Comparison of Reduction Methods for Finite Element Geometrically Nonlinear Beam Structures
Yichang Shen,Alessandra Vizzaccaro,Nassim Kesmia,Ting Yu,Loic Salles,Olivier Thomas,Cyril Touzé +6 more
- Vol. 4, Iss: 1, pp 175-204
TLDR
In this paper, numerical comparisons of model-order reduction methods for geometrically nonlinear structures in the general framework of finite element (FE) procedures are presented, and a simple analytical example is used to analyze how different treatments of quadratic nonlinearities by the three methods can affect the predictions.Abstract:
The aim of this contribution is to present numerical comparisons of model-order reduction methods for geometrically nonlinear structures in the general framework of finite element (FE) procedures. Three different methods are compared: the implicit condensation and expansion (ICE), the quadratic manifold computed from modal derivatives (MD), and the direct normal form (DNF) procedure, the latter expressing the reduced dynamics in an invariant-based span of the phase space. The methods are first presented in order to underline their common points and differences, highlighting in particular that ICE and MD use reduction subspaces that are not invariant. A simple analytical example is then used in order to analyze how the different treatments of quadratic nonlinearities by the three methods can affect the predictions. Finally, three beam examples are used to emphasize the ability of the methods to handle curvature (on a curved beam), 1:1 internal resonance (on a clamped-clamped beam with two polarizations), and inertia nonlinearity (on a cantilever beam).read more
Citations
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Journal ArticleDOI
Model order reduction methods for geometrically nonlinear structures: a review of nonlinear techniques
TL;DR: In this article, a review of nonlinear methods for model order reduction in structures with geometric nonlinearity is presented, with a special emphasis on the techniques based on invariant manifold theory.
Journal ArticleDOI
Direct computation of nonlinear mapping via normal form for reduced-order models of finite element nonlinear structures
TL;DR: The direct computation of the third-order normal form for a geometrically nonlinear structure discretised with the finite element (FE) method, is detailed, allowing to define a nonlinear mapping in order to derive accurate reduced-order models (ROM) relying on invariant manifold theory.
Journal ArticleDOI
Model order reduction based on direct normal form: application to large finite element MEMS structures featuring internal resonance
TL;DR: A reduction method based on direct normal form computation for large finite element (FE) models is detailed, avoiding the computation of the complete eigenfunctions spectrum and making a direct link with the parametrisation of invariant manifolds.
Journal ArticleDOI
High order direct parametrisation of invariant manifolds for model order reduction of finite element structures: application to large amplitude vibrations and uncovering of a folding point
TL;DR: In this article , the parametrisation method of invariant manifolds is used and adapted to the case of mechanical systems in oscillatory form expressed in the physical basis, so that the technique is directly applicable to mechanical problems discretised by the finite element method.
Posted Content
High order direct parametrisation of invariant manifolds for model order reduction of finite element structures: application to large amplitude vibrations and uncovering of a folding point.
Alessandra Vizzaccaro,Alessandra Vizzaccaro,Andrea Opreni,Loic Salles,Attilio Frangi,Cyril Touzé +5 more
TL;DR: In this paper, the parametrisation method of invariant manifolds is used and adapted to the case of mechanical systems expressed in the physical basis, so that the technique is directly applicable to problems discretised by the finite element method.
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