Fast dynamical simulation combining harmonic-modal hybrid formulations with space separated representations
In our previous works, we addressed degenerated 3D domains by proposing the use of Proper Generalized Decomposition (PGD)-based separated representations, enabling efficient and accurate resolutions in complex geometries. Separately, we also developed a harmonic-modal analysis approach that combined...
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Elsevier
2025-03-01
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| Series: | Results in Engineering |
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| Online Access: | http://www.sciencedirect.com/science/article/pii/S2590123024021406 |
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| author | Claudia Germoso Sebastian Rodriguez Angelo Pasquale Francisco Chinesta |
| author_facet | Claudia Germoso Sebastian Rodriguez Angelo Pasquale Francisco Chinesta |
| author_sort | Claudia Germoso |
| collection | DOAJ |
| description | In our previous works, we addressed degenerated 3D domains by proposing the use of Proper Generalized Decomposition (PGD)-based separated representations, enabling efficient and accurate resolutions in complex geometries. Separately, we also developed a harmonic-modal analysis approach that combined modal and harmonic ingredients to efficiently perform time-integration of nonlinear soil behavior. This was achieved through the offline construction of a parametric dynamic response solution using PGD-based model order reduction techniques.Building upon these advancements, this paper extends the use of harmonic-modal hybrid formulations to dynamical problems in degenerated domains. The integration of space-separated representations allows for extremely fine 3D resolutions while maintaining computational complexity at a significantly reduced order of magnitude. The primary contribution of this work lies in coupling harmonic-modal analysis with space-separated representations, combining the strengths of these methods.The performance and versatility of the proposed approach are demonstrated through the resolution of three illustrative problems: a 3D thermal analysis of a thin plate, a laminated plate, and a 3D elastodynamic analysis of a plate. These examples highlight the method's capability to handle high-resolution 3D problems efficiently, reducing it to a sequence of 1D or 2D problems, enabling significant computational time savings compared to the Finite Element Method (FEM). |
| format | Article |
| id | doaj-art-10ce1c382ff54253811f2fc97d9c2413 |
| institution | Kabale University |
| issn | 2590-1230 |
| language | English |
| publishDate | 2025-03-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Results in Engineering |
| spelling | doaj-art-10ce1c382ff54253811f2fc97d9c24132025-01-11T06:41:53ZengElsevierResults in Engineering2590-12302025-03-0125103897Fast dynamical simulation combining harmonic-modal hybrid formulations with space separated representationsClaudia Germoso0Sebastian Rodriguez1Angelo Pasquale2Francisco Chinesta3Instituto tecnológico de Santo Domingo, Avenida de Los Próceres #49, Los Jardines del Norte 10602, Santo Domingo, 41704, Dominican RepublicPIMM Lab, Arts et Métiers Institute of Technology, 151 Boulevard de l'Hôpital, Paris, F-75013, France; ESI Group Chair @ Arts et Métiers Institute of Technology, 151 Boulevard de l'Hôpital, Paris, F-75013, FrancePIMM Lab, Arts et Métiers Institute of Technology, 151 Boulevard de l'Hôpital, Paris, F-75013, France; ESI Group Chair @ Arts et Métiers Institute of Technology, 151 Boulevard de l'Hôpital, Paris, F-75013, France; Corresponding author at: PIMM Lab, Arts et Métiers Institute of Technology, 151 Boulevard de l'Hôpital, Paris, F-75013, France.PIMM Lab, Arts et Métiers Institute of Technology, 151 Boulevard de l'Hôpital, Paris, F-75013, France; ESI Group Chair @ Arts et Métiers Institute of Technology, 151 Boulevard de l'Hôpital, Paris, F-75013, France; CNRS@CREATE LTD, 1 Create Way, #08-01 CREATE Tower, Singapore, 138602, SingaporeIn our previous works, we addressed degenerated 3D domains by proposing the use of Proper Generalized Decomposition (PGD)-based separated representations, enabling efficient and accurate resolutions in complex geometries. Separately, we also developed a harmonic-modal analysis approach that combined modal and harmonic ingredients to efficiently perform time-integration of nonlinear soil behavior. This was achieved through the offline construction of a parametric dynamic response solution using PGD-based model order reduction techniques.Building upon these advancements, this paper extends the use of harmonic-modal hybrid formulations to dynamical problems in degenerated domains. The integration of space-separated representations allows for extremely fine 3D resolutions while maintaining computational complexity at a significantly reduced order of magnitude. The primary contribution of this work lies in coupling harmonic-modal analysis with space-separated representations, combining the strengths of these methods.The performance and versatility of the proposed approach are demonstrated through the resolution of three illustrative problems: a 3D thermal analysis of a thin plate, a laminated plate, and a 3D elastodynamic analysis of a plate. These examples highlight the method's capability to handle high-resolution 3D problems efficiently, reducing it to a sequence of 1D or 2D problems, enabling significant computational time savings compared to the Finite Element Method (FEM).http://www.sciencedirect.com/science/article/pii/S2590123024021406Model-order reductionStructural dynamicsSeparated representationsHarmonic-modal analysis |
| spellingShingle | Claudia Germoso Sebastian Rodriguez Angelo Pasquale Francisco Chinesta Fast dynamical simulation combining harmonic-modal hybrid formulations with space separated representations Results in Engineering Model-order reduction Structural dynamics Separated representations Harmonic-modal analysis |
| title | Fast dynamical simulation combining harmonic-modal hybrid formulations with space separated representations |
| title_full | Fast dynamical simulation combining harmonic-modal hybrid formulations with space separated representations |
| title_fullStr | Fast dynamical simulation combining harmonic-modal hybrid formulations with space separated representations |
| title_full_unstemmed | Fast dynamical simulation combining harmonic-modal hybrid formulations with space separated representations |
| title_short | Fast dynamical simulation combining harmonic-modal hybrid formulations with space separated representations |
| title_sort | fast dynamical simulation combining harmonic modal hybrid formulations with space separated representations |
| topic | Model-order reduction Structural dynamics Separated representations Harmonic-modal analysis |
| url | http://www.sciencedirect.com/science/article/pii/S2590123024021406 |
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