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timoshenko beams

ESAIM: Mathematical Modelling and Numerical Analysis (1)

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A locking-free finite element method for the buckling problem of a non-homogeneous Timoshenko beam
Carlo Lovadina, David Mora, Rodolfo Rodríguez
Journal:

ESAIM: Mathematical Modelling and Numerical Analysis / Volume 45 / Issue 4 / July 2011

Published online by Cambridge University Press:

10 December 2010, pp. 603-626

Print publication:

July 2011
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The aim of this paper is to develop a finite element method which allows computingthe 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 isolatedeigenvalues of finite multiplicity.Optimal order error estimates are proved for the eigenfunctionsas well as a double order of convergence forthe eigenvalues using classical abstract spectral approximation theory for non-compact operators.These estimates are valid independently of the thickness of the beam, whichleads to the conclusion that the method is locking-free.Numerical tests are reported in order to assess the performance of the method.