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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 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.
@article{M2AN_2012__46_2_291_0,
author = {Dur\'an, Ricardo and Rodr{\'\i}guez, Rodolfo and Sanhueza, Frank},
title = {A finite element method for stiffened plates},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
pages = {291--315},
publisher = {EDP-Sciences},
volume = {46},
number = {2},
year = {2012},
doi = {10.1051/m2an/2011011},
mrnumber = {2855644},
zbl = {1272.74399},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.1051/m2an/2011011/}
}
TY - JOUR AU - Durán, Ricardo AU - Rodríguez, Rodolfo AU - Sanhueza, Frank TI - A finite element method for stiffened plates JO - ESAIM: Mathematical Modelling and Numerical Analysis PY - 2012 SP - 291 EP - 315 VL - 46 IS - 2 PB - EDP-Sciences UR - http://geodesic.mathdoc.fr/articles/10.1051/m2an/2011011/ DO - 10.1051/m2an/2011011 LA - en ID - M2AN_2012__46_2_291_0 ER -
%0 Journal Article %A Durán, Ricardo %A Rodríguez, Rodolfo %A Sanhueza, Frank %T A finite element method for stiffened plates %J ESAIM: Mathematical Modelling and Numerical Analysis %D 2012 %P 291-315 %V 46 %N 2 %I EDP-Sciences %U http://geodesic.mathdoc.fr/articles/10.1051/m2an/2011011/ %R 10.1051/m2an/2011011 %G en %F M2AN_2012__46_2_291_0
Durán, Ricardo; Rodríguez, Rodolfo; Sanhueza, Frank. A finite element method for stiffened plates. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 46 (2012) no. 2, pp. 291-315. doi: 10.1051/m2an/2011011
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