多相材料微结构布局及宏观结构拓扑并发优化

摘要

在传统双向渐进结构优化(BESO)方法基础上，充分考虑材料和结构的尺度关联性，基于均匀化理论将材料微结构胞元设计和宏观结构拓扑优化相结合，按照材料属性排序引入材料插值函数依次进行灵敏分析，建立周期性多相材料微结构布局及宏观结构拓扑并发优化设计方法。优化过程中，宏观结构受力的特性嵌入微观敏度生成过程，使得新型材料具备了特定宏观结构力学需求的更加轻型、高强的最佳力学性能；同时，微观材料胞元的等效材料属性又是宏观结构优化的基础材料，从而使得材料/结构具有尺度上的统一。相关算例说明该方法在解决多相材料微观分布优化和周期性多相材料微结构布局及宏观结构拓扑并发优化问题时具有边界清晰和收敛快等优点。%Considering the mutual coordination between the role of micro-scale and macro-scale,the structure-material concurrent optimization method is established based on the traditional BESO method. The elasticity tensor of the heterogeneous material is obtained from the microstructure through the homogenization theory,and this property is integrated into the analysis of the macrostructure.And the constituent phases are categorized into some groups and sensitivity analyses are performed to assess the contribution of elements within each group.Here,the sensitivity for the material unit cell is established from the macrostructure displacement field,so the creating novel material properties are determined by the special macrostructure and its given boundary conditions.At the same time,the material properties for the macrostructure are getting from the material unit cell.So the unified properties are setting up between micro and macro level.Several numerical examples are presented to validate the proposed optimization algorithm can be used to design periodic multiphase composite materials and macrostructure optimization.And the identification of the phases’boundaries and convergence speed are also demon-strated.