复合材料周期性线弹性微结构的拓扑优化设计

提出复合材料周期性线弹性微结构拓扑优化设计的模型，模型1设计具有极值弹性特性的复合材料，模型2设计工况最刚微结构单胞。通过该模型和均匀化技术可以获得优化的微结构单胞，进而改善或者得到最优宏观特性的复合材料。为了便于制造和应用，用胞体材料而不是多相材料来得到复合材料的极值弹性特性和最大刚度。优化结果表明，该模型与数值方法相结合可以有效地实现微结构的拓扑优化设计。

TOPOLOGY OPTIMIZATION FOR PERIODIC LINEAR ELASTIC MICROSTRUCTURES OF COMPOSITE MATERIALS

In conjunction with the homogenization method and the finite element method, two computational models are suggested to design the periodic microstructures of composite. Model 1 addresses the problem of finding the optimal representative microstructural element that maximizes linear combintion of the equivalent elastic properties, model 2 is about the problem of finding the stiffest microstructure for a multi-load situation. Optimal microstructures obtained through the new models and homogenization method can be used to improve and optimize naturally occurring or man-made materials. In order to be more practical for engineering applications, cellular materials rather than ranked material are used in optimal process in the existence of optimal bounds for the elastic properties. The optimal results show that the two models with the numerical technique are effective in obtaining composite with extremal elastic properties or extremal rigidity.