 
Summary: MATHEMATICS OF COMPUTATION
Volume 66, Number 217, January 1997, Pages 114
S 00255718(97)007850
LOCKINGFREE 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
