A topology optimization (TO) algorithm for periodic mechanical structures with orthotropic materials is established by using the element-free Galerkin method (EFGM) and imposing periodic constraints on design subdomains. The effectiveness of the presented TO algorithm is verified by two numerical examples compared with the finite element method (FEM). The comparisons demonstrate that the EFGM periodic structures without using any filtering techniques have smoother boundaries and fewer intermediate relative densities. These optimal periodic structures can be manufactured by 3D printing from the extracted "*.stl" files. The effects of the number of design subdomains, Poisson's ratio factor, and off-angle on minimum compliance and periodic structures are studied, and reasonable ranges of parameters are recommended to improve the mechanical performance of periodic structures. The results indicate that the increase of the number of design subdomains in any direction leads to inevitable stiffness loss, but the minimum compliance can be further reduced by decreasing Poisson's ratio factor and adjusting off-angle properly for specific number of design subdomains. Optimal periodic structures with orthotropic materials are of better mechanical performance to resist deformation and reduce von Mises stress than those with isotropic materials.

采用无单元伽辽金法（EFGM），对设计子域施加周期性约束，建立了正交各向异性材料周期性机械结构的拓扑优化（TO）算法。所提出的 TO 算法的有效性通过与有限元法 (FEM) 进行比较的两个数值例子进行了验证。比较表明，不使用任何滤波技术的 EFGM 周期性结构具有更平滑的边界和更少的中间相对密度。这些最佳的周期性结构可以通过 3D 打印从提取的“*.stl”文件中制造出来。研究了设计子域的数量、泊松比因子和偏角对最小柔度和周期性结构的影响，并推荐合理的参数范围以提高周期性结构的力学性能。结果表明，在任何方向上增加设计子域的数量都会导致不可避免的刚度损失，但可以通过降低泊松比因子并针对特定数量的设计子域适当调整偏角来进一步降低最小柔度。正交各向异性材料的最佳周期结构比各向同性材料具有更好的抗变形和降低冯米塞斯应力的机械性能。s 比率因子并针对特定数量的设计子域适当调整偏角。正交各向异性材料的最佳周期结构比各向同性材料具有更好的抗变形和降低冯米塞斯应力的机械性能。s 比率因子并针对特定数量的设计子域适当调整偏角。正交各向异性材料的最佳周期结构比各向同性材料具有更好的抗变形和降低冯米塞斯应力的机械性能。