A finite element method for stiffened plates

R. G. DURÁN; R. RODRÍGUEZ; F. SANHUEZA

ESAIM-MATHEMATICAL MODELLING AND NUMERICAL ANALYSIS-MODELISATION MATHEEMATIQUE ET ANALYSE NUMERIQUE

EDP SCIENCES S A

Lugar: Paris; Año: 2012 vol. 46 p. 291 - 315

0764-583X

The aim of this paper is to analyze a low order finite element method for a stiffenedplate. The plate is modeled by Reissner-Mindlin equations and the stiffener by Timoshenko beamsequations. The resulting problem is shown to be well posed. In the case of concentric stiffeners itdecouples into two problems, one for the in-plane plate deformation and the other for the bendingof the plate. The analysis and discretization of the first one is straightforward. The second oneis 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 plateand 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.ad-hoc elements for the stiffener is proposed. Optimal order error estimates are proved for displacements, rotations and shear stresses for the plateand 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. Optimal order error estimates are proved for displacements, rotations and shear stresses for the plateand 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. Optimal order error estimates are proved for displacements, rotations and shear stresses for the plateand 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.ad-hoc elements for the stiffener is proposed. Optimal order error estimates are proved for displacements, rotations and shear stresses for the plateand 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. Optimal order error estimates are proved for displacements, rotations and shear stresses for the plateand 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. Optimal order error estimates are proved for displacements, rotations and shear stresses for the plateand 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.ad-hoc elements for the stiffener is proposed. Optimal order error estimates are proved for displacements, rotations and shear stresses for the plateand 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. Optimal order error estimates are proved for displacements, rotations and shear stresses for the plateand 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. ad-hoc elements for the stiffener is proposed. Optimal order error estimates are proved for displacements, rotations and shear stresses for the plateand 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.