基于随机场正交展开理论的Cell-based随机光滑有限元方法  

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

作　　者：周立明[1] 孟广伟[1] 李锋[1] 郭学东[2] 

机构地区：[1]吉林大学机械科学与工程学院,吉林长春130025 [2]吉林大学交通学院,吉林长春130025

出　　处：《东北大学学报（自然科学版）》2015年第8期1164-1169,共6页Journal of Northeastern University(Natural Science)

基　　金：国家重大科学仪器设备开发专项(2012YQ030075);吉林省科技厅基金资助项目(20130305006GX)

摘　　要：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.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-Lo^ve 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.

关 键 词：Cell-based随机光滑有限元 Karhunen-Loève展开 混沌多项式 梯度光滑技术 随机场 

分 类 号：O344[理学—固体力学]