Analysis of a linear-linear finite element for the
                         Reissner-Mindlin plate model

                    Douglas N. Arnold and Richard S. Falk

                                   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

Subj. class.:  65N30, 73K10, 73K25

To appear in Math. Models and Methods in Appl. Sci. 7 (1997)

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