Volume 46, Number 2, November-December 2012
|Page(s)||291 - 315|
|Published online||12 October 2011|
A finite element method for stiffened plates
Departamento de Matemática, Facultad de Ciencias Exactas y
Naturales, Universidad de Buenos Aires,
1428 Buenos Aires,
2 CI2MA, Departamento de Ingeniería Matemática, Universidad de Concepción, Casilla 160-C, Chile. firstname.lastname@example.org
3 Escuela de Obras Civiles, Universidad Andres Bello, Autopista Concepción, Talcahuano 7100, Concepción, Chile. email@example.com
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.
Mathematics Subject Classification: 65N30 / 74K10 / 74K20
Key words: Stiffened plates / Reissner-Mindlin model / Timoshenko beam / finite elements / error estimates / locking
© EDP Sciences, SMAI, 2011
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