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

Mostrar todas las versiones(3)

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...

Descripción completa

Detalles Bibliográficos
Autores principales: Durán, Ricardo Guillermo, Hervella Nieto, L., Liberman, Elsa, Rodríguez, Rodolfo, Solomín, Jorge Eduardo
Formato: Articulo
Lenguaje:Inglés
Publicado: 1999
Materias:
Matemática
Eigenfunction
Mathematical analysis
Finite element method
Approximation theory
Eigenvalues and eigenvectors
Interpolation
Elliptic curve
Vibration
Normal mode
Mathematics
Acceso en línea:http://sedici.unlp.edu.ar/handle/10915/123520
Aporte de:
SEDICI (UNLP) de Universidad Nacional de La Plata
id I19-R120-10915-123520
record_format dspace
institution Universidad Nacional de La Plata
institution_str I-19
repository_str R-120
collection SEDICI (UNLP)
language Inglés
topic Matemática
Eigenfunction
Mathematical analysis
Finite element method
Approximation theory
Eigenvalues and eigenvectors
Interpolation
Elliptic curve
Vibration
Normal mode
Mathematics
spellingShingle Matemática
Eigenfunction
Mathematical analysis
Finite element method
Approximation theory
Eigenvalues and eigenvectors
Interpolation
Elliptic curve
Vibration
Normal mode
Mathematics
Durán, Ricardo Guillermo
Hervella Nieto, L.
Liberman, Elsa
Rodríguez, Rodolfo
Solomín, Jorge Eduardo
Approximation of the vibration modes of a plate by Reissner-Mindlin equations
topic_facet Matemática
Eigenfunction
Mathematical analysis
Finite element method
Approximation theory
Eigenvalues and eigenvectors
Interpolation
Elliptic curve
Vibration
Normal mode
Mathematics
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 L 2 -estimate for a load problem which is proven here. This optimal order L 2 -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.
format Articulo
Articulo
author Durán, Ricardo Guillermo
Hervella Nieto, L.
Liberman, Elsa
Rodríguez, Rodolfo
Solomín, Jorge Eduardo
author_facet Durán, Ricardo Guillermo
Hervella Nieto, L.
Liberman, Elsa
Rodríguez, Rodolfo
Solomín, Jorge Eduardo
author_sort Durán, 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 http://sedici.unlp.edu.ar/handle/10915/123520
work_keys_str_mv AT duranricardoguillermo approximationofthevibrationmodesofaplatebyreissnermindlinequations
AT hervellanietol approximationofthevibrationmodesofaplatebyreissnermindlinequations
AT libermanelsa approximationofthevibrationmodesofaplatebyreissnermindlinequations
AT rodriguezrodolfo approximationofthevibrationmodesofaplatebyreissnermindlinequations
AT solominjorgeeduardo approximationofthevibrationmodesofaplatebyreissnermindlinequations
bdutipo_str Repositorios
_version_ 1764820449695367168

Ejemplares similares