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A locking-free finite element method for the buckling problem of a non-homogeneous Timoshenko beam

Published online by Cambridge University Press:  10 December 2010

Carlo Lovadina ,
David Mora  and
Rodolfo Rodríguez
Carlo Lovadina
Affiliation:
Dipartimento di Matematica, Università di Pavia, Via Ferrata 1, 27100 Pavia, Italy. carlo.lovadina@unipv.it
David Mora
Affiliation:
Departamento de Matemática, Facultad de Ciencias, Universidad del Bío Bío, Casilla 5-C, Concepción, Chile. dmora@ubiobio.cl
Rodolfo Rodríguez
Affiliation:
CIMA, Departamento de Ingeniería Matemática, Universidad de Concepción, Casilla 160-C, Concepción, Chile. rodolfo@ing-mat.udec.cl
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Abstract

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.

Keywords

Finite element approximationeigenvalue problemsTimoshenko beams
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 45 , Issue 4 , July 2011 , pp. 603 - 626
Copyright
© EDP Sciences, SMAI, 2010

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