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Non-intrusive reduced order modelling for the dynamics of geometrically nonlinear flat structures using three-dimensional finite elements

Type
Articles dans des revues avec comité de lecture
Author
VIZZACCARO, Alessandra
69530 Imperial College London
GIVOIS, Arthur
12568 Laboratoire de Mécanique des Structures et des Systèmes Couplés [LMSSC]
543315 Laboratoire d’Ingénierie des Systèmes Physiques et Numériques [LISPEN]
LONGOBARDI, Pierluigi
69530 Imperial College London
SHEN, Yichang
421305 Institut des Sciences de la mécanique et Applications industrielles [IMSIA - UMR 9219]
DEÜ, Jean-François
12568 Laboratoire de Mécanique des Structures et des Systèmes Couplés [LMSSC]
SALLES, Loïc
69530 Imperial College London
TOUZÉ, Cyril
421305 Institut des Sciences de la mécanique et Applications industrielles [IMSIA - UMR 9219]
THOMAS, Olivier
543315 Laboratoire d’Ingénierie des Systèmes Physiques et Numériques [LISPEN]

URI
http://hdl.handle.net/10985/19598
DOI
10.1007/s00466-020-01902-5
Date
2020
Journal
Computational Mechanics

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.

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