A finite element method for stiffened plates

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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Detalles Bibliográficos
Autor principal:	Duran, Ricardo Guillermo
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:	https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_0764583X_v46_n2_p291_Duran http://hdl.handle.net/20.500.12110/paper_0764583X_v46_n2_p291_Duran
Aporte de:	Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires

id	paper:paper_0764583X_v46_n2_p291_Duran
record_format	dspace
spelling	paper:paper_0764583X_v46_n2_p291_Duran2023-06-08T15:45:46Z A finite element method for stiffened plates Duran, Ricardo Guillermo 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 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. 2012 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_0764583X_v46_n2_p291_Duran http://hdl.handle.net/20.500.12110/paper_0764583X_v46_n2_p291_Duran
institution	Universidad de Buenos Aires
institution_str	I-28
repository_str	R-134
collection	Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (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 Duran, Ricardo Guillermo 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.
author	Duran, Ricardo Guillermo
author_facet	Duran, Ricardo Guillermo
author_sort	Duran, Ricardo Guillermo
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	https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_0764583X_v46_n2_p291_Duran http://hdl.handle.net/20.500.12110/paper_0764583X_v46_n2_p291_Duran
work_keys_str_mv	AT duranricardoguillermo afiniteelementmethodforstiffenedplates AT duranricardoguillermo finiteelementmethodforstiffenedplates
_version_	1768545837688815616

A finite element method for stiffened plates

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