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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.
Aiming at the problem that the method based on perturbation theory is not suitable for analyzing the large variation of random structural parameters, a spectral stochastic mesh-free Galerkin method is proposed. Based on the theory of random field orthogonal decomposition, the method is developed using Karhunen-Loève series As a series of uncorrelated random variables, chaotic polynomial decomposition of random response of structure displacement is introduced. Combined with the element-free Galerkin method, the random stochastic Galerkin method for composite laminates with random variables is derived. The formula of the statistical eigenvalue of the structure response is presented. The proposed method is not only suitable for the large variation of random parameters but also has the advantage of meshless method. The numerical example shows that the method is correct and effective.