周期性复合材料构型及结构一体化优化

在传统双向渐进结构优化(BESO)方法基础上，充分考虑微观尺度和宏观尺度之间的相互耦合作用，通过等效弹性模量和灵敏度分析将复合材料微结构胞元设计和宏观结构拓扑优化相结合，建立周期性复合材料构型及结构一体化优化设计方法.为了消除“灰色区域”，假设了材料微结构0 1属性及在宏观结构空间排列的均一性，提高了优化结果的实际工程适用性.相关算例说明该方法可以有效地在宏观结构优化的同时得到与之相对应的材料微观最佳拓扑形状，也为不同给定宏观结构的微观周期性复合材料设计提供了有效手段.

Collaborative Optimization of Structures With Periodic Composite Materials

In view of the coupling effects between the micro scale and macro scale, the structure-material collaborative optimization method was established based on the traditional bi-directional evolutionary topology optimization method. The equivalent elastic modulus and sensitivities were obtained with the homogenization theory, and these properties were integrated into the material unit cell design and macrostructure optimization. To eliminate the gray area, the 0-1 properties of the materials and uniformity of the macrostructure permutation were hypothesized for deduction, which made the results manufacturable. Several numerical examples were presented to validate that the proposed optimization algorithm is effective for the material unit cell design and macrostructure optimization. The method also can be used for the periodic composite material design under given macrostructures.