The aim of this paper is to develop a finite element method which allows computing the buckling coefficients and modes of a non-homogeneous Timoshenko beam. Studying the spectral properties of a non-compact operator, we show that the relevant buckling coefficients correspond to isolated eigenvalues of finite multiplicity. Optimal order error estimates are proved for the eigenfunctions as well as a double order of convergence for the eigenvalues using classical abstract spectral approximation theory for non-compact operators. These estimates are valid independently of the thickness of the beam, which leads to the conclusion that the method is locking-free. Numerical tests are reported in order to assess the performance of the method.
@article{M2AN_2011__45_4_603_0,
author = {Lovadina, Carlo and Mora, David and Rodr\'\i guez, Rodolfo},
title = {A locking-free finite element method for the buckling problem of a non-homogeneous Timoshenko beam},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
volume = {45},
year = {2011},
pages = {603-626},
doi = {10.1051/m2an/2010071},
mrnumber = {2804652},
zbl = {1267.74049},
language = {en},
url = {http://dml.mathdoc.fr/item/M2AN_2011__45_4_603_0}
}
Lovadina, Carlo; Mora, David; Rodríguez, Rodolfo. A locking-free finite element method for the buckling problem of a non-homogeneous Timoshenko beam. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Tome 45 (2011) pp. 603-626. doi : 10.1051/m2an/2010071. http://gdmltest.u-ga.fr/item/M2AN_2011__45_4_603_0/
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