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