Cellular topology optimization on differentiable Voronoi diagrams
Cellular topology optimization on differentiable Voronoi diagrams
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DOI：
10.1002/nme.7121
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发表时间：
2022-04
影响因子：
2.9
通讯作者：
F. Feng;S. Xiong;Ziyue Liu;Zangyueyang Xian;Yuqing Zhou;Hiroki Kobayashi;A. Kawamoto;T. Nomura-T.-Nomu
中科院分区：
文献类型：
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作者：
F. Feng;S. Xiong;Ziyue Liu;Zangyueyang Xian;Yuqing Zhou;Hiroki Kobayashi;A. Kawamoto;T. Nomura-T.-Nomu
细胞结构在许多生物系统中表现出突出的力学性能。设计和优化这些几何复杂结构的一个关键挑战在于设计一个有效的几何表示来表征系统的空间变化的细胞进化驱动的目标灵敏度。传统的离散细胞结构，例如，Voronoi图，其表示依赖于离散的Voronoi单元和面，缺乏其可微性以促进大规模的基于梯度的拓扑优化。我们提出了一个拓扑优化算法的基础上可微和广义Voronoi表示，可以演变的细胞结构作为一个连续的字段。我们方法的核心部分是一种混合粒子网格表示，将先前离散的Voronoi图编码为欧几里得空间中定义的连续密度场。基于这种可微表示，我们进一步扩展它来处理各向异性细胞，自由边界和功能梯度细胞结构。我们的可微Voronoi图能够将有效的细胞表示集成到最先进的拓扑优化管道中，这为细胞结构定义了一个新的设计空间，以有效地探索以前方法不切实际的设计选项。我们展示了我们的方法的有效性，通过优化细胞结构与多达数千个各向异性的细胞，包括股骨骨和蜻蜓翅膀。
Cellular structures manifest their outstanding mechanical properties in many biological systems. One key challenge for designing and optimizing these geometrically complicated structures lies in devising an effective geometric representation to characterize the system's spatially varying cellular evolution driven by objective sensitivities. A conventional discrete cellular structure, for example, a Voronoi diagram, whose representation relies on discrete Voronoi cells and faces, lacks its differentiability to facilitate large‐scale, gradient‐based topology optimizations. We propose a topology optimization algorithm based on a differentiable and generalized Voronoi representation that can evolve the cellular structure as a continuous field. The central piece of our method is a hybrid particle‐grid representation to encode the previously discrete Voronoi diagram into a continuous density field defined in a Euclidean space. Based on this differentiable representation, we further extend it to tackle anisotropic cells, free boundaries, and functionally‐graded cellular structures. Our differentiable Voronoi diagram enables the integration of an effective cellular representation into the state‐of‐the‐art topology optimization pipelines, which defines a novel design space for cellular structures to explore design options effectively that were impractical for previous approaches. We showcase the efficacy of our approach by optimizing cellular structures with up to thousands of anisotropic cells, including femur bone and Odonata wing.