Title:         Remarks on quadrilateral Reissner-Mindlin plate elements

Authors:       Douglas N. Arnold, Daniele Boffi, and Richard S. Falk

Source:        Proceedings of Fifth World Congress on Computational Mechanics,
               On-line publication: http://wccm.tuwien.ac.at/, Paper-ID:
               81482, July, 2002, Vienna, Austria

Status:        Published

Abstract:      Over the last two decades, there has been an extensive effort
               to devise and analyze finite elements schemes for the
               approximation of the Reissner--Mindlin plate equations which
               avoid "locking," numerical overstiffness resulting in a loss of
               accuracy when the plate is thin.  There are now many triangular
               and rectangular finite elements, for which a mathematical
               analysis exists to certify them as free of locking.  Generally
               speaking, the analysis for rectangular elements extends to the
               case of parallograms, which are defined by affine mappings of
               rectangles.  However, for more general convex quadrilaterals,
               defined by bilinear mappings of rectangles, the analysis is
               more complicated.  Recent results by the authors on the
               Recent results by the authors on the approximation properties
               of quadrilateral finite elements shed some light on the problems
               encountered.  In particular, they show that for some finite
               element methods for the approximation of the Reissner-Mindlin
               plate, the obvious generalization of rectangular elements to
               general quadrilateral meshes produce methods which lose
               accuracy.  In this paper, we present an overview of this 
               situation.


Keywords:      Reissner-Mindlin plate, finite element, locking-free,
               isoparametric 

Subj. Class:   65N30, 41A10, 73K10, 73K25

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