Approximation of the vibration modes of a plate by Reissner-Mindlin equations

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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 pa...

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Autor principal: Duran, Ricardo Guillermo
Publicado: 1999
Materias:
Eigenvalues
Mixed methods
Plates
Reissner-Mindlin
Acceso en línea:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00255718_v68_n228_p1447_Duran
http://hdl.handle.net/20.500.12110/paper_00255718_v68_n228_p1447_Duran
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Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
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spelling paper:paper_00255718_v68_n228_p1447_Duran2023-06-08T14:53:13Z Approximation of the vibration modes of a plate by Reissner-Mindlin equations Duran, Ricardo Guillermo Eigenvalues Mixed methods Plates Reissner-Mindlin 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. Fil:Durán, R.G. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. 1999 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00255718_v68_n228_p1447_Duran http://hdl.handle.net/20.500.12110/paper_00255718_v68_n228_p1447_Duran
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-134
collection Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
topic Eigenvalues
Mixed methods
Plates
Reissner-Mindlin
spellingShingle Eigenvalues
Mixed methods
Plates
Reissner-Mindlin
Duran, Ricardo Guillermo
Approximation of the vibration modes of a plate by Reissner-Mindlin equations
topic_facet Eigenvalues
Mixed methods
Plates
Reissner-Mindlin
description 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.
author Duran, Ricardo Guillermo
author_facet Duran, Ricardo Guillermo
author_sort Duran, Ricardo Guillermo
title Approximation of the vibration modes of a plate by Reissner-Mindlin equations
title_short Approximation of the vibration modes of a plate by Reissner-Mindlin equations
title_full Approximation of the vibration modes of a plate by Reissner-Mindlin equations
title_fullStr Approximation of the vibration modes of a plate by Reissner-Mindlin equations
title_full_unstemmed Approximation of the vibration modes of a plate by Reissner-Mindlin equations
title_sort approximation of the vibration modes of a plate by reissner-mindlin equations
publishDate 1999
url https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00255718_v68_n228_p1447_Duran
http://hdl.handle.net/20.500.12110/paper_00255718_v68_n228_p1447_Duran
work_keys_str_mv AT duranricardoguillermo approximationofthevibrationmodesofaplatebyreissnermindlinequations
_version_ 1768546103704158208

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