随机响应约束下的桁架结构拓扑优化(英文)

Topology Optimization of Truss Structures with Random Response Constraints

研究随机响应约束下的桁架结构拓扑优化问题具有重要的工程应用前景。文章采用自适应遗传算法(AGA)求解了随机响应约束下的桁架结构拓扑优化问题。通过引入海明距离生成高质量的初始种群、采用自适应的交叉和变异算子以及对适应度函数进行线性标定这三个步骤改进了遗传算法的搜索效率以及收敛性。在拓扑优化列式中考虑杆件以及各自由度的拓扑变量以精确地模拟优化过程中杆件和结点的删除。建立了随机载荷作用下结构均方响应的表达式,并以此作为拓扑优化问题的约束条件。另外,提出了一些启发式算法来引导杆件和结点的删除。最后,通过对随机激励下的二维桁架以及三维桁架进行拓扑优化计算,证明了本文方法的实用性和有效性。

This paper studies topology optimization problems of truss structures with random excitations by using Adaptive Genetic Algorithm （AGA）. Topology variables for bars and degrees of freedom are added to the formulation of topology optimization. The random dynamic theory is applied to establish an expression of random dynamic response constraints.Some heuristic strategies are put forward to direct the deletion of the extra bars and nodes on truss structures. Finally, several examples, includ- ing 2D and 3D truss structures, are presented to demonstrate the effectiveness of the proposed method for the engineering design.