Volume 45, Number 4, July-August 2011
|Page(s)||603 - 626|
|Published online||10 December 2010|
A locking-free finite element method for the buckling problem of a non-homogeneous Timoshenko beam
Dipartimento di Matematica, Università di Pavia,
Via Ferrata 1, 27100 Pavia, Italy.
2 Departamento de Matemática, Facultad de Ciencias, Universidad del Bío Bío, Casilla 5-C, Concepción, Chile. email@example.com
3 CIMA, Departamento de Ingeniería Matemática, Universidad de Concepción, Casilla 160-C, Concepción, Chile. firstname.lastname@example.org
Revised: 15 July 2010
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.
Mathematics Subject Classification: 65N25 / 65N30 / 74S05 / 74K10
Key words: Finite element approximation / eigenvalue problems / Timoshenko beams
© EDP Sciences, SMAI, 2010
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.