1. Non-intrusive reduced order modelling for the dynamics of geometrically nonlinear flat structures using three-dimensional finite elements
- Author
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Loic Salles, Arthur Givois, Yichang Shen, Alessandra Vizzaccaro, Olivier Thomas, Jean-François Deü, Pierluigi Longobardi, Cyril Touzé, Imperial College London, Laboratoire d’Ingénierie des Systèmes Physiques et Numériques (LISPEN), Arts et Métiers Sciences et Technologies, HESAM Université (HESAM)-HESAM Université (HESAM), Institut des Sciences de la mécanique et Applications industrielles (IMSIA - UMR 9219), Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-École Nationale Supérieure de Techniques Avancées (ENSTA Paris)-Centre National de la Recherche Scientifique (CNRS)-Université Paris-Saclay-EDF R&D (EDF R&D), EDF (EDF)-EDF (EDF), Conservatoire National des Arts et Métiers [CNAM] (CNAM), HESAM Université - Communauté d'universités et d'établissements Hautes écoles Sorbonne Arts et métiers université (HESAM)-HESAM Université - Communauté d'universités et d'établissements Hautes écoles Sorbonne Arts et métiers université (HESAM), Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-École Nationale Supérieure de Techniques Avancées (ENSTA Paris)-Université Paris-Saclay-Centre National de la Recherche Scientifique (CNRS)-EDF R&D (EDF R&D), and Laboratoire de Mécanique des Structures et des Systèmes Couplés (LMSSC)
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FOS: Computer and information sciences ,Technology ,geometric nonlinearities ,Computational Mechanics ,Degrees of freedom (statistics) ,02 engineering and technology ,0915 Interdisciplinary Engineering ,01 natural sciences ,Modal derivatives ,VIBRATIONS ,Nonlinear modes ,Computational Engineering, Finance, and Science (cs.CE) ,[SPI]Engineering Sciences [physics] ,0203 mechanical engineering ,Mécanique: Mécanique des structures [Sciences de l'ingénieur] ,Computer Science - Computational Engineering, Finance, and Science ,010301 acoustics ,Physics ,Applied Mathematics ,Mathematical analysis ,Stiffness ,Computational mathematics ,modal derivatives ,Finite element method ,Computational Mathematics ,020303 mechanical engineering & transports ,Computational Theory and Mathematics ,thickness modes ,Physical Sciences ,SPHERICAL-SHELLS ,Thickness modes ,medicine.symptom ,nonlinear modes ,BEHAVIOR ,0913 Mechanical Engineering ,Mathematics, Interdisciplinary Applications ,Reduced order modeling ,Structure (category theory) ,Ocean Engineering ,Context (language use) ,Mechanics ,COMPUTATION ,0905 Civil Engineering ,Modified STiffness Evaluation Procedure ,SYSTEMS ,0103 physical sciences ,medicine ,NORMAL-MODES ,Science & Technology ,IDENTIFICATION ,Mechanical Engineering ,REDUCTION METHOD ,three-dimensional effect ,[SPI.MECA.VIBR]Engineering Sciences [physics]/Mechanics [physics.med-ph]/Vibrations [physics.class-ph] ,FRAMEWORK ,Nonlinear system ,Modal ,[SPI.MECA.STRU]Engineering Sciences [physics]/Mechanics [physics.med-ph]/Structural mechanics [physics.class-ph] ,Three-dimensional effect ,Geometric nonlinearities ,TURBULENCE ,Mathematics ,reduced order modeling - Abstract
Non-intrusive methods have been used since two decades to derive reduced-order models for geometrically nonlinear structures, with a particular emphasis on the so-called STiffness Evaluation Procedure (STEP), relying on the static application of prescribed displacements in a finite-element context. We show that a particularly slow convergence of the modal expansion is observed when applying the method with 3D elements, because of nonlinear couplings occurring with very high frequency modes involving 3D thickness deformations. Focusing on the case of flat structures, we first show by computing all the modes of the structure that a converged solution can be exhibited by using either static condensation or normal form theory. We then show that static modal derivatives provide the same solution with fewer calculations. Finally, we propose a modified STEP, where the prescribed displacements are imposed solely on specific degrees of freedom of the structure, and show that this adjustment also provides efficiently a converged solution., Comment: 6 tables, 14 figures, 27 pages
- Published
- 2020
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