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