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
- Institución
- Consejo Nacional de Investigaciones Científicas y Técnicas
- OAI Identificador
- oai:ri.conicet.gov.ar:11336/19896
Ver los metadatos del registro completo
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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 Técnicas2025-09-29T09:33:38Zoai: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:34982025-09-29 09:33:38.727CONICET 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 |
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13.070432 |