# A finite element method for stiffened plates

Ricardo Durán; Rodolfo Rodríguez; Frank Sanhueza

ESAIM: Mathematical Modelling and Numerical Analysis (2011)

- Volume: 46, Issue: 2, page 291-315
- ISSN: 0764-583X

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topDurán, Ricardo, Rodríguez, Rodolfo, and Sanhueza, Frank. "A finite element method for stiffened plates." ESAIM: Mathematical Modelling and Numerical Analysis 46.2 (2011): 291-315. <http://eudml.org/doc/222136>.

@article{Durán2011,

abstract = {
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.
},

author = {Durán, Ricardo, Rodríguez, Rodolfo, Sanhueza, Frank},

journal = {ESAIM: Mathematical Modelling and Numerical Analysis},

keywords = {Stiffened plates; Reissner-Mindlin model; Timoshenko beam; finite elements; error estimates; locking; stiffened plates},

language = {eng},

month = {10},

number = {2},

pages = {291-315},

publisher = {EDP Sciences},

title = {A finite element method for stiffened plates},

url = {http://eudml.org/doc/222136},

volume = {46},

year = {2011},

}

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

DA - 2011/10//

PB - EDP Sciences

VL - 46

IS - 2

SP - 291

EP - 315

AB -
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.

LA - eng

KW - Stiffened plates; Reissner-Mindlin model; Timoshenko beam; finite elements; error estimates; locking; stiffened plates

UR - http://eudml.org/doc/222136

ER -

## References

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