A Modified Computational Scheme for the Stochastic Perturbation Finite Element Method

被引：25

作者：

Wu, Feng ^{[1
]}

Gao, Qiang ^{[1
]}

Xu, Xiao-Ming ^{[1
]}

Zhong, Wan-Xie ^{[1
]}

机构：

[1] Dalian Univ Technol, State Key Lab Struct Anal Ind Equipment, Dept Engn Mech, Fac Vehicle Engn & Mech, Dalian 116023, Peoples R China

来源：

LATIN AMERICAN JOURNAL OF SOLIDS AND STRUCTURES | 2015年 / 12卷 / 13期

关键词：

Stochastic finite element method; Uncertain structures; Perturbation; Computational scheme; REINFORCED COMPOSITE-MATERIAL; HOMOGENIZATION ANALYSIS; UNCERTAINTY;

D O I：

10.1590/1679-78251772

中图分类号：

TU [建筑科学];

学科分类号：

0813 ;

摘要：

A modified computational scheme of the stochastic perturbation finite element method (SPFEM) is developed for structures with low-level uncertainties. The proposed scheme can provide second-order estimates of the mean and variance without differentiating the system matrices with respect to the random variables. When the proposed scheme is used, it involves finite analyses of deterministic systems. In the case of one random variable with a symmetric probability density function, the proposed computational scheme can even provide a result with fifth-order accuracy. Compared with the traditional computational scheme of SPFEM, the proposed scheme is more convenient for numerical implementation. Four numerical examples demonstrate that the proposed scheme can be used in linear or nonlinear structures with correlated or uncorrelated random variables.

引用

页码：2480 / 2505

页数：26

共 32 条

[1] A fast Monte-Carlo method with a reduced basis of control variates applied to uncertainty propagation and Bayesian estimation [J].

Boyaval, Sebastien .

COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, 2012, 241 :190-205

[2] Finite element analysis of nonlinear shell structures with uncertain material property [J].

Chang, T. -P. ;

Liu, M. -F. ;

Chang, H. -C. .

THIN-WALLED STRUCTURES, 2008, 46 (10) :1055-1065

[3] Solution of stochastic partial differential equations using Galerkin finite element techniques [J].

Deb, MK ;

Babuska, IM ;

Oden, JT .

COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, 2001, 190 (48) :6359-6372

[4] An exact solution for the static and dynamic analysis of FE discretized uncertain structures [J].

Falsone, G. ;

Ferro, G. .

COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, 2007, 196 (21-24) :2390-2400

[5] A new approach for the stochastic analysis of finite element modelled structures with uncertain parameters [J].

Falsone, G ;

Impollonia, N .

COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, 2002, 191 (44) :5067-5085

[6] Sparse grid collocation schemes for stochastic natural convection problems [J].

Ganapathysubramanian, Baskar ;

Zabaras, Nicholas .

JOURNAL OF COMPUTATIONAL PHYSICS, 2007, 225 (01) :652-685

[7]

Holtz M., 2011, Sparse Grid Quadrature in High Dimensions with Applications in Finance and Insurance, volume 77 of Lecture Notes in Computational Science and Engineering

[8] Parallel processing in computational stochastic dynamics [J].

Johnson, EA ;

Proppe, C ;

Spencer, BF ;

Bergman, LA ;

Székely, GS ;

Schuëller, GI .

PROBABILISTIC ENGINEERING MECHANICS, 2003, 18 (01) :37-60

[9] On generalized stochastic perturbation-based finite element method [J].

Kaminski, M .

COMMUNICATIONS IN NUMERICAL METHODS IN ENGINEERING, 2006, 22 (01) :23-31

[10]

Kaminski M., 2013, STOCHASTIC PERTURBAT

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