Multiscale modeling of prismatic heterogeneous structures based on a localized hyperreduced-order method

This work aims at deriving special types of one-dimensional Finite Elements (1D FE) for efficiently modeling heterogeneous prismatic structures, in the small strains regime, by means of reduced-order modeling (ROM) and domain decomposition techniques. The employed partitioning framework introduces “...

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Autores: Giuliodori Picco, Agustina|||0000-0002-8550-6953, Hernández Ortega, Joaquín Alberto|||0000-0001-9334-4002, Soudah Prieto, Eduardo|||0000-0002-2301-4718
Tipo de recurso: artículo
Fecha de publicación:2023
País:España
Institución:Universitat Politècnica de Catalunya (UPC)
Repositorio:UPCommons. Portal del coneixement obert de la UPC
Idioma:inglés
OAI Identifier:oai:upcommons.upc.edu:2117/383422
Acceso en línea:https://hdl.handle.net/2117/383422
https://dx.doi.org/10.1016/j.cma.2023.115913
Access Level:acceso abierto
Palabra clave:Orthogonal decompositions
Multiscale method
Reduced-order modeling
Localized model order reduction
Singular value decomposition
Domain decomposition
Finite element analysis
Descomposició (Matemàtica)
Àrees temàtiques de la UPC::Matemàtiques i estadística::Anàlisi numèrica::Mètodes numèrics
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repository_id_str
spelling Multiscale modeling of prismatic heterogeneous structures based on a localized hyperreduced-order methodGiuliodori Picco, Agustina|||0000-0002-8550-6953Hernández Ortega, Joaquín Alberto|||0000-0001-9334-4002Soudah Prieto, Eduardo|||0000-0002-2301-4718Orthogonal decompositionsMultiscale methodReduced-order modelingLocalized model order reductionSingular value decompositionDomain decompositionFinite element analysisDescomposició (Matemàtica)Àrees temàtiques de la UPC::Matemàtiques i estadística::Anàlisi numèrica::Mètodes numèricsThis work aims at deriving special types of one-dimensional Finite Elements (1D FE) for efficiently modeling heterogeneous prismatic structures, in the small strains regime, by means of reduced-order modeling (ROM) and domain decomposition techniques. The employed partitioning framework introduces “fictitious” interfaces between contiguous subdomains, leading to a formulation with both subdomain and interface fields. We propose a low-dimensional parameterization at both subdomain and interface levels by using reduced-order bases precomputed in an offline stage by applying the Singular Value Decomposition (SVD) on solution snapshots. In this parameterization, the amplitude of the fictitious interfaces play the role of coarse-scale displacement unknowns. We demonstrate that, with this partitioned framework, it is possible to arrive at a solution strategy that avoids solving the typical nested local/global problem of other similar methods (such as the FE method). Rather, in our approach, the coarse-grid cells can be regarded as special types of finite elements, whose nodes coincides with the centroids of the interfaces, and whose kinematics are dictated by the modes of the “fictitious” interfaces. This means that the kinematics of our coarse-scale FE are not pre-defined by the user, but extracted from the set of “training” computational experiments. Likewise, we demonstrate that the coarse-scale and fine-scale displacements are related by inter-scale operators that can be precomputed in the offline stage. Lastly, a hyperreduced scheme is considered for the evaluation of the internal forces, allowing us to deal with possible material nonlinearities.This work has received support from the Spanish Ministry of Economy and Competitiveness, through the “Severo Ochoa Programme for Centres of Excellence in R&D” (CEX2018-000797-S)”. A. Giuliodori also gratefully acknowledges the support of “Secretaria d’Universitats i Recerca de la Generalitat de Catalunya i del Fons Social Europeu” through the FI grant (00939/2020), and J.A. Hernández the support of, on the one hand, the European High-Performance Computing Joint Undertaking (JU) under grant agreement No. 955558 (the JU receives, in turn, support from the European Union’s Horizon 2020 research and innovation program and from Spain, Germany, France, Italy, Poland, Switzerland, Norway), and the European Union’s Horizon 2020 research and innovation program under Grant Agreement No. 952966 (project FIBREGY).Peer Reviewed20232023-03-0120232023-02-15journal articlehttp://purl.org/coar/resource_type/c_6501VoRhttp://purl.org/coar/version/c_970fb48d4fbd8a85info:eu-repo/semantics/articleapplication/pdfhttps://hdl.handle.net/2117/383422https://dx.doi.org/10.1016/j.cma.2023.115913reponame:UPCommons. Portal del coneixement obert de la UPCinstname:Universitat Politècnica de Catalunya (UPC)InglésengEuropean Commission http://doi.org/10.13039/100010661 Horizon 2020 Framework Programme 952966 Development, engineering, production and life-cycle management of improved FIBRE-based material solutions for structure and functional components of large offshore wind enerGY and tidal power platformopen accesshttp://purl.org/coar/access_right/c_abf2Attribution-NonCommercial-NoDerivatives 4.0 Internationalhttp://creativecommons.org/licenses/by-nc-nd/4.0/info:eu-repo/semantics/openAccessoai:upcommons.upc.edu:2117/3834222026-05-27T15:37:01Z
dc.title.none.fl_str_mv Multiscale modeling of prismatic heterogeneous structures based on a localized hyperreduced-order method
title Multiscale modeling of prismatic heterogeneous structures based on a localized hyperreduced-order method
