基于随机场正交展开理论的Cell-based随机光滑有限元方法

为解决工程结构中随机参数大变异问题,提出基于正交展开理论的Cell-based随机光滑有限元方法.该方法采用Karhunen-Loève级数将随机场分解为不相关随机变量,再使用混沌多项式将位移随机响应展开,将展开后的随机场及位移响应引入到Cell-based光滑有限元中.详细推导了基于正交展开理论的Cell-based随机光滑有限元平衡方程,进一步给出了结构位移均值与协方差矩阵的计算公式,具有对网格要求低、计算精度高的优点,并对材料特性具有随机性的带孔方板的随机响应问题进行了分析,数值算例结果表明该方法是正确有效的.

Cell-based Stochastic Smoothed Finite Element Method Based on the Orthogonal Expansion Theory of Random Field

To solve the stochastic parameter variation problem in engineering structures， the cell-based stochastic smoothed finite element method was proposed based on the orthogonal expansion theory. In the method， the Karhunen-Loève series orthogonally decompose the random field into independent random variables and the chaotic polynomial expands the random displacement response， and then the expended random field and displacement response are introduced into the cell-based stochastic smoothed finite element. The equilibrium equation of the proposed method is derived， and the computational formulas of the covariance matrix and the mean structural displacement are given. The numerical calculation indicates that the method has low meshing requirements and high precision. The random response of the square plate with a hole which has random material characteristics was further analyzed. The numerical results show that the proposed method is correct and feasible.