几何特征演化驱动的多胞结构自支撑拓扑优化设计

doi:10.3901/JME.2025.17.300

摘要/Abstract

摘要： 多胞结构是一类具有复杂孔洞特征且兼具特定力学性能的跨尺度结构。多胞结构在设计空间中几何特征的复杂拓扑关系，增加了其在制造空间中成形难度。本文为突破多胞结构的自支撑特性设计，提出基于几何特征演化的多胞结构设计方法。从几何特征出发，研究了杆单元的叠加组合方式，分析了杆单元空间位姿、单胞刚度矩阵、单胞密度之间的映射关系，建立了杆单元几何特征驱动的二维与三维单胞模型；结合拓扑优化方法，推导了多胞结构的灵敏度，构建了单胞匹配的多胞结构优化模型；结合胞体中杆单元的空间位姿，分析了单胞间共享杆单元以及单胞内独享杆单元的成形角分布范围，设计了杆单元成形角匹配的搜索算法，建立了具有自支撑特性的制造体素，实现了多胞结构的自支撑设计。最后通过二维悬臂梁与三维支架的优化实例，详细说明了多胞结构制造体素构建过程，并利用增材制造设备的模型切片软件，验证了所提方法的有效性，为多胞结构的自支撑设计提供了新的理论依据和方法途径。

关键词: 拓扑优化, 自支撑结构, 几何特征, 制造体素

Abstract: Multicellular structures are a class of cross-scale structures characterized by complex pore features and specific mechanical properties. The intricate topological relationships inherent in the geometrical features of multicellular structures within the design space introduce significant challenges to their formation in the fabrication space. In this paper, in order to break through the self-supporting characteristic design of multi-cellular structures, a multi-cellular structure design method based on the evolution of geometric features is proposed. Starting from the geometric features, the superposition and combination mode of the rod unit is investigated, and the mapping relationship between the spatial position of the rod unit, the single-cell stiffness matrix, and the density of the single cell is analysed, and the two-dimensional and three-dimensional single-cell models driven by the geometric features of the rod unit are established; When employed in conjunction with the topological optimization method, the sensitivity of the multicellular structure is deduced, and the optimization model of the multicellular structure with single-cell matching is constructed. The distribution range of the forming angles of the shared rod units between single cells, as well as the exclusive rod units within a single cell, is analysed in conjunction with the spatial position of the rod units in the cell. The search algorithm for matching the forming angles of the rod units is designed to establish the manufacturing voxel with self-supporting characteristics and realize the self-supporting design of multi-cellular structures. This paper provides a comprehensive illustration of the multi-cellular structure manufacturing voxel construction process through the optimization example of a 2D cantilever beam and a 3D bracket. It also verifies the validity of the proposed method by using the model slicing software of the additive manufacturing equipment. This provides a new theoretical basis and methodological approach for the self-supporting design of multi-cellular structures.

Key words: topology optimization, self-supporting structure, geometric features, manufacturing voxels

中图分类号:

TP319

吴紫俊, 肖人彬. 几何特征演化驱动的多胞结构自支撑拓扑优化设计[J]. 机械工程学报, 2025, 61(17): 300-313.

WU Zijun, XIAO Renbin. Geometric Feature Evolution-driven Topology Design for the Supporting-free Multicell Structure[J]. Journal of Mechanical Engineering, 2025, 61(17): 300-313.

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