Title: Analysis of a linear-linear finite element for the
Reissner-Mindlin plate model
Authors: Douglas N. Arnold and Richard S. Falk
Source: Math. Models Methods Appl. Sci., 7(2):217-238, 1997.
Status: Published
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.
Keywords: Reissner, Mindlin, plate, finite element, nonconforming
URL: http://www.math.rutgers.edu/~falk/papers/ozf.pdf