A finite element method for stiffened plates

Autores
Duran, Ricardo Guillermo; Rodríguez, Rodolfo; Sanhueza, Frank
Año de publicación
2012
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
The aim of this paper is to analyze a low order finite element method for a stiffened plate. The plate is modeled by Reissner-Mindlin equations and the stiffener by Timoshenko beams equations. The resulting problem is shown to be well posed. In the case of concentric stiffeners it decouples into two problems, one for the in-plane plate deformation and the other for the bending of the plate. The analysis and discretization of the first one is straightforward. The second one is shown to have a solution bounded above and below independently of the thickness of the plate. A discretization based on DL3 finite elements combined with ad-hoc elements for the stiffener is proposed. Optimal order error estimates are proved for displacements, rotations and shear stresses for the plate and the stiffener. Numerical tests are reported in order to assess the performance of the method. These numerical computations demonstrate that the error estimates are independent of the thickness, providing a numerical evidence that the method is locking-free.

Fil: Duran, Ricardo Guillermo. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; Argentina
Fil: Rodríguez, Rodolfo. Universidad de Concepción; Chile
Fil: Sanhueza, Frank. Universidad Andres Bello; Chile
Materia
Stiffened Plates
Reissner-Mindlin Model
Timoshenko Beam
Finite Elements
Error Estimates
Locking
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:11336/19896
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/19896
network_acronym_str CONICETDig
repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling A finite element method for stiffened platesDuran, Ricardo GuillermoRodríguez, RodolfoSanhueza, FrankStiffened PlatesReissner-Mindlin ModelTimoshenko BeamFinite ElementsError EstimatesLockinghttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1The aim of this paper is to analyze a low order finite element method for a stiffened plate. The plate is modeled by Reissner-Mindlin equations and the stiffener by Timoshenko beams equations. The resulting problem is shown to be well posed. In the case of concentric stiffeners it decouples into two problems, one for the in-plane plate deformation and the other for the bending of the plate. The analysis and discretization of the first one is straightforward. The second one is shown to have a solution bounded above and below independently of the thickness of the plate. A discretization based on DL3 finite elements combined with ad-hoc elements for the stiffener is proposed. Optimal order error estimates are proved for displacements, rotations and shear stresses for the plate and the stiffener. Numerical tests are reported in order to assess the performance of the method. These numerical computations demonstrate that the error estimates are independent of the thickness, providing a numerical evidence that the method is locking-free.
Fil: Duran, Ricardo Guillermo. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; ArgentinaFil: Rodríguez, Rodolfo. Universidad de Concepción; ChileFil: Sanhueza, Frank. Universidad Andres Bello; ChileEDP Sciences2012-12info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/19896Duran, Ricardo Guillermo; Rodríguez, Rodolfo; Sanhueza, Frank; A finite element method for stiffened plates; EDP Sciences; Esaim-mathematical Modelling And Numerical Analysis-modelisation Matheematique Et Analyse Numerique; 46; 2; 12-2012; 291-3150764-583XCONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/doi/10.1051/m2an/2011011info:eu-repo/semantics/altIdentifier/url/https://www.esaim-m2an.org/articles/m2an/abs/2012/02/m2an110011/m2an110011.htmlinfo:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-10-22T11:01:39Zoai:ri.conicet.gov.ar:11336/19896instacron: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:34982025-10-22 11:01:39.333CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv A finite element method for stiffened plates
title A finite element method for stiffened plates
spellingShingle A finite element method for stiffened plates
Duran, Ricardo Guillermo
Stiffened Plates
Reissner-Mindlin Model
Timoshenko Beam
Finite Elements
Error Estimates
Locking
title_short A finite element method for stiffened plates
title_full A finite element method for stiffened plates
title_fullStr A finite element method for stiffened plates
title_full_unstemmed A finite element method for stiffened plates
title_sort A finite element method for stiffened plates
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 Stiffened Plates
Reissner-Mindlin Model
Timoshenko Beam
Finite Elements
Error Estimates
Locking
topic Stiffened Plates
Reissner-Mindlin Model
Timoshenko Beam
Finite Elements
Error Estimates
Locking
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv The aim of this paper is to analyze a low order finite element method for a stiffened plate. The plate is modeled by Reissner-Mindlin equations and the stiffener by Timoshenko beams equations. The resulting problem is shown to be well posed. In the case of concentric stiffeners it decouples into two problems, one for the in-plane plate deformation and the other for the bending of the plate. The analysis and discretization of the first one is straightforward. The second one is shown to have a solution bounded above and below independently of the thickness of the plate. A discretization based on DL3 finite elements combined with ad-hoc elements for the stiffener is proposed. Optimal order error estimates are proved for displacements, rotations and shear stresses for the plate and the stiffener. Numerical tests are reported in order to assess the performance of the method. These numerical computations demonstrate that the error estimates are independent of the thickness, providing a numerical evidence that the method is locking-free.

Fil: Duran, Ricardo Guillermo. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; Argentina
Fil: Rodríguez, Rodolfo. Universidad de Concepción; Chile
Fil: Sanhueza, Frank. Universidad Andres Bello; Chile
description The aim of this paper is to analyze a low order finite element method for a stiffened plate. The plate is modeled by Reissner-Mindlin equations and the stiffener by Timoshenko beams equations. The resulting problem is shown to be well posed. In the case of concentric stiffeners it decouples into two problems, one for the in-plane plate deformation and the other for the bending of the plate. The analysis and discretization of the first one is straightforward. The second one is shown to have a solution bounded above and below independently of the thickness of the plate. A discretization based on DL3 finite elements combined with ad-hoc elements for the stiffener is proposed. Optimal order error estimates are proved for displacements, rotations and shear stresses for the plate and the stiffener. Numerical tests are reported in order to assess the performance of the method. These numerical computations demonstrate that the error estimates are independent of the thickness, providing a numerical evidence that the method is locking-free.

publishDate 2012
dc.date.none.fl_str_mv 2012-12
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/11336/19896
Duran, Ricardo Guillermo; Rodríguez, Rodolfo; Sanhueza, Frank; A finite element method for stiffened plates; EDP Sciences; Esaim-mathematical Modelling And Numerical Analysis-modelisation Matheematique Et Analyse Numerique; 46; 2; 12-2012; 291-315
0764-583X
CONICET Digital
CONICET
url http://hdl.handle.net/11336/19896
identifier_str_mv Duran, Ricardo Guillermo; Rodríguez, Rodolfo; Sanhueza, Frank; A finite element method for stiffened plates; EDP Sciences; Esaim-mathematical Modelling And Numerical Analysis-modelisation Matheematique Et Analyse Numerique; 46; 2; 12-2012; 291-315
0764-583X
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/doi/10.1051/m2an/2011011
info:eu-repo/semantics/altIdentifier/url/https://www.esaim-m2an.org/articles/m2an/abs/2012/02/m2an110011/m2an110011.html
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 EDP Sciences
publisher.none.fl_str_mv EDP Sciences
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
_version_ 1846781205598437376
score 12.982451

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