A finite element method for stiffened plates

Autores
Durán, R.; Rodríguez, R.; Sanhueza, F.
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. © EDP Sciences, SMAI, 2011.
Fil:Durán, R. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina.
Fuente
ESAIM: Math. Model. Numer. Anal. 2012;46(2):291-315
Materia
Error estimates
Finite elements
Locking
Reissner-Mindlin model
Stiffened plates
Timoshenko beam
Error estimates
Finite Element
Locking
Reissner-Mindlin model
Stiffened plate
Timoshenko beams
Bending (deformation)
Estimation
Mindlin plates
Numerical methods
Particle beams
Finite element method
Nivel de accesibilidad
acceso abierto
Condiciones de uso
http://creativecommons.org/licenses/by/2.5/ar
Repositorio
Biblioteca Digital (UBA-FCEN)
Institución
Universidad Nacional de Buenos Aires. Facultad de Ciencias Exactas y Naturales
OAI Identificador
paperaa:paper_0764583X_v46_n2_p291_Duran
Acceder
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oai_identifier_str paperaa:paper_0764583X_v46_n2_p291_Duran
network_acronym_str BDUBAFCEN
repository_id_str 1896
network_name_str Biblioteca Digital (UBA-FCEN)
spelling A finite element method for stiffened platesDurán, R.Rodríguez, R.Sanhueza, F.Error estimatesFinite elementsLockingReissner-Mindlin modelStiffened platesTimoshenko beamError estimatesFinite ElementLockingReissner-Mindlin modelStiffened plateTimoshenko beamsBending (deformation)EstimationMindlin platesNumerical methodsParticle beamsFinite element methodThe 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. © EDP Sciences, SMAI, 2011.Fil:Durán, R. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina.2012info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfhttp://hdl.handle.net/20.500.12110/paper_0764583X_v46_n2_p291_DuranESAIM: Math. Model. Numer. Anal. 2012;46(2):291-315reponame:Biblioteca Digital (UBA-FCEN)instname:Universidad Nacional de Buenos Aires. Facultad de Ciencias Exactas y Naturalesinstacron:UBA-FCENenginfo:eu-repo/semantics/openAccesshttp://creativecommons.org/licenses/by/2.5/ar2025-10-16T09:30:13Zpaperaa:paper_0764583X_v46_n2_p291_DuranInstitucionalhttps://digital.bl.fcen.uba.ar/Universidad públicaNo correspondehttps://digital.bl.fcen.uba.ar/cgi-bin/oaiserver.cgiana@bl.fcen.uba.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:18962025-10-16 09:30:14.815Biblioteca Digital (UBA-FCEN) - Universidad Nacional de Buenos Aires. Facultad de Ciencias Exactas y Naturalesfalse
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
Durán, R.
Error estimates
Finite elements
Locking
Reissner-Mindlin model
Stiffened plates
Timoshenko beam
Error estimates
Finite Element
Locking
Reissner-Mindlin model
Stiffened plate
Timoshenko beams
Bending (deformation)
Estimation
Mindlin plates
Numerical methods
Particle beams
Finite element method
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 Durán, R.
Rodríguez, R.
Sanhueza, F.
author Durán, R.
author_facet Durán, R.
Rodríguez, R.
Sanhueza, F.
author_role author
author2 Rodríguez, R.
Sanhueza, F.
author2_role author
author
dc.subject.none.fl_str_mv Error estimates
Finite elements
Locking
Reissner-Mindlin model
Stiffened plates
Timoshenko beam
Error estimates
Finite Element
Locking
Reissner-Mindlin model
Stiffened plate
Timoshenko beams
Bending (deformation)
Estimation
Mindlin plates
Numerical methods
Particle beams
Finite element method
topic Error estimates
Finite elements
Locking
Reissner-Mindlin model
Stiffened plates
Timoshenko beam
Error estimates
Finite Element
Locking
Reissner-Mindlin model
Stiffened plate
Timoshenko beams
Bending (deformation)
Estimation
Mindlin plates
Numerical methods
Particle beams
Finite element method
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. © EDP Sciences, SMAI, 2011.
Fil:Durán, R. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina.
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. © EDP Sciences, SMAI, 2011.
publishDate 2012
dc.date.none.fl_str_mv 2012
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/20.500.12110/paper_0764583X_v46_n2_p291_Duran
url http://hdl.handle.net/20.500.12110/paper_0764583X_v46_n2_p291_Duran
dc.language.none.fl_str_mv eng
language eng
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
http://creativecommons.org/licenses/by/2.5/ar
eu_rights_str_mv openAccess
rights_invalid_str_mv http://creativecommons.org/licenses/by/2.5/ar
dc.format.none.fl_str_mv application/pdf
dc.source.none.fl_str_mv ESAIM: Math. Model. Numer. Anal. 2012;46(2):291-315
reponame:Biblioteca Digital (UBA-FCEN)
instname:Universidad Nacional de Buenos Aires. Facultad de Ciencias Exactas y Naturales
instacron:UBA-FCEN
reponame_str Biblioteca Digital (UBA-FCEN)
collection Biblioteca Digital (UBA-FCEN)
instname_str Universidad Nacional de Buenos Aires. Facultad de Ciencias Exactas y Naturales
instacron_str UBA-FCEN
institution UBA-FCEN
repository.name.fl_str_mv Biblioteca Digital (UBA-FCEN) - Universidad Nacional de Buenos Aires. Facultad de Ciencias Exactas y Naturales
repository.mail.fl_str_mv ana@bl.fcen.uba.ar
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score 12.712165

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