Title:         Locking-free Reissner-Mindlin elements without
               reduced integration

Authors:       Douglas N. Arnold, Franco Brezzi, Richard S. Falk, 
               and L. Donatella Marini

Source:        Computer Methods in Applied Mechanics and Engineering,
               196 (2007), pp. 3660-3671.

Status:        Published

Abstract: In a recent paper of Arnold, Brezzi, and Marini \cite{a-b-m}, the
ideas of discontinuous Galerkin methods were used to obtain and analyze two
new families of locking free finite element methods for the approximation of
the Reissner--Mindlin plate problem. By following their basic approach, but
making different choices of finite element spaces, we develop and analyze
other families of locking free finite elements that eliminate the need for the
introduction of a reduction operator, which has been a central feature of many
locking-free methods.  For $k \ge 2$, all the methods use piecewise
polynomials of degree $k$ to approximate the transverse displacement and
(possibly subsets) of piecewise polynomials of degree $k-1$ to approximate
both the rotation and shear stress vectors.  The approximation spaces for the
rotation and the shear stress are always identical.  The methods vary in the
amount of interelement continuity required.  In terms of smallest number of
degrees of freedom, the simplest method approximates the transverse
displacement with continuous, piecewise quadratics and both the rotation and
shear stress with rotated linear Brezzi-Douglas-Marini elements.

URL:           http://www.math.rutgers.edu/~falk/papers/dgrm2.pdf