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Mathematical Models and Methods in Applied Sciences c World Scientific Publishing Company
 

Summary: Mathematical Models and Methods in Applied Sciences
c World Scientific Publishing Company
ANALYSIS OF A LINEAR­LINEAR FINITE ELEMENT
FOR THE REISSNER­MINDLIN PLATE MODEL
DOUGLAS N. ARNOLD
Department of Mathematics
Penn State University
University Park, PA 16802, USA
RICHARD S. FALK
Department of Mathematics
Rutgers University
New Brunswick, NJ 08903, USA
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

  

Source: Arnold, Douglas N. - School of Mathematics, University of Minnesota

 

Collections: Mathematics