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。 Studying the topological optimization of truss structures under the random response constraints has an important engineering application prospect. In this paper, adaptive genetic algorithm (AGA) is used to solve the truss structure topology optimization problem under random response constraints. The three steps of generating high-quality initial population by introducing Hamming distance, using adaptive crossover and mutation operators and linearly calibrating the fitness function improve the search efficiency and convergence of genetic algorithm. In the topology optimization column, the rod and topological variables of each degree of freedom are considered to accurately simulate the deletion of the rod and node in the optimization process. The expression of the mean square response under random load is established and used as the constraint of the topology optimization problem. In addition, some heuristic algorithms are proposed to guide the deletion of the bars and nodes. Finally, the topological optimization of two-dimensional truss and three-dimensional truss under random excitation is proved, which proves the practicability and effectiveness of the proposed method.