中文摘要：

研究了考虑参数随机性的结构静动态特性稳健性优化设计问题的数学模型和数值求解。在考虑结构设计变量和其他参数随机分布的前二阶矩的条件下，采用基于二阶摄动法的随机有限元方法对结构响应的平均值和方差进行近似求解。在摄动法有限元分析的框架下，提出以一般函数形式表达的结构性能的平均值和标准差及其灵敏度的计算格式。将结构稳健性优化设计问题构造为双目标优化问题，优化目标包含结构性能函数的期望值和标准差，约束函数的变异也给予考虑。优化问题采用基于函数梯度的算法进行求解。文中给出的数值算例显示了方法的有效性。

英文摘要：

The perturbation-based stochastic finite element analysis incorporating structural optimization techniques is employed in the structural robust design problem. In the framework of the second-order perturbationbased stochastic finite element method, the computational schemes for the expected value and the variance of the structural performance functional as well as their sensitivity are proposed. The robust design of structures is formulated as a multi-criteria optimization problem, in which both the expected value and the standard deviation of the objective function are to be minimized. The robustness of the design feasibility is also accounted for by involving the variability of the structural response in the constraints. The optimization problem is converted into a scalar one and solved by a gradient based optimization algorithm. To demonstrate the applicability of the presented method, numerical examples are given.