基于随机有限元的非线性结构稳健性优化设计

结合结构优化技术和摄动随机有限元方法研究了非线性结构稳健设计问题。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，并采用基于函数梯度的算法进行求解。为对具有路径相关特征的非线性结构性能及结构响应的平均值及标准差进行分析。本文采用缩减的随机变量，提出了基于增量法的摄动随机有限元计算格式。在此框架下，进一步提出以一般泛函形式表达的结构性能的平均值和方差及其灵敏度的计算格式。为显示方法的有效性。文中给出几个数值算例。

Structural robust design based on perturbation stochastic finite element method

The perturbation-based stochastic finite element analysis incorporating structural optimization techniques is employed in the robust design of path-dependent nonlinear structures.The problem 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 feasibility is also accounted for by involving the variability of the structural response in the constraints.An incremental scheme based on a reduced set of random variables is proposed for evaluating the expected value and the variance of the structural performance functional,as well as their sensitivities.The optimization problem is converted into a scalar one and solved by a gradient based mathematical programming approach.Numerical examples are given to demonstrate the applicability of the presented method.