基于Karhunen-Loève级数的改进摄动随机有限元法  

Karhunen-Loève series based modified perturbed stochastic finite element method

作　　者：李秀梅[1] 邵湛钧 李朝阳[1] 张永兵[1] LI Xiu-mei;SHAO Zhan-jun;LI Zhao-yang;ZHANG Yong-bing(College of Civil Engineering and Architecture, Guangxi University, Nanning 530004, China)

机构地区：[1]广西大学土木建筑工程学院,广西南宁530004

出　　处：《广西大学学报（自然科学版）》2021年第1期74-82,共9页Journal of Guangxi University（Natural Science Edition）

基　　金：国家自然科学基金资助项目(51868004)。

摘　　要：为了更加准确快捷地对小变异情况下的结构进行随机分析,提出了基于Karhunen-Loève级数的改进摄动随机有限元法(KLSMPSFEM),并给出计算格式。利用Karhunen-Loève(K-L)级数展开法将随机场离散成若干随机变量,并研究了随机场的性质。将得到的随机变量代入改进的摄动随机有限元法进行计算,得到结构响应的二阶估计值,并将KLSMPSFEM与基于K-L级数的蒙特卡洛有限元法(MCM)、基于K-L级数的摄动随机有限元法(PSM)在二维随机场的情况下进行对比。结果表明:KLSMPSFEM的精度要高于PSM,效率要远高于MCM,且能处理一些PSM很难处理的问题。因此该方法是一种兼顾精度与效率的随机有限元法,可广泛应用于多种结构的随机分析。In order to analyze the structures with low-level uncertainties more accurately and efficiently,Karhunen-Loève series based modified perturbation stochastic finite element method(KLSMPSFEM for short)and its calculation procedures are proposed.Karhunen-Loève(K-L for short)series expansion method is applied to discretize random fields into random variables,and the properties of the random fields are studied.The random variables are substituted into modified perturbation stochastic finite element method to obtain the second-order estimates of the structural responses.KLSMPSFEM is taken to compare with Karhunen-Loève series based Monte-Carlo finite element method(MCM for short)and Karhunen-Loève series based perturbation stochastic finite element method(PSM for short)in the case of two-dimensional random fields.The results show that KLSMPSFEM is more accurate than PSM,and it is more efficient than MCM.At the same time,KLSMPSFEM can handle some problems,which are difficult to deal with by PSM.Therefore,KLSMPSFEM is a stochastic finite element method with both accuracy and efficiency,and it can be widely applied in stochastic analysis of various structures.

关 键 词：不确定性结构 随机场 Karhunen-Loève级数展开法 随机有限元法 摄动法 

分 类 号：O302[理学—力学]