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.
Mots-clés : finite element approximation, eigenvalue problems, Timoshenko beams
@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 },
pages = {603--626},
publisher = {EDP-Sciences},
volume = {45},
number = {4},
year = {2011},
doi = {10.1051/m2an/2010071},
mrnumber = {2804652},
zbl = {1267.74049},
language = {en},
url = {http://archive.numdam.org/articles/10.1051/m2an/2010071/}
}
TY - JOUR AU - Lovadina, Carlo AU - Mora, David AU - Rodríguez, Rodolfo TI - A locking-free finite element method for the buckling problem of a non-homogeneous Timoshenko beam JO - ESAIM: Mathematical Modelling and Numerical Analysis PY - 2011 SP - 603 EP - 626 VL - 45 IS - 4 PB - EDP-Sciences UR - http://archive.numdam.org/articles/10.1051/m2an/2010071/ DO - 10.1051/m2an/2010071 LA - en ID - M2AN_2011__45_4_603_0 ER -
%0 Journal Article %A Lovadina, Carlo %A Mora, David %A Rodríguez, Rodolfo %T A locking-free finite element method for the buckling problem of a non-homogeneous Timoshenko beam %J ESAIM: Mathematical Modelling and Numerical Analysis %D 2011 %P 603-626 %V 45 %N 4 %I EDP-Sciences %U http://archive.numdam.org/articles/10.1051/m2an/2010071/ %R 10.1051/m2an/2010071 %G en %F 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 , Tome 45 (2011) no. 4, pp. 603-626. doi : 10.1051/m2an/2010071. http://archive.numdam.org/articles/10.1051/m2an/2010071/
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