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Projection methods for stochastic dynamic systems: A frequency domain approach

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

Computer Methods in Applied Mechanics and Engineering, Volume: 338, Pages: 412 - 439

Swansea University Author: Sondipon Adhikari Orcid Logo

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DOI (Published version): 10.1016/j.cma.2018.04.025

Abstract

A collection of hybrid projection approaches are proposed for approximating the response of stochastic partial differential equations which describe structural dynamic systems. In this study, an optimal basis for the approximation of the response of a stochastically parametrized structural dynamic s...

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Published in: Computer Methods in Applied Mechanics and Engineering
ISSN: 00457825
Published: 2018
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URI: https://cronfa.swan.ac.uk/Record/cronfa39849
first_indexed 2018-05-01T19:39:34Z
last_indexed 2019-01-14T13:50:15Z
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spelling 2019-01-14T11:43:08.6987225 v2 39849 2018-05-01 Projection methods for stochastic dynamic systems: A frequency domain approach 4ea84d67c4e414f5ccbd7593a40f04d3 0000-0003-4181-3457 Sondipon Adhikari Sondipon Adhikari true false 2018-05-01 ACEM A collection of hybrid projection approaches are proposed for approximating the response of stochastic partial differential equations which describe structural dynamic systems. In this study, an optimal basis for the approximation of the response of a stochastically parametrized structural dynamic system has been computed from its generalized eigenmodes. By applying appropriate approximations in conjunction with a reduced set of modal basis functions, a collection of hybrid projection methods are obtained. These methods have been further improved by the implementation of a sample based Galerkin error minimization approach. In total six methods are presented and compared for numerical accuracy and computational efficiency. Expressions for the lower order statistical moments of the hybrid projection methods have been derived and discussed. The proposed methods have been implemented to solve two numerical examples: the bending of a Euler–Bernoulli cantilever beam and the bending of a Kirchhoff–Love plate where both structures have stochastic elastic parameters. The response and accuracy of the proposed methods are subsequently discussed and compared with the benchmark solution obtained using an expensive Monte Carlo method. Journal Article Computer Methods in Applied Mechanics and Engineering 338 412 439 00457825 Stochastic differential equations; Eigenfunctions; Galerkin; Finite element; Eigendecomposition; Projection methods; Reduced methods 31 12 2018 2018-12-31 10.1016/j.cma.2018.04.025 COLLEGE NANME Aerospace, Civil, Electrical, and Mechanical Engineering COLLEGE CODE ACEM Swansea University 2019-01-14T11:43:08.6987225 2018-05-01T15:37:39.9402398 Faculty of Science and Engineering School of Engineering and Applied Sciences - Uncategorised S.E. Pryse 1 A. Kundu 2 S. Adhikari 3 Sondipon Adhikari 0000-0003-4181-3457 4 0039849-01052018153923.pdf pryse2018.pdf 2018-05-01T15:39:23.9800000 Output 2046499 application/pdf Accepted Manuscript true 2019-05-01T00:00:00.0000000 true eng 0039849-12112018124854.pdf pryse2018(2).pdf 2018-11-12T12:48:54.1630000 Output 583075 application/pdf Version of Record true 2018-11-12T00:00:00.0000000 true eng
title Projection methods for stochastic dynamic systems: A frequency domain approach
spellingShingle Projection methods for stochastic dynamic systems: A frequency domain approach
Sondipon Adhikari
title_short Projection methods for stochastic dynamic systems: A frequency domain approach
title_full Projection methods for stochastic dynamic systems: A frequency domain approach
title_fullStr Projection methods for stochastic dynamic systems: A frequency domain approach
title_full_unstemmed Projection methods for stochastic dynamic systems: A frequency domain approach
title_sort Projection methods for stochastic dynamic systems: A frequency domain approach
author_id_str_mv 4ea84d67c4e414f5ccbd7593a40f04d3
author_id_fullname_str_mv 4ea84d67c4e414f5ccbd7593a40f04d3_***_Sondipon Adhikari
author Sondipon Adhikari
author2 S.E. Pryse
A. Kundu
S. Adhikari
Sondipon Adhikari
format Journal article
container_title Computer Methods in Applied Mechanics and Engineering
container_volume 338
container_start_page 412
publishDate 2018
institution Swansea University
issn 00457825
doi_str_mv 10.1016/j.cma.2018.04.025
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
active_str 0
description A collection of hybrid projection approaches are proposed for approximating the response of stochastic partial differential equations which describe structural dynamic systems. In this study, an optimal basis for the approximation of the response of a stochastically parametrized structural dynamic system has been computed from its generalized eigenmodes. By applying appropriate approximations in conjunction with a reduced set of modal basis functions, a collection of hybrid projection methods are obtained. These methods have been further improved by the implementation of a sample based Galerkin error minimization approach. In total six methods are presented and compared for numerical accuracy and computational efficiency. Expressions for the lower order statistical moments of the hybrid projection methods have been derived and discussed. The proposed methods have been implemented to solve two numerical examples: the bending of a Euler–Bernoulli cantilever beam and the bending of a Kirchhoff–Love plate where both structures have stochastic elastic parameters. The response and accuracy of the proposed methods are subsequently discussed and compared with the benchmark solution obtained using an expensive Monte Carlo method.
published_date 2018-12-31T19:35:50Z
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score 11.048302

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