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LOCKING-FREE REISSNERMINDLIN ELEMENTS WITHOUT REDUCED INTEGRATION
 

Summary: LOCKING-FREE REISSNER­MINDLIN ELEMENTS WITHOUT
REDUCED INTEGRATION
DOUGLAS N. ARNOLD, FRANCO BREZZI, RICHARD S. FALK, AND L. DONATELLA MARINI
Abstract. In a recent paper of Arnold, Brezzi, and Marini [4], 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 Reissner­Mindlin plate problem. By follow-
ing 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 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.
1. Introduction
In the Reissner­Mindlin model of a clamped plate, one seeks to determine the rotation
vector and the transverse displacement w which minimize over H1

  

Source: Arnold, Douglas N. - School of Mathematics, University of Minnesota
Brezzi, Franco - Istituto di Matematica Applicata e Tecnologie Informatiche del C.N.R., & Dipartimento di Matematica, Universitą di Pavia
Falk, Richard S.- Department of Mathematics, Rutgers University
Marini, Donatella - Faculty of Engineering, University of Pavia

 

Collections: Engineering; Mathematics