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

Alessandra Vizzaccaro*, Arthur Givois, Pierluigi Longobardi, Yichang Shen, Jean François Deü, Loïc Salles, Cyril Touzé, Olivier Thomas

*Corresponding author for this work

Research output: Contribution to journalArticle (Academic Journal)peer-review

12 Citations (Scopus)
8 Downloads (Pure)

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.

Original languageEnglish
Pages (from-to)1293-1319
Number of pages27
JournalComputational Mechanics
Volume66
Issue number6
DOIs
Publication statusPublished - 2 Dec 2020

Keywords

  • reduced order modeling
  • geometric nonlinearities
  • three-dimensional effect
  • thickness modes
  • Modified STiffness Evaluation Procedure
  • nonlinear modes
  • modal derivatives

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