Nonintrusive parametric solutions in structural dynamics

Cavaliere, F.; Zlotnik, S.; Sevilla, Rubén; Larrayoz, X.; Díez, P.

doi:10.1016/j.cma.2021.114336

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Nonintrusive parametric solutions in structural dynamics

F. Cavaliere, S. Zlotnik, Rubén Sevilla

, X. Larrayoz, P. Díez

Computer Methods in Applied Mechanics and Engineering, Volume: 389, Start page: 114336

Swansea University Author: Rubén Sevilla

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DOI (Published version): 10.1016/j.cma.2021.114336

Abstract

A nonintrusive reduced order method able to solve a parametric modal analysis is proposed in this work. The main objective is being able to efficiently identify how a variation of user-dened parameters affects the dynamic response of the structure in terms of fundamental natural frequencies and corr...

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Published in:	Computer Methods in Applied Mechanics and Engineering
ISSN:	0045-7825
Published:	Elsevier BV 2022
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The main objective is being able to efficiently identify how a variation of user-dened parameters affects the dynamic response of the structure in terms of fundamental natural frequencies and corresponding mode shapes.A parametric version of the inverse power method (IPM) is presented by using the proper generalised decomposition (PGD) rationale. The proposed approach utilises the so-called encapsulated PGD toolbox and includes a new algorithm for computing the square root of a parametric object. With only one offline computation, the proposed PGD-IPM approach provides an analytical parametric expression of the smallest (in magnitude) eigenvalue (or natural frequency) and corresponding eigenvector (mode shape), which contains all the possible solutions for every combination of the parameters within pre-dened ranges. A Lagrange multiplier deation technique is introduced in order to compute subsequent eigenpairs, which is also valid to overcome the stiff-ness matrix singularity in the case of a free-free structure. The proposed approach is nonintrusive and it is therefore possible to be integrated with commercial nite element (FE) packages. Two numerical examples are shown to underline the properties of the technique. The rst example includes one material and one geometricparameter. The second example shows a more realistic industrial example, where the nonintrusivity of the approach is demonstrated by employing a commercial FE package for assembling the FE matrices. Finally, a multi-objective optimisation study is performed proving that the developed method could signicantly assist the decision-making during the preliminary phase of a new design process.</abstract><type>Journal Article</type><journal>Computer Methods in Applied Mechanics and Engineering</journal><volume>389</volume><journalNumber/><paginationStart>114336</paginationStart><paginationEnd/><publisher>Elsevier BV</publisher><placeOfPublication/><isbnPrint/><isbnElectronic/><issnPrint>0045-7825</issnPrint><issnElectronic/><keywords>Algebraic PGD; Parametric Modal Analysis; Reduced Order Model; Shape Optimisation</keywords><publishedDay>1</publishedDay><publishedMonth>2</publishedMonth><publishedYear>2022</publishedYear><publishedDate>2022-02-01</publishedDate><doi>10.1016/j.cma.2021.114336</doi><url/><notes/><college>COLLEGE NANME</college><department>Civil Engineering</department><CollegeCode>COLLEGE CODE</CollegeCode><DepartmentCode>CIVL</DepartmentCode><institution>Swansea University</institution><apcterm/><funders>This project is part of the Marie Skłodowska-Curie ITN-EJD ProTechTion funded by the European Union Horizon 2020 research and innovation program with Grant Number 764636. 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spelling	2022-10-31T19:14:47.9877390 v2 58773 2021-11-24 Nonintrusive parametric solutions in structural dynamics b542c87f1b891262844e95a682f045b6 0000-0002-0061-6214 Rubén Sevilla Rubén Sevilla true false 2021-11-24 CIVL A nonintrusive reduced order method able to solve a parametric modal analysis is proposed in this work. The main objective is being able to efficiently identify how a variation of user-dened parameters affects the dynamic response of the structure in terms of fundamental natural frequencies and corresponding mode shapes.A parametric version of the inverse power method (IPM) is presented by using the proper generalised decomposition (PGD) rationale. The proposed approach utilises the so-called encapsulated PGD toolbox and includes a new algorithm for computing the square root of a parametric object. With only one offline computation, the proposed PGD-IPM approach provides an analytical parametric expression of the smallest (in magnitude) eigenvalue (or natural frequency) and corresponding eigenvector (mode shape), which contains all the possible solutions for every combination of the parameters within pre-dened ranges. A Lagrange multiplier deation technique is introduced in order to compute subsequent eigenpairs, which is also valid to overcome the stiff-ness matrix singularity