基于局部相对密度映射的变密度多孔结构设计方法

针对变密度多孔结构设计依据的拓扑优化密度信息不能被充分有效利用的问题，提出一种基于拓扑优化局部相对密度映射的变密度多孔结构设计方法。该方法根据多孔结构力学特点建立等效连续体的拓扑优化模型，通过拓扑优化密度的局部映射策略和调整方法，将拓扑优化的密度信息映射到多孔结构单元并根据映射的相对密度生成变密度多孔结构。此外，为检验多孔结构与拓扑优化密度信息的匹配程度，提出一种基于体素化和矩阵相似度的分析评价方法。最后以不同尺度的二维蜂窝为案例，验证了所提变密度多孔结构设计方法的可行性和有效性。

Variable Density Cellular Structure Design Method Base on Local Relative Density Mapping

To solve the problem that cellular structure design result cannot effectively reflect the topology optimization density information in the design process of variable density cellular structure, a variable density cellular structure design method based on topology optimization local relative density mapping strategy is proposed. According to the mechanics characteristics of cellular structure, the equivalent continuum solid topology optimization is established. The variable cellular structure can be constructed according to the cell's local relative density which is gained through unitizing local density mapping and density adjustment method. Besides, an analysis method is proposed to estimate matching relationship between the relativity density of topology optimization outcome and design outcome of cellular structure based on the voxelization and matrix similarity computation. Finally, the different size 2D honeycomb variable density cellular structures are designed and taken as the cases to verify the feasibility and effectiveness of proposed method.