基于随机场和Monte-Carlo法的随机有限元分析  

Random Finite Element Analysis Based on Random Field and Monte-Carlo Method

作　　者：张小强[1] 韩宪军[1] 孟晓欢 

机构地区：[1]河南理工大学土木工程学院,河南焦作454000

出　　处：《洛阳理工学院学报（自然科学版）》2014年第4期27-30,54,共5页Journal of Luoyang Institute of Science and Technology：Natural Science Edition

基　　金：河南省教育厅自然科学研究计划项目(2009B130003);河南理工大学博士基金(B2009-13);河南省高等学校:深部矿井建设重点学科开放实验室开放基金(2012KF-04)

摘　　要：首先利用所分析的工程结构建立随机场,对随机场进行离散处理,然后求得所需的特征量协方差矩阵,把协方差矩阵进行Cholesky分解,用Cholesky分解后的特殊矩阵与对随机变量随机抽样得到的随机数矩阵作用得到所需随机变量的随机数,对进行随机场离散后的模型再进行有限元网格的离散,在此基础上对所建立的模型用有限元法进行求解。用Matlab编程来实现以上的分析和处理过程。通过算例表明:结合随机场和Monte-Carlo法与传统的monte-carlo法相比,在保证计算精度的前提下,可以有效地减少随机抽样的次数。Through the analyzed engineering structure,a random field is set up to obtain the required characteristic quality of covariance matrix in the discrete processing.The covariance matrix has a Cholesky decomposition to generate a special matrix which acts with the random matrix sampled from random variables to obtain the needed random numbers of the random variables.Finite grid discretization happens on the model with random field discretization,which offers a base for the solution to the setup model with finite element method.Matlab programming has been used to realize the above analysis and processing.Examples show that compared with the traditional monte-carlo method,the combination of random field and Monte-Carlo method will effectively reduce the random sample times with the calculation accuracy guaranteed.

关 键 词：随机场 协方差矩阵 MONTE-CARLO法 有限元法 

分 类 号：O242.21[理学—计算数学]