基于能量法的复合材料热残余应力的拓扑优化

TOPOLOGY OPTIMIZATION OF COMPOSITE MATERIALS FOR RESIDUAL STRESS USING STRAIN ENERGY-BASED METHOD

提出提出复合材料在考虑热残余应力时平面微结构的拓扑优化设计模型。在给定的材料体积含量的情况下,以材料的弹性模量主对角线值为目标函数,以单元的相对密度作为设计变量,对微结构进行拓扑优化设计。等效弹性常数通过能量法计算得到,采用移动渐进线法求解优化问题,利用敏度过滤去除拓扑优化中存在的数值不稳定性问题。数值算例验证了拓扑优化模型和算法的有效性。

A topology optimization model is presented for the 2-D mircrostructure of composite material while thermal residual stress exist. Under the given volume fraction, constraints on the material volume fraction, the mircrostructure will be optimized .The topology takes the main diagonal elastic modulus value as the objective function and the relative density of element as the design variable. The equivalent elastic constants can be obtained by the strain energy-based method and. the MMA method for solving the optimal problem. The numerical instability will be eliminated by means of the sensitivities filter and the numerical example indicates the effectiveness of the algorithm.