何方式实现。与传统的优化方法不同，该方法利用特殊的变形算法从零类曲面生成最优拓扑。在这种方法中，首先将初始几何图形转换为三角形网格并存储为半边数据结构。然后，采用网格操作（即细分，分割和细化）来激活几何体，以便在下面的有限元网格上移动，分割和变形，以便可以通过优化网格的位置和方向来实现导电拓扑。三角形网格。网格操作的独特之处在于拆分，这使得几何图形具有不同数量的面，边，顶点作为初始几何图形，因此这些几何图形之间的属数不同。此方法使优化过程更具灵活性。最后，给出一些带有验证结果的示例，以证明与常规密度方法相比，TTM算法能够提出具有几乎相同的冷却效率且计算资源更少的解决方案。