含裂纹结构的模糊随机无网格伽辽金法研究

为了分析实际工程结构中材料特性、几何特性或载荷中的某些参数同时具有随机性和模糊性，基于模糊随机变量、区间数分解法、摄动理论和无网格伽辽金法，提出了模糊随机无网格伽辽金法．推导出了水平截集下的随机无网格区间平衡方程，并将随机无网格区间平衡方程中的刚度矩阵、位移向量和载荷向量在初始随机向量的均值处进行泰勒级数展开，利用小参数摄动理论和区间数分解推导出了随机无网格区间平衡方程的求解公式，并给出了模糊随机位移数字特征的计算公式，将其应用到含裂纹结构的不确定性问题中．通过算例验证了本方法的正确性．

Fuzzy stochastic element-free Galerkin method for planes with cracks

Fuzzy Stochastic element-free Galerkin method was proposed in order to analyze the parameter fuzzy and stochastic in material characteristics,geometrical property or loading condition of engineering structures.This method was based on fuzzy random variable,resolution of interval numbers,perturbation theory and element-free Galerkin method.Firstly fuzzy stochastic element-free equilibrium equations were deduced.The stiffness matrix,displacement vector and loading vector in the equations were expanded by Taylor series at the mean of initial random vector.Then parameter perturbation and interval decomposition method were used to deduce the formula for solving random interval equations,and the numerical characteristic equations of stochastic displacement were also given.Furthermore,fuzzy stochastic element-free Galerkin method was applied on the uncertainty problem of crack structure,and the correctness of this method was verified through this example.