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Finite element of slender beams in finite transformations: a geometrically exact approach
Author(s) -
Boyer Frédéric,
Primault Dominique
Publication year - 2003
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.879
Subject(s) - finite element method , statics , beam (structure) , torsion (gastropod) , bernoulli's principle , euler's formula , extended finite element method , mathematics , numerical analysis , mathematical analysis , structural engineering , classical mechanics , physics , engineering , thermodynamics , medicine , surgery
This article is devoted to the modelling of thin beams undergoing finite deformations essentially due to bending and torsion and to their numerical resolution by the finite element method. The solution proposed here differs from the approaches usually implemented to treat thin beams, as it can be qualified as ‘geometrically exact’. Two numerical models are proposed. The first one is a non‐linear Euler–Bernoulli model while the second one is a non‐linear Rayleigh model. The finite element method is tested on several numerical examples in statics and dynamics, and validated through comparison with analytical solutions, experimental observations and the geometrically exact approach of the Reissner beam theory initiated by Simo. The numerical result shows that this approach is a good alternative to the modelling of non‐linear beams, especially in statics. Copyright © 2003 John Wiley & Sons, Ltd.