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MATHEMATICS OF COMPUTATION Volume 66, Number 217, January 1997, Pages 114
 

Summary: MATHEMATICS OF COMPUTATION
Volume 66, Number 217, January 1997, Pages 114
S 0025-5718(97)00785-0
LOCKING-FREE FINITE ELEMENT METHODS FOR SHELLS
DOUGLAS N. ARNOLD AND FRANCO BREZZI
Abstract. We propose a new family of finite element methods for the Naghdi
shell model, one method associated with each nonnegative integer k. The
methods are based on a nonstandard mixed formulation, and the kth method
employs triangular Lagrange finite elements of degree k+2 augmented by bub-
ble functions of degree k + 3 for both the displacement and rotation variables,
and discontinuous piecewise polynomials of degree k for the shear and mem-
brane stresses. This method can be implemented in terms of the displacement
and rotation variables alone, as the minimization of an altered energy func-
tional over the space mentioned. The alteration consists of the introduction of
a weighted local projection into part, but not all, of the shear and membrane
energy terms of the usual Naghdi energy. The relative error in the method,
measured in a norm which combines the H1 norm of the displacement and ro-
tation fields and an appropriate norm of the shear and membrane stress fields,
converges to zero with order k +1 uniformly with respect to the shell thickness
for smooth solutions, at least under the assumption that certain geometrical

  

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

 

Collections: Mathematics