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Stochastic finite element response analysis using random eigenfunction expansion

S.E. Pryse, S. Adhikari, Sondipon Adhikari Orcid Logo

Computers & Structures, Volume: 192, Pages: 1 - 15

Swansea University Author: Sondipon Adhikari Orcid Logo

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DOI (Published version): 10.1016/j.compstruc.2017.06.014

Abstract

A mathematical form for the response of the stochastic finite element analysis of elliptical partial differential equations has been established through summing products of random scalars and random vectors. The method is based upon the eigendecomposition of a system's stiffness matrix. The com...

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Published in: Computers & Structures
ISSN: 0045-7949
Published: 2017
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URI: https://cronfa.swan.ac.uk/Record/cronfa34858
first_indexed 2017-08-03T14:42:40Z
last_indexed 2018-02-09T05:25:24Z
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spelling 2017-09-20T16:22:31.9888850 v2 34858 2017-08-03 Stochastic finite element response analysis using random eigenfunction expansion 4ea84d67c4e414f5ccbd7593a40f04d3 0000-0003-4181-3457 Sondipon Adhikari Sondipon Adhikari true false 2017-08-03 ACEM A mathematical form for the response of the stochastic finite element analysis of elliptical partial differential equations has been established through summing products of random scalars and random vectors. The method is based upon the eigendecomposition of a system's stiffness matrix. The computational reduction is achieved by only summing the dominant terms and by approximating the random eigenvalues and the random eigenvectors. An error analysis has been conducted to investigate the effect of the truncation and the approximations. Consequently, a novel error minimisation technique has been applied through the Galerkin error minimisation approach. This has been implemented by utilising the orthogonal nature of the random eigenvectors. The proposed method is used to solve three numerical examples: the bending of a stochastic beam, the flow through a porous media with stochastic permeability and the bending of a stochastic plate. The results obtained through the proposed random eigenfunction expansion approach are compared with those obtained by using direct Monte Carlo Simulations and by using polynomial chaos. Journal Article Computers & Structures 192 1 15 0045-7949 Stochastic differential equations; Eigenfunctions; Galerkin; Finite element; Eigendecomposition; Spectral decomposition; Reduced methods 30 11 2017 2017-11-30 10.1016/j.compstruc.2017.06.014 COLLEGE NANME Aerospace, Civil, Electrical, and Mechanical Engineering COLLEGE CODE ACEM Swansea University 2017-09-20T16:22:31.9888850 2017-08-03T09:40:54.6476306 Faculty of Science and Engineering School of Engineering and Applied Sciences - Uncategorised S.E. Pryse 1 S. Adhikari 2 Sondipon Adhikari 0000-0003-4181-3457 3 0034858-20092017162128.pdf pryse2017(2).pdf 2017-09-20T16:21:28.9330000 Output 1145649 application/pdf Accepted Manuscript true 2018-08-29T00:00:00.0000000 false eng
title Stochastic finite element response analysis using random eigenfunction expansion
spellingShingle Stochastic finite element response analysis using random eigenfunction expansion
Sondipon Adhikari
title_short Stochastic finite element response analysis using random eigenfunction expansion
title_full Stochastic finite element response analysis using random eigenfunction expansion
title_fullStr Stochastic finite element response analysis using random eigenfunction expansion
title_full_unstemmed Stochastic finite element response analysis using random eigenfunction expansion
title_sort Stochastic finite element response analysis using random eigenfunction expansion
author_id_str_mv 4ea84d67c4e414f5ccbd7593a40f04d3
author_id_fullname_str_mv 4ea84d67c4e414f5ccbd7593a40f04d3_***_Sondipon Adhikari
author Sondipon Adhikari
author2 S.E. Pryse
S. Adhikari
Sondipon Adhikari
format Journal article
container_title Computers & Structures
container_volume 192
container_start_page 1
publishDate 2017
institution Swansea University
issn 0045-7949
doi_str_mv 10.1016/j.compstruc.2017.06.014
college_str Faculty of Science and Engineering
hierarchytype
hierarchy_top_id facultyofscienceandengineering
hierarchy_top_title Faculty of Science and Engineering
hierarchy_parent_id facultyofscienceandengineering
hierarchy_parent_title Faculty of Science and Engineering
department_str School of Engineering and Applied Sciences - Uncategorised{{{_:::_}}}Faculty of Science and Engineering{{{_:::_}}}School of Engineering and Applied Sciences - Uncategorised
document_store_str 1
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description A mathematical form for the response of the stochastic finite element analysis of elliptical partial differential equations has been established through summing products of random scalars and random vectors. The method is based upon the eigendecomposition of a system's stiffness matrix. The computational reduction is achieved by only summing the dominant terms and by approximating the random eigenvalues and the random eigenvectors. An error analysis has been conducted to investigate the effect of the truncation and the approximations. Consequently, a novel error minimisation technique has been applied through the Galerkin error minimisation approach. This has been implemented by utilising the orthogonal nature of the random eigenvectors. The proposed method is used to solve three numerical examples: the bending of a stochastic beam, the flow through a porous media with stochastic permeability and the bending of a stochastic plate. The results obtained through the proposed random eigenfunction expansion approach are compared with those obtained by using direct Monte Carlo Simulations and by using polynomial chaos.
published_date 2017-11-30T13:14:59Z
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score 11.048042

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