Artículo
Durán, R.G.; Hervella-Nieto, L.; Liberman, E.; Rodríguez, R.; Solomin, J. "Approximation of the vibration modes of a plate by Reissner-Mindlin equations" (1999) Mathematics of Computation. 68(228):1447-1463
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Abstract:
This paper deals with the approximation of the vibration modes of a plate modelled by the Reissner-Mindlin equations. It is well known that, in order to avoid locking, some kind of reduced integration or mixed interpolation has to be used when solving these equations by finite element methods. In particular, one of the most widely used procedures is the mixed interpolation tensorial components, based on the family of elements called MITC. We use the lowest order method of this family. Applying a general approximation theory for spectral problems, we obtain optimal order error estimates for the eigenvectors and the eigenvalues. Under mild assumptions, these estimates are valid with constants independent of the plate thickness. The optimal double order for the eigenvalues is derived from a corresponding L2-estimate for a load problem which is proven here. This optimal order L2-estimate is of interest in itself. Finally, we present several numerical examples showing the very good behavior of the numerical procedure even in some cases not covered by our theory.
Registro:
| Documento: | Artículo |
| Título: | Approximation of the vibration modes of a plate by Reissner-Mindlin equations |
| Autor: | Durán, R.G.; Hervella-Nieto, L.; Liberman, E.; Rodríguez, R.; Solomin, J. |
| Filiación: | Departamento de Matemática, Fac. de Ciencias Exactas y Naturales, Universidad de Buenos Aires, 1428 Buenos Aires, Argentina Depto. de Matemática Aplicada, Univ. de Santiago de Compostela, 15706 Santiago de Compostela, Spain Comn. Invest. Cie. Provincia B., Facultad de Ciencias Exactas, Universidad Nacional de La Plata, C.C. 172, 1900 La Plata, Argentina Depto. de Ing. Matemática, Universidad de Concepción, Casilla 4009, Concepción, Chile Departamento de Matemática, Facultad de Ciencias Exactas, Universidad Nacional de la Plata, C.C. 172, 1900 La Plata, Argentina |
| Palabras clave: | Eigenvalues; Mixed methods; Plates; Reissner-Mindlin |
| Año: | 1999 |
| Volumen: | 68 |
| Número: | 228 |
| Página de inicio: | 1447 |
| Página de fin: | 1463 |
| Título revista: | Mathematics of Computation |
| Título revista abreviado: | Math. Comput. |
| ISSN: | 00255718 |
| Registro: | https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00255718_v68_n228_p1447_Duran |
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Citas:
---------- APA ----------
Durán, R.G., Hervella-Nieto, L., Liberman, E., Rodríguez, R. & Solomin, J. (1999) . Approximation of the vibration modes of a plate by Reissner-Mindlin equations. Mathematics of Computation, 68(228), 1447-1463.Recuperado de https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00255718_v68_n228_p1447_Duran [ ]
---------- CHICAGO ----------
Durán, R.G., Hervella-Nieto, L., Liberman, E., Rodríguez, R., Solomin, J. "Approximation of the vibration modes of a plate by Reissner-Mindlin equations" . Mathematics of Computation 68, no. 228 (1999) : 1447-1463.Recuperado de https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00255718_v68_n228_p1447_Duran [ ]
---------- MLA ----------
Durán, R.G., Hervella-Nieto, L., Liberman, E., Rodríguez, R., Solomin, J. "Approximation of the vibration modes of a plate by Reissner-Mindlin equations" . Mathematics of Computation, vol. 68, no. 228, 1999, pp. 1447-1463.Recuperado de https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00255718_v68_n228_p1447_Duran [ ]
---------- VANCOUVER ----------
Durán, R.G., Hervella-Nieto, L., Liberman, E., Rodríguez, R., Solomin, J. Approximation of the vibration modes of a plate by Reissner-Mindlin equations. Math. Comput. 1999;68(228):1447-1463.Available from: https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00255718_v68_n228_p1447_Duran [ ]
