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A ROTATED NONCONFORMING RECTANGULAR MIXED ELEMENT FOR ELASTICITY
 

Summary: A ROTATED NONCONFORMING RECTANGULAR MIXED
ELEMENT FOR ELASTICITY
GERARD AWANOU
Abstract. We present in this paper a low order nonconforming mixed element
for plane elasticity on rectangular meshes. The 3 dimensional space of rigid body
motions is used to approximate the displacement and a 16 dimensional space is used
to discretize the space of symmetric tensors. This element may be viewed as the
rectangular analogue of the nonconforming Arnold-Winther element and is related
to a discrete version of the elasticity differential complex with a nonconforming H2
element related to the rotated Q1 element.
1. Introduction
It is well known that it is extremely difficult to construct mixed finite elements for elas-
ticity in stress displacement formulation. In a pioneering work, Arnold and Winther
constructed the first mixed elements for plane elasticity with symmetric stress fields,
using polynomial shape functions, [2].
Previous works circumvent the difficulty of the symmetry condition by using com-
posite elements, weakening or abandoning the symmetry condition, cf. [2] and the
references therein. As explained in [2], vertex degrees of freedom are unavoidable
for a finite element space for the stress field with continuous symmetric matrix fields
if one imposes interelement continuity only by means of quantities defined on the

  

Source: Awanou, Gerard - Department of Mathematical Sciences, Northern Illinois University

 

Collections: Mathematics