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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2012
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| Acceso en línea: | http://hdl.handle.net/20.500.12110/paper_0764583X_v46_n2_p291_Duran |
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paperaa:paper_0764583X_v46_n2_p291_Duran2023-06-12T16:48:17Z A finite element method for stiffened plates ESAIM: Math. Model. Numer. Anal. 2012;46(2):291-315 Durán, R. Rodríguez, R. Sanhueza, F. 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 info:eu-repo/semantics/article info:ar-repo/semantics/artículo info:eu-repo/semantics/publishedVersion application/pdf eng info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar 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) |
| language |
Inglés |
| orig_language_str_mv |
eng |
| 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 |
| work_keys_str_mv |
AT duranr afiniteelementmethodforstiffenedplates AT rodriguezr afiniteelementmethodforstiffenedplates AT sanhuezaf afiniteelementmethodforstiffenedplates AT duranr finiteelementmethodforstiffenedplates AT rodriguezr finiteelementmethodforstiffenedplates AT sanhuezaf finiteelementmethodforstiffenedplates |
| _version_ |
1769810290508038144 |