Lattice structures offer significant advantages, including high strength-to-weight ratios, efficient material use, and customizable properties, making them ideal for applications ranging from aerospace components to biomedical implants. However, existing lattice structure design and optimization methods either do not consider the self-supporting property of the generated lattice structures or construct the struts with fixed radii. As a result, the printability and the performance of the generated lattice structures may be seriously affected. Motivated by these issues, this paper presents a method to generate variable radii self-supporting lattice structures for additive manufacturing. A lattice unit cell, namely the Symmetric Triangular Dodecahedron Lattice Unit Cell (STDLUC), is designed, which can be uniquely determined with several parameters. Each node of the STDLUC is associated with a radius. The relationship between the self-supporting property of the STDLUC and these parameters is investigated, and a self-supporting constraint is proposed for the variable-radius struts. Next, the Hexagonal Close-Packed-like packing method is used to construct the initial self-supporting lattice structure, with all struts designed as variable-radius struts. Subsequently, the node positions and radii are optimized using the proposed optimization formulation with the self-supporting constraint to enhance the performance of the lattice structure. To ensure the printability of the generated lattice structure, the radius range of the nodes used in the optimization is analyzed according to the minimum printable feature size of the 3D printer and buckling conditions. The effectiveness of the proposed method and the performance of the lattice structures generated with this method have been demonstrated through extensive numerical and physical experiments and comparisons.

中文翻译：

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可变半径自支撑晶格结构的设计和优化


晶格结构具有显著的优势，包括高强度重量比、高效的材料使用和可定制的特性，使其成为从航空航天部件到生物医学植入物等应用的理想选择。然而，现有的晶格结构设计和优化方法要么不考虑生成的晶格结构的自支撑特性，要么构建具有固定半径的支柱。因此，生成的晶格结构的适印性和性能可能会受到严重影响。在这些问题的推动下，本文提出了一种为增材制造生成可变半径自支撑晶格结构的方法。设计了一个晶格晶胞，即对称三角形十二面体晶格晶胞 （STDLUC），它可以通过几个参数唯一地确定。STDLUC 的每个节点都与一个半径相关联。研究了 STDLUC 的自支撑特性与这些参数之间的关系，并为可变半径支柱提出了一种自支撑约束。接下来，使用 Hexagonal Close-Packed-like 填充方法构建初始自支撑晶格结构，所有支柱设计为可变半径支柱。随后，使用所提出的具有自支撑约束的优化公式优化节点位置和半径，以提高晶格结构的性能。为了确保生成的晶格结构的可打印性，根据 3D 打印机的最小可打印特征尺寸和屈曲条件分析优化中使用的节点的半径范围。 通过广泛的数值和物理实验和比较，证明了所提出的方法的有效性和用该方法生成的晶格结构的性能。