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A finite element method for stiffened plates

Published online by Cambridge University Press:  12 October 2011

Ricardo Durán ,
Rodolfo Rodríguez  and
Frank Sanhueza
Ricardo Durán
Affiliation:
Departamento de Matemática, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, 1428 Buenos Aires, Argentina. rduran@dm.uba.ar
Rodolfo Rodríguez
Affiliation:
CI2MA, Departamento de Ingeniería Matemática, Universidad de Concepción, Casilla 160-C, Chile. rodolfo@ing-mat.udec.cl
Frank Sanhueza
Affiliation:
Escuela de Obras Civiles, Universidad Andres Bello, Autopista Concepción, Talcahuano 7100, Concepción, Chile. fsanhueza@unab.cl

Abstract

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The aim of this paper is to analyze a low order finite element methodfor a stiffened plate. The plate is modeled by Reissner-Mindlinequations and the stiffener by Timoshenko beams equations. Theresulting problem is shown to be well posed. In the case of concentricstiffeners it decouples into two problems, one for the in-plane plate deformation and the other for the bending of the plate. The analysisand discretization of the first one is straightforward. The second oneis shown to have a solution bounded above and below independently of thethickness of the plate. A discretization based on DL3 finite elementscombined with ad-hoc elements for the stiffener is proposed.Optimal order error estimates are proved for displacements, rotationsand shear stresses for the plate and the stiffener. Numerical tests arereported in order to assess the performance of the method. Thesenumerical computations demonstrate that the error estimates areindependent of the thickness, providing a numerical evidence that themethod is locking-free.


Keywords

Stiffened platesReissner-Mindlin modelTimoshenko beamfinite elementserror estimateslocking

Information

Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 46 , Issue 2 , March 2012 , pp. 291 - 315
Copyright
© EDP Sciences, SMAI, 2011

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