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A piecewise linear finite element method for the buckling and the vibration problems of thin plates


Authors: David Mora and Rodolfo Rodríguez
Journal: Math. Comp. 78 (2009), 1891-1917
MSC (2000): Primary 65N25, 74K10, 65N30
DOI: https://doi.org/10.1090/S0025-5718-09-02228-5
Published electronically: February 3, 2009
MathSciNet review: 2521271
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Abstract: The aim of this paper is to analyze a piecewise linear finite element method to approximate the buckling and the vibration problems of a thin plate. The method is based on a conforming discretization of a bending moment formulation for the Kirchhoff-Love model. The analysis restricts to simply connected polygonal clamped plates, not necessarily convex. The method is proved to converge with optimal order for both spectral problems, including an improved order for the eigenvalues. Numerical experiments are reported to assess its performance and to compare it with other low-order finite element methods.


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Additional Information

David Mora
Affiliation: Departamento de Ingeniería Matemática, Universidad de Concepción, Casilla 160-C, Concepción, Chile
Email: david@ing-mat.udec.cl

Rodolfo Rodríguez
Affiliation: Departamento de Ingeniería Matemática, Universidad de Concepción, Casilla 160-C, Concepción, Chile
Email: rodolfo@ing-mat.udec.cl

DOI: https://doi.org/10.1090/S0025-5718-09-02228-5
Keywords: Buckling, Kirchhoff plates, spectral problems, low-order finite elements.
Received by editor(s): November 23, 2007
Received by editor(s) in revised form: September 3, 2008
Published electronically: February 3, 2009
Additional Notes: The first author was supported by a CONICYT fellowship (Chile).
The second author was partially supported by FONDAP and BASAL projects CMM, Universidad de Chile (Chile).
Article copyright: © Copyright 2009 American Mathematical Society

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