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 “...
| Authors: | ; ; |
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| Format: | Article |
| Publication date: | 2023 |
| Country: | España |
| Institution: | Universitat Politècnica de Catalunya (UPC) |
| Repository: | UPCommons. Portal del coneixement obert de la UPC |
| Language: | English |
| OAI Identifier: | oai:upcommons.upc.edu:2117/383422 |
| Online Access: | https://hdl.handle.net/2117/383422 https://dx.doi.org/10.1016/j.cma.2023.115913 |
| Access Level: | Open access |
| Keyword: | 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 |
| _version_ | 1878729640560820224 |
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| author | Giuliodori Picco, Agustina|||0000-0002-8550-6953 |
| author2 | Hernández Ortega, Joaquín Alberto|||0000-0001-9334-4002 Soudah Prieto, Eduardo|||0000-0002-2301-4718 |
| author2_role | author author |
| author_browse | Giuliodori Picco, Agustina|||0000-0002-8550-6953 Hernández Ortega, Joaquín Alberto|||0000-0001-9334-4002 Soudah Prieto, Eduardo|||0000-0002-2301-4718 |
| 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 |
| collection | UPCommons. Portal del coneixement obert de la UPC |
| 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. |
| eu_rights_str_mv | openAccess |
| format | article |
| id | ES_0bfdfd8d2ed2b21b105fda37892ba01d |
| institution | Universitat Politècnica de Catalunya (UPC) |
| instname_str | Universitat Politècnica de Catalunya (UPC) |
| language | eng |
| network_acronym_str | ES |
| network_name_str | España |
| oai_identifier_str | oai:upcommons.upc.edu:2117/383422 |
| publishDate | 2023 |
| publishDateSort | 2023 |
| reponame_str | UPCommons. Portal del coneixement obert de la UPC |
| spelling | Multiscale modeling of prismatic heterogeneous structures based on a localized hyperreduced-order method Giuliodori Picco, Agustina|||0000-0002-8550-6953 Hernández Ortega, Joaquín Alberto|||0000-0001-9334-4002 Soudah Prieto, Eduardo|||0000-0002-2301-4718 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 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. 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 Reviewed https://hdl.handle.net/2117/383422 https://dx.doi.org/10.1016/j.cma.2023.115913 |
| 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 | 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_short | 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 |
| 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 |
| topic_facet | 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 |
| url | https://hdl.handle.net/2117/383422 https://dx.doi.org/10.1016/j.cma.2023.115913 |