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Abstract:

This paper deals with the finite element approximation of the vibration modes of a laminated plate modeled by the Reissner-Mindlin equations; DL3 elements are used for the bending terms and standard piecewise linear continuous elements for the in-plane displacements. An a priori estimate of the regularity of the solution, independent of the plate thickness, is proved for the corresponding load problem. This allows using the abstract approximation theory for spectral problems to study the convergence of the proposed finite element method. Thus, optimal order error estimates including a double order for the vibration frequencies are obtained under appropriate assumptions. These estimates are independent of the plate thickness, which leads to the conclusion that the method is locking-free. Numerical tests are reported to assess the performance of the method. © 2011 American Mathematical Society.

Registro:

Documento: Artículo
Título:Numerical analysis of a finite element method to compute the vibration modes of a reissner-mindlin laminated plate
Autor:Durán, R.G.; Rodríguez, R.; Sanhueza, F.
Filiación:Departamento de Matemática, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, 1428, Buenos Aires, Argentina
CI2MA, Departamento de Ingeniería Matemática, Universidad de Concepción, Casilla 160-C, Concepción, Chile
Escuela de Obras Civiles, Universidad Andres Bello, Autopista 7100, Concepción, Chile
Palabras clave:Laminated plates; Reissner-Mindlin; Spectral problems
Año:2011
Volumen:80
Número:275
Página de inicio:1239
Página de fin:1264
DOI: http://dx.doi.org/10.1090/S0025-5718-2011-02456-7
Título revista:Mathematics of Computation
Título revista abreviado:Math. Comput.
ISSN:00255718
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00255718_v80_n275_p1239_Duran

Referencias:

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Citas:

---------- APA ----------
Durán, R.G., Rodríguez, R. & Sanhueza, F. (2011) . Numerical analysis of a finite element method to compute the vibration modes of a reissner-mindlin laminated plate. Mathematics of Computation, 80(275), 1239-1264.
http://dx.doi.org/10.1090/S0025-5718-2011-02456-7
---------- CHICAGO ----------
Durán, R.G., Rodríguez, R., Sanhueza, F. "Numerical analysis of a finite element method to compute the vibration modes of a reissner-mindlin laminated plate" . Mathematics of Computation 80, no. 275 (2011) : 1239-1264.
http://dx.doi.org/10.1090/S0025-5718-2011-02456-7
---------- MLA ----------
Durán, R.G., Rodríguez, R., Sanhueza, F. "Numerical analysis of a finite element method to compute the vibration modes of a reissner-mindlin laminated plate" . Mathematics of Computation, vol. 80, no. 275, 2011, pp. 1239-1264.
http://dx.doi.org/10.1090/S0025-5718-2011-02456-7
---------- VANCOUVER ----------
Durán, R.G., Rodríguez, R., Sanhueza, F. Numerical analysis of a finite element method to compute the vibration modes of a reissner-mindlin laminated plate. Math. Comput. 2011;80(275):1239-1264.
http://dx.doi.org/10.1090/S0025-5718-2011-02456-7