基于随机场正交展开理论的Cell-based随机光滑有限元方法

doi:10.12068/j.issn.1005-3026.2015.08.022

东北大学学报:自然科学版 ›› 2015, Vol. 36 ›› Issue (8): 1164-1169.DOI: 10.12068/j.issn.1005-3026.2015.08.022

基于随机场正交展开理论的Cell-based随机光滑有限元方法

周立明¹，孟广伟¹，李锋¹，郭学东²

(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)

收稿日期:2013-12-18 修回日期:2013-12-18 出版日期:2015-08-15 发布日期:2015-08-28
通讯作者: 周立明
作者简介:周立明(1982 -)，男，吉林白山人，吉林大学讲师，博士；孟广伟(1959 -)，男，吉林长春人，吉林大学教授，博士生导师.
基金资助:
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).

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

ZHOU Li-ming1， MENG Guang-wei¹， LI Feng¹， GUO Xue-dong²

1.College of Mechanical Science and Engineering， Jilin University， Changchun 130025，China; 2. College of Traffic， Jilin University， Changchun 130025， China.

Received:2013-12-18 Revised:2013-12-18 Online:2015-08-15 Published:2015-08-28
Contact: MENG Guang-wei
About author:-
Supported by:
-

摘要/Abstract

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.

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

Abstract: 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.

Key words: cell-based stochastic smoothed finite element, Karhunen-Loève expansion, chaotic polynomial, gradient smoothing technology, random field

中图分类号:

O344

周立明，孟广伟，李锋，郭学东. 基于随机场正交展开理论的Cell-based随机光滑有限元方法[J]. 东北大学学报:自然科学版, 2015, 36(8): 1164-1169.

ZHOU Li-ming ， MENG Guang-wei， LI Feng， GUO Xue-dong. Cell-based Stochastic Smoothed Finite Element Method Based on the Orthogonal Expansion Theory of Random Field[J]. Journal of Northeastern University Natural Science, 2015, 36(8): 1164-1169.

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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

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