The current paper presents a perturbation-based stochastic eigenvalue buckling analysis of thin plates using element free Galerkin method. Spatial variation in Young’s modulus is modeled as a homogeneous random field and moving least square-based shape function method is employed for discretizing the random field. Perturbation method is used to evaluate the statistics of buckling loads. Numerical examples wherein rectangular plates with different boundary conditions are solved and the statistics obtained are compared with those calculated using Monte Carlo simulation. Different parametric studies are also conducted. The results obtained from perturbation method are found to be reasonably accurate for coefficient of variation (CV) values less than 20% for random fields with normal distribution. Further it is observed that for random fields with lognormal distribution, the proposed method produces reasonably accurate results up to a CV of 30%.

中文翻译：

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板屈曲分析的基于微扰的随机无网格方法

本文提出了一种基于微扰的使用无单元 Galerkin 方法的薄板随机特征值屈曲分析。杨氏模量的空间变化被建模为均匀随机场，并采用基于移动最小二乘的形状函数方法对随机场进行离散化。扰动法用于评估屈曲载荷的统计量。求解具有不同边界条件的矩形板并将获得的统计数据与使用蒙特卡罗模拟计算得到的统计数据进行比较的数值示例。还进行了不同的参数研究。对于正态分布的随机场，从摄动法获得的结果对于小于 20% 的变异系数 (CV) 值是相当准确的。