线弹性结构的高阶摄动随机有限元法

计算精度和误差控制是摄动随机有限元法在数值计算中的重要问题。根据随机理论和摄动有限元方法，推导了随机变量均值和n阶中心矩的计算公式；提出了摄动随机有限元实施过程中精度的控制方法，能够在计算结构响应均值和方差之前就分别确定计算结果的精度；研究了摄动随机有限元0~n阶递推方程组计算列式；运用高阶摄动随机有限元方法对受轴向拉力的一维线弹性杆进行了分析，结果表明：与二阶摄动法相比，n阶摄动技术能有效地改进计算精度。

Nth perturbation stochastic finite element

Computational precision and error control are very important to the numerical computation of the stochastic finite element method. Based on theory of random fields and perturbation finite element method, computational formulas of expected values and nth order central probabilistic moments of the random variable were derived. A computational precision control algorithm in perturbation-based stochastic finite element method was proposed here, which makes it possible to specify the accuracy of the solution before expected values and variances of structural responses were calculated separately. The 0th-Nth order equilibrium equations of the perturbation-based stochastic finite element method were formulated. One dimension linear elastic prismatic bar subjected simple unidirectional tension was studied with this method.The results of this analysis show that comparing with second order perturbation approach, the Nth order method can improve efficiently the accuracy of stochastic perturbation technique.