spellingShingle Multiscale modeling of prismatic heterogeneous structures based on a localized hyperreduced-order method
Giuliodori Picco, Agustina|||0000-0002-8550-6953
Orthogonal decompositions
Multiscale method
Reduced-order modeling
Localized model order reduction
Singular value decomposition
Domain decomposition
Finite element analysis
Descomposició (Matemàtica)
Àrees temàtiques de la UPC::Matemàtiques i estadística::Anàlisi numèrica::Mètodes numèrics
title_short Multiscale modeling of prismatic heterogeneous structures based on a localized hyperreduced-order method
title_full Multiscale modeling of prismatic heterogeneous structures based on a localized hyperreduced-order method
title_fullStr Multiscale modeling of prismatic heterogeneous structures based on a localized hyperreduced-order method
title_full_unstemmed Multiscale modeling of prismatic heterogeneous structures based on a localized hyperreduced-order method
title_sort Multiscale modeling of prismatic heterogeneous structures based on a localized hyperreduced-order method
dc.creator.none.fl_str_mv Giuliodori Picco, Agustina|||0000-0002-8550-6953
Hernández Ortega, Joaquín Alberto|||0000-0001-9334-4002
Soudah Prieto, Eduardo|||0000-0002-2301-4718
author Giuliodori Picco, Agustina|||0000-0002-8550-6953
author_facet Giuliodori Picco, Agustina|||0000-0002-8550-6953
Hernández Ortega, Joaquín Alberto|||0000-0001-9334-4002
Soudah Prieto, Eduardo|||0000-0002-2301-4718
author_role author
author2 Hernández Ortega, Joaquín Alberto|||0000-0001-9334-4002
Soudah Prieto, Eduardo|||0000-0002-2301-4718
author2_role author
author
dc.subject.none.fl_str_mv Orthogonal decompositions
Multiscale method
Reduced-order modeling
Localized model order reduction
Singular value decomposition
Domain decomposition
Finite element analysis
Descomposició (Matemàtica)
Àrees temàtiques de la UPC::Matemàtiques i estadística::Anàlisi numèrica::Mètodes numèrics
topic Orthogonal decompositions
Multiscale method
Reduced-order modeling
Localized model order reduction
Singular value decomposition
Domain decomposition
Finite element analysis
Descomposició (Matemàtica)
Àrees temàtiques de la UPC::Matemàtiques i estadística::Anàlisi numèrica::Mètodes numèrics
description This work aims at deriving special types of one-dimensional Finite Elements (1D FE) for efficiently modeling heterogeneous prismatic structures, in the small strains regime, by means of reduced-order modeling (ROM) and domain decomposition techniques. The employed partitioning framework introduces “fictitious” interfaces between contiguous subdomains, leading to a formulation with both subdomain and interface fields. We propose a low-dimensional parameterization at both subdomain and interface levels by using reduced-order bases precomputed in an offline stage by applying the Singular Value Decomposition (SVD) on solution snapshots. In this parameterization, the amplitude of the fictitious interfaces play the role of coarse-scale displacement unknowns. We demonstrate that, with this partitioned framework, it is possible to arrive at a solution strategy that avoids solving the typical nested local/global problem of other similar methods (such as the FE method). Rather, in our approach, the coarse-grid cells can be regarded as special types of finite elements, whose nodes coincides with the centroids of the interfaces, and whose kinematics are dictated by the modes of the “fictitious” interfaces. This means that the kinematics of our coarse-scale FE are not pre-defined by the user, but extracted from the set of “training” computational experiments. Likewise, we demonstrate that the coarse-scale and fine-scale displacements are related by inter-scale operators that can be precomputed in the offline stage. Lastly, a hyperreduced scheme is considered for the evaluation of the internal forces, allowing us to deal with possible material nonlinearities.
publishDate 2023
dc.date.none.fl_str_mv 2023
2023-03-01
2023
2023-02-15
dc.type.none.fl_str_mv journal article
http://purl.org/coar/resource_type/c_6501
VoR
http://purl.org/coar/version/c_970fb48d4fbd8a85
dc.type.openaire.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv https://hdl.handle.net/2117/383422
https://dx.doi.org/10.1016/j.cma.2023.115913
url https://hdl.handle.net/2117/383422
https://dx.doi.org/10.1016/j.cma.2023.115913
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.relation.none.fl_str_mv European Commission http://doi.org/10.13039/100010661 Horizon 2020 Framework Programme 952966 Development, engineering, production and life-cycle management of improved FIBRE-based material solutions for structure and functional components of large offshore wind enerGY and tidal power platform
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2
Attribution-NonCommercial-NoDerivatives 4.0 International
http://creativecommons.org/licenses/by-nc-nd/4.0/
dc.rights.openaire.fl_str_mv info:eu-repo/semantics/openAccess
rights_invalid_str_mv open access
http://purl.org/coar/access_right/c_abf2
Attribution-NonCommercial-NoDerivatives 4.0 International
http://creativecommons.org/licenses/by-nc-nd/4.0/
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.source.none.fl_str_mv reponame:UPCommons. Portal del coneixement obert de la UPC
instname:Universitat Politècnica de Catalunya (UPC)
instname_str Universitat Politècnica de Catalunya (UPC)
reponame_str UPCommons. Portal del coneixement obert de la UPC
collection UPCommons. Portal del coneixement obert de la UPC
repository.name.fl_str_mv
repository.mail.fl_str_mv
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