Summary: A Mixed 3D Finite Element for Modelling Thick Plates
Laboratoire d'Analyse Num´erique,
Universit´e Paris XI, 91405 Orsay , FRANCE.
Bertold Badler Chair of Computer Science,
Hebrew University of Jerusalem, Givat-Ram, ISRAEL.
May, 1993 (revised version)
Based on the Hellinger-Reissner variational principle, we formulate a mixed 3-d finite element for
plate bending. This element is used to model thick plates and alleviates the problem of shear-locking in
plates with large length/thickness ratios. The computer code which was used here, is available.
The approach of  to the plate-bending problem has no a priori assumptions of the "small thickness" type.
It is an asymptotic theory based on the mixed variational principle of Hellinger and Reissner . This
enables one to treat the plate-bending problem as a fully three-dimensinal problem in linear elasticity.
In this paper, we express the above theory in a computational form to which we apply a finite element
method. This is a mixed method in which we approximate both displacement and stress on brick type
elements. We carefully choose and explain the spaces of polynomials used for the displacements and stresses.
We then present the results of numerical simulations and draw conclusions from these.