J. Fish et R. Guttal, ON THE ASSUMED STRAIN FORMULATION WITH SELECTIVE POLYNOMIAL ORDER ENRICHMENT FOR P-VERSION SHELLS, Computers & structures, 63(5), 1997, pp. 899-913
A family of hierarchical shell elements based on assumed strain formul
ation has been developed to enhance the performance of displacement-ba
sed hierarchical shell elