基于均匀化理论，建立与微观材料拓扑形状相关的宏观结构材料等效弹性张量。集成宏观结构所得到的位移场，推导出带有宏观结构力学特性的微观敏度。从而实现在给定材料体积分数前提下，以宏观结构最大刚度为目标，对材料微结构进行拓扑优化的目的。相关算例说明该方法可以得到与宏观力学性能相对应的各种微观结构蜂窝材料或复合材料。揭示了材料的微观结构拓扑形状依赖于宏观结构尺寸、载荷及初始边界条件等因素。
The elasticity tensor of the heterogeneous material was obtained from the microstructure through the homogenization theory,and this property was integrated into the analysis of the macrostructure.Then,the sensitivity analysis for the material unit cell was established from the macrostructure displacement field.The optimum of cellular material and composites with periodic microstructures was designed from given material so that the macrostructure has the maximum stiffness.Several numerical examples are presented to validate this optimization algorithm efficaciously,and it can be used for variety of anisotropic microstructures of cellular ma-terials and composites design.The various effects on the topological design of the material microstructure are discussed.It was also shown that the topology of material microstructure was related to the load and shapes of the macrostructure.
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