scholarly journals Stabilised finite element methods for a bending moment formulation of the Reissner-Mindlin plate model

CALCOLO ◽  
2014 ◽  
Vol 52 (3) ◽  
pp. 343-369
Author(s):  
Gabriel R. Barrenechea ◽  
Tomás P. Barrios ◽  
Andreas Wachtel
Keyword(s):  
Finite Element ◽  
Finite Element Methods ◽  
Bending Moment ◽  
Mindlin Plate ◽  
Plate Model

AN OPTIMAL LOW-ORDER LOCKING-FREE FINITE ELEMENT METHOD FOR REISSNER–MINDLIN PLATES

1998 ◽  
Vol 08 (03) ◽  
pp. 407-430 ◽  
Author(s):  
D. CHAPELLE ◽  
R. STENBERG
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Convergence Rates ◽  
A Priori ◽  
Mindlin Plate ◽  
Plate Model ◽  
Simple Modification ◽  
Optimal Convergence Rates ◽  
Priori Error Estimates ◽  
Element Method

We propose a simple modification of a recently introduced locking-free finite element method for the Reissner–Mindlin plate model. By this modification, we are able to obtain optimal convergence rates on numerical benchmarks. These results are substantiated by a complete mathematical analysis which provides optimal a priori error estimates.

scholarly journals Analysis of a Linear–Linear Finite Element for the Reissner–Mindlin Plate Model

1997 ◽  
Vol 07 (02) ◽  
pp. 217-238 ◽  
Author(s):  
Douglas N. Arnold ◽  
Richard S. Falk
Keyword(s):  
Finite Element ◽  
Plate Thickness ◽  
Mesh Size ◽  
Mindlin Plate ◽  
Optimal Order ◽  
Plate Model ◽  
Order Error ◽  
Linear Finite Element ◽  
Optimal Order Error Estimates ◽  
Linear Elements

An analysis is presented for a recently proposed finite element method for the Reissner–Mindlin plate problem. The method is based on the standard variational principle, uses nonconforming linear elements to approximate the rotations and conforming linear elements to approximate the transverse displacements, and avoids the usual "locking problem" by interpolating the shear stress into a rotated space of lowest order Raviart-Thomas elements. When the plate thickness t = O(h), it is proved that the method gives optimal order error estimates uniform in t. However, the analysis suggests and numerical calculations confirm that the method can produce poor approximations for moderate sized values of the plate thickness. Indeed, for t fixed, the method does not converge as the mesh size h tends to zero.

Sign in / Sign up

Export Citation Format

Share Document