in the case of a free-free structure. The proposed approach is nonintrusive and it is therefore possible to be integrated with commercial nite element (FE) packages. Two numerical examples are shown to underline the properties of the technique. The rst example includes one material and one geometricparameter. The second example shows a more realistic industrial example, where the nonintrusivity of the approach is demonstrated by employing a commercial FE package for assembling the FE matrices. Finally, a multi-objective optimisation study is performed proving that the developed method could signicantly assist the decision-making during the preliminary phase of a new design process. Journal Article Computer Methods in Applied Mechanics and Engineering 389 114336 Elsevier BV 0045-7825 Algebraic PGD; Parametric Modal Analysis; Reduced Order Model; Shape Optimisation 1 2 2022 2022-02-01 10.1016/j.cma.2021.114336 COLLEGE NANME Civil Engineering COLLEGE CODE CIVL Swansea University This project is part of the Marie Skłodowska-Curie ITN-EJD ProTechTion funded by the European Union Horizon 2020 research and innovation program with Grant Number 764636. The work of Fabiola Cavaliere, Sergio Zlotnik and Pedro D´ıez is partially supported by the MCIN/AEI/10.13039/501100011033, Spain (Grant Number: PID2020-113463RB-C32, PID2020-113463RB-C33 and CEX2018-000797-S). Ruben Sevilla also acknowledges the support of the Engineering and Physical Sciences Research Council (Grant Number: EP/P033997/1). 2022-10-31T19:14:47.9877390 2021-11-24T14:11:37.8620725 Faculty of Science and Engineering School of Aerospace, Civil, Electrical, General and Mechanical Engineering - Civil Engineering F. Cavaliere 1 S. Zlotnik 2 Rubén Sevilla 0000-0002-0061-6214 3 X. Larrayoz 4 P. Díez 5 58773__22222__9f39f9a738584402b03807076e7cd41f.pdf 58773.pdf 2022-01-25T15:04:04.8794148 Output 2872778 application/pdf Version of Record true © 2021 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license true eng http://creativecommons.org/licenses/by-nc-nd/4.0/
title	Nonintrusive parametric solutions in structural dynamics
spellingShingle	Nonintrusive parametric solutions in structural dynamics Rubén Sevilla
title_short	Nonintrusive parametric solutions in structural dynamics
title_full	Nonintrusive parametric solutions in structural dynamics
title_fullStr	Nonintrusive parametric solutions in structural dynamics
title_full_unstemmed	Nonintrusive parametric solutions in structural dynamics
title_sort	Nonintrusive parametric solutions in structural dynamics
author_id_str_mv	b542c87f1b891262844e95a682f045b6
author_id_fullname_str_mv	b542c87f1b891262844e95a682f045b6_***_Rubén Sevilla
author	Rubén Sevilla
author2	F. Cavaliere S. Zlotnik Rubén Sevilla X. Larrayoz P. Díez
format	Journal article
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container_volume	389
container_start_page	114336
publishDate	2022
institution	Swansea University
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doi_str_mv	10.1016/j.cma.2021.114336
publisher	Elsevier BV
college_str	Faculty of Science and Engineering
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description	A nonintrusive reduced order method able to solve a parametric modal analysis is proposed in this work. The main objective is being able to efficiently identify how a variation of user-dened parameters affects the dynamic response of the structure in terms of fundamental natural frequencies and corresponding mode shapes.A parametric version of the inverse power method (IPM) is presented by using the proper generalised decomposition (PGD) rationale. The proposed approach utilises the so-called encapsulated PGD toolbox and includes a new algorithm for computing the square root of a parametric object. With only one offline computation, the proposed PGD-IPM approach provides an analytical parametric expression of the smallest (in magnitude) eigenvalue (or natural frequency) and corresponding eigenvector (mode shape), which contains all the possible solutions for every combination of the parameters within pre-dened ranges. A Lagrange multiplier deation technique is introduced in order to compute subsequent eigenpairs, which is also valid to overcome the stiff-ness matrix singularity in the case of a free-free structure. The proposed approach is nonintrusive and it is therefore possible to be integrated with commercial nite element (FE) packages. Two numerical examples are shown to underline the properties of the technique. The rst example includes one material and one geometricparameter. The second example shows a more realistic industrial example, where the nonintrusivity of the approach is demonstrated by employing a commercial FE package for assembling the FE matrices. Finally, a multi-objective optimisation study is performed proving that the developed method could signicantly assist the decision-making during the preliminary phase of a new design process.
published_date	2022-02-01T04:15:34Z
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score	10.997433

Nonintrusive parametric solutions in structural dynamics

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