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Locking‐free finite elements for shear deformable orthotropic thin‐walled beams
Author(s) -
Minghini F.,
Tullini N.,
Laudiero F.
Publication year - 2007
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.2034
Subject(s) - orthotropic material , torsion (gastropod) , timoshenko beam theory , isotropy , image warping , finite element method , hermitian matrix , beam (structure) , pure bending , structural engineering , mathematical analysis , geometry , physics , mathematics , bending , optics , engineering , medicine , surgery , quantum mechanics , artificial intelligence , computer science
Numerical models for finite element analyses of assemblages of thin‐walled open‐section profiles are presented. The assumed kinematical model is based on Timoshenko–Reissner theory so as to take shear strain effects of non‐uniform bending and torsion into account. Hence, strain elastic‐energy coupling terms arise between bending in the two principal planes and between bending and torsion. The adopted model holds for both isotropic and orthotropic beams. Several displacement interpolation fields are compared with the available numerical examples. In particular, some shape functions are obtained from ‘modified’ Hermitian polynomials that produce a locking‐free Timoshenko beam element. Analogously, numerical interpolation for torsional rotation and cross‐section warping are proposed resorting to one Hermitian and six Lagrangian formulation. Analyses of beams with mono‐symmetric and non‐symmetric cross‐sections are performed to verify convergence rate and accuracy of the proposed formulations, especially in the presence of coupling terms due to shear deformations, pointing out the decay length of end effects. Profiles made of both isotropic and fibre‐reinforced plastic materials are considered. The presented beam models are compared with results given by plate‐shell models. Copyright © 2007 John Wiley & Sons, Ltd.