Analysis of a Linear-Linear Finite Element
for the Reissner-Mindlin Plate Model

Douglas N. Arnold
Deparpartment of Mathematics
Penn State University
University Park, PA 16802

Richard S. Falk
Deparpartment of Mathematics
Rutgers University
New Brunswick, NJ 08903

Abstract

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.

Key Words: Reissner, Mindlin, plate, finite element, nonconforming

Subject classification: 65N30, 73K10, 73K25


Contributed June 28, 1996.