Geodesic
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

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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 : 10.1051/m2an/2010071
Classification : 65N25, 65N30, 74S05, 74K10
Keywords: finite element approximation, eigenvalue problems, Timoshenko beams 
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     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},
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     doi = {10.1051/m2an/2010071},
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     zbl = {1267.74049},
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     url = {http://geodesic.mathdoc.fr/articles/10.1051/m2an/2010071/}
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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

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