摘 要 研究几何和物理参数均为随机变量的平面连续体结构在结构基频约束下的拓扑优化设计问题。以结构总质量均值极小化为目标函数，以结构的形状拓扑信息为设计变量，以结构基频概率可靠性指标为约束条件，构建了随机结构拓扑优化设计数学模型。利用代数综合法，导出了随机参数结构动力响应的均值和均方差的计算表达式。采用渐进结构优化的求解策略与方法，通过两个算例验证了文中模型及求解方法的合理性和可行性。

Topology optimization design problem for planar continuum structure with the randomness of both the geometry and physical parameters under the structural foundamental frequency constraint is studied. Mathematical model of topology optimization design with random structure is established, in which the minimum the mean of structural weight is taken as objective function, the structural shape topology information is taken as design variables, the probabilistic reliability index of structural foundamental frequency is taken as constraint conditon. The computational expressions of the mean value and mean variance of the structural dynamic response are presented by the algebra method. Evolutionary structural optimization method is used in the optimization. Through two examples, the rationality and feasibility of the optimization model and solving method are validated.