A finite element method for stiffened plates

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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...

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Autores principales:	Durán, R., Rodríguez, R., Sanhueza, F.
Formato:	Artículo publishedVersion
Publicado:	2012
Materias:	Error estimates Finite elements Locking Reissner-Mindlin model Stiffened plates Timoshenko beam Finite Element Stiffened plate Timoshenko beams Bending (deformation) Estimation Mindlin plates Numerical methods Particle beams Finite element method
Acceso en línea:	http://hdl.handle.net/20.500.12110/paper_0764583X_v46_n2_p291_Duran http://repositoriouba.sisbi.uba.ar/gsdl/cgi-bin/library.cgi?a=d&c=artiaex&d=paper_0764583X_v46_n2_p291_Duran_oai
Aporte de:	Repositorio Digital de la Universidad de Buenos Aires (UBA) de Universidad de Buenos Aires

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spelling	I28-R145-paper_0764583X_v46_n2_p291_Duran_oai2020-10-19 Durán, R. Rodríguez, R. Sanhueza, F. 2012 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. application/pdf http://hdl.handle.net/20.500.12110/paper_0764583X_v46_n2_p291_Duran info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar ESAIM: Math. Model. Numer. Anal. 2012;46(2):291-315 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 A finite element method for stiffened plates info:eu-repo/semantics/article info:ar-repo/semantics/artículo info:eu-repo/semantics/publishedVersion http://repositoriouba.sisbi.uba.ar/gsdl/cgi-bin/library.cgi?a=d&c=artiaex&d=paper_0764583X_v46_n2_p291_Duran_oai
institution	Universidad de Buenos Aires
institution_str	I-28
repository_str	R-145
collection	Repositorio Digital de la Universidad de Buenos Aires (UBA)
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
spellingShingle	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 Durán, R. Rodríguez, R. Sanhueza, F. A finite element method for stiffened plates
topic_facet	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
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.
format	Artículo Artículo publishedVersion
author	Durán, R. Rodríguez, R. Sanhueza, F.
author_facet	Durán, R. Rodríguez, R. Sanhueza, F.
author_sort	Durán, R.
title	A finite element method for stiffened plates
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	finite element method for stiffened plates
publishDate	2012
url	http://hdl.handle.net/20.500.12110/paper_0764583X_v46_n2_p291_Duran http://repositoriouba.sisbi.uba.ar/gsdl/cgi-bin/library.cgi?a=d&c=artiaex&d=paper_0764583X_v46_n2_p291_Duran_oai
work_keys_str_mv	AT duranr afiniteelementmethodforstiffenedplates AT rodriguezr afiniteelementmethodforstiffenedplates AT sanhuezaf afiniteelementmethodforstiffenedplates AT duranr finiteelementmethodforstiffenedplates AT rodriguezr finiteelementmethodforstiffenedplates AT sanhuezaf finiteelementmethodforstiffenedplates
_version_	1766026712645107712

A finite element method for stiffened plates

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