The topology optimization framework based on element-free Galerkin (EFG) method for orthotropic multi-material structures with length-scale control (LSC) strategy is proposed, including maximum and minimum LSC of solid and void phase. The alternating active-phase algorithm is integrated with the meshless multi-material interpolation model, and the gradient algorithm is used to update the relative density of the meshless nodes. This method is easy to implement and can realize the LSC of single or multiple phase orthotropic materials accurately in the EFG optimal topological structure. The effects of orthotropic off-angles, LSC strategies, filtering radius, and control domain radius on EFG topological structures and minimum compliance are investigated through numerical examples. The results show that the length scale of the EFG optimal topological structure can meet the requirement of the additive manufacturing, and there will be desirable dimensional gaps between the members using the LSC strategy. The appropriate combination of orthotropic multi-material off-angles can reduce the compliance and improve mechanical performance greatly. The sizes and gaps of topological members become more uniform, and the minimum length scale and compliance of the optimal topological structure will increase with the filtering radius which should be smaller than the control domain radius of the maximum LSC.

中文翻译：

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基于无单元伽辽金法的长度尺度控制正交各向异性多材料结构拓扑优化

提出了基于无单元伽辽金（EFG）方法的具有长度尺度控制（LSC）策略的正交各向异性多材料结构的拓扑优化框架，包括固相和空相的最大和最小LSC。将交替活性相算法与无网格多材料插值模型相结合，利用梯度算法更新无网格节点的相对密度。该方法易于实现，能够在EFG最优拓扑结构下准确实现单相或多相正交各向异性材料的LSC。通过数值算例研究了正交各向异性偏角、LSC策略、滤波半径和控制域半径对EFG拓扑结构和最小柔度的影响。结果表明，EFG最优拓扑结构的长度尺度能够满足增材制造的要求，并且采用LSC策略的构件之间会存在理想的尺寸间隙。正交各向异性多材料斜角的适当组合可以降低柔度并大大提高机械性能。拓扑成员的尺寸和间隙变得更加均匀，最优拓扑结构的最小长度尺度和顺应性将随着过滤半径的增加而增加，过滤半径应小于最大LSC的控制域半径。