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, Volume 45 (2011) no. 4, p. 603-626

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.

DOI : https://doi.org/10.1051/m2an/2010071
Classification:  65N25,  65N30,  74S05,  74K10
Keywords: 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 - Mod\'elisation Math\'ematique et Analyse Num\'erique},
     publisher = {EDP-Sciences},
     volume = {45},
     number = {4},
     year = {2011},
     pages = {603-626},
     doi = {10.1051/m2an/2010071},
     zbl = {1267.74049},
     mrnumber = {2804652},
     language = {en},
     url = {http://www.numdam.org/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, Volume 45 (2011) no. 4, pp. 603-626. doi : 10.1051/m2an/2010071. http://www.numdam.org/item/M2AN_2011__45_4_603_0/

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