复合材料层合板的谱随机无网格伽辽金法

针对基于摄动理论的计算方法不适用于分析随机结构参数大变异问题，提出谱随机无网格伽辽金法，该方法基于随机场正交分解理论，将随机场采用Karhunen-Loève级数展开为一系列不相关随机变量，再引入结构位移随机响应的混沌多项式分解，结合无网格伽辽金法，从而导出含随机变量的复合材料层合板的谱随机无网格伽辽金法，给出结构响应的统计特征值的计算公式，该方法既适用于随机参数大变异情况，又具有无网格法的优势；数值算例结果表明该方法是正确有效的。

Spectral stochastic element-free Galerkin method for laminated composite plates

A spectral stochastic element-free Galerkin method is proposed to solve the stochastic structural problems with parameters having big changes, which can not be solved by the methods based on the perturbation theory. Based on the orthogonal decomposition theory of random fields, this method applied the Karhunen-Loève series to expand a random field into a series of uncorrelated random variables. A spectral expansion with use of polynomial chaos is employed to represent the stochastic nodal displacements in terms of standard normal random variables. The spectral stochastic element-free Galerkin method of the composite laminated plates with random variables was derived, with the computational formulas of the statistical characteristics of structural responses being given. This method will not be subject to the size constraints of the coefficient of variation and have an advantage of the element-free Galerkin method. Numerical results show that the method is correct and effective.