Numerical analysis of a finite element method to compute the vibration modes of a Reissner-Mindlin laminated plate

Autores
Duran, Ricardo Guillermo; Rodríguez, Rodolfo; Sanhueza, Frank
Año de publicación
2011
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
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.
Fil: Duran, Ricardo Guillermo. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; Argentina
Fil: Rodríguez, Rodolfo. Universidad de Concepción; Chile
Fil: Sanhueza, Frank. Universidad de Concepción; Chile
Materia
REISSNER-MINDLIN
LAMINATED PLATES
SPECTRAL PROBLEMS
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/14918
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/14918
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repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling Numerical analysis of a finite element method to compute the vibration modes of a Reissner-Mindlin laminated plateDuran, Ricardo GuillermoRodríguez, RodolfoSanhueza, FrankREISSNER-MINDLINLAMINATED PLATESSPECTRAL PROBLEMShttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1This 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.Fil: Duran, Ricardo Guillermo. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; ArgentinaFil: Rodríguez, Rodolfo. Universidad de Concepción; ChileFil: Sanhueza, Frank. Universidad de Concepción; ChileAmerican Mathematical Society2011-10info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/14918Duran, Ricardo Guillermo; Rodríguez, Rodolfo; Sanhueza, Frank; Numerical analysis of a finite element method to compute the vibration modes of a Reissner-Mindlin laminated plate; American Mathematical Society; Mathematics Of Computation; 80; 275; 10-2011; 1239-12640025-5718enginfo:eu-repo/semantics/altIdentifier/url/http://www.ams.org/journals/mcom/2011-80-275/S0025-5718-2011-02456-7/info:eu-repo/semantics/altIdentifier/doi/10.1090/S0025-5718-2011-02456-7info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-29T09:56:51Zoai:ri.conicet.gov.ar:11336/14918instacron:CONICETInstitucionalhttp://ri.conicet.gov.ar/Organismo científico-tecnológicoNo correspondehttp://ri.conicet.gov.ar/oai/requestdasensio@conicet.gov.ar; lcarlino@conicet.gov.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:34982025-09-29 09:56:51.484CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Numerical analysis of a finite element method to compute the vibration modes of a Reissner-Mindlin laminated plate
title Numerical analysis of a finite element method to compute the vibration modes of a Reissner-Mindlin laminated plate
spellingShingle Numerical analysis of a finite element method to compute the vibration modes of a Reissner-Mindlin laminated plate
Duran, Ricardo Guillermo
REISSNER-MINDLIN
LAMINATED PLATES
SPECTRAL PROBLEMS
title_short Numerical analysis of a finite element method to compute the vibration modes of a Reissner-Mindlin laminated plate
title_full Numerical analysis of a finite element method to compute the vibration modes of a Reissner-Mindlin laminated plate
title_fullStr Numerical analysis of a finite element method to compute the vibration modes of a Reissner-Mindlin laminated plate
title_full_unstemmed Numerical analysis of a finite element method to compute the vibration modes of a Reissner-Mindlin laminated plate
title_sort Numerical analysis of a finite element method to compute the vibration modes of a Reissner-Mindlin laminated plate
dc.creator.none.fl_str_mv Duran, Ricardo Guillermo
Rodríguez, Rodolfo
Sanhueza, Frank
author Duran, Ricardo Guillermo
author_facet Duran, Ricardo Guillermo
Rodríguez, Rodolfo
Sanhueza, Frank
author_role author
author2 Rodríguez, Rodolfo
Sanhueza, Frank
author2_role author
author
dc.subject.none.fl_str_mv REISSNER-MINDLIN
LAMINATED PLATES
SPECTRAL PROBLEMS
topic REISSNER-MINDLIN
LAMINATED PLATES
SPECTRAL PROBLEMS
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv 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.
Fil: Duran, Ricardo Guillermo. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; Argentina
Fil: Rodríguez, Rodolfo. Universidad de Concepción; Chile
Fil: Sanhueza, Frank. Universidad de Concepción; Chile
description 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.
publishDate 2011
dc.date.none.fl_str_mv 2011-10
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
http://purl.org/coar/resource_type/c_6501
info:ar-repo/semantics/articulo
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/11336/14918
Duran, Ricardo Guillermo; Rodríguez, Rodolfo; Sanhueza, Frank; Numerical analysis of a finite element method to compute the vibration modes of a Reissner-Mindlin laminated plate; American Mathematical Society; Mathematics Of Computation; 80; 275; 10-2011; 1239-1264
0025-5718
url http://hdl.handle.net/11336/14918
identifier_str_mv Duran, Ricardo Guillermo; Rodríguez, Rodolfo; Sanhueza, Frank; Numerical analysis of a finite element method to compute the vibration modes of a Reissner-Mindlin laminated plate; American Mathematical Society; Mathematics Of Computation; 80; 275; 10-2011; 1239-1264
0025-5718
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/url/http://www.ams.org/journals/mcom/2011-80-275/S0025-5718-2011-02456-7/
info:eu-repo/semantics/altIdentifier/doi/10.1090/S0025-5718-2011-02456-7
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
dc.publisher.none.fl_str_mv American Mathematical Society
publisher.none.fl_str_mv American Mathematical Society
dc.source.none.fl_str_mv reponame:CONICET Digital (CONICET)
instname:Consejo Nacional de Investigaciones Científicas y Técnicas
reponame_str CONICET Digital (CONICET)
collection CONICET Digital (CONICET)
instname_str Consejo Nacional de Investigaciones Científicas y Técnicas
repository.name.fl_str_mv CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicas
repository.mail.fl_str_mv dasensio@conicet.gov.ar; lcarlino@conicet.gov.ar
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score 13.070432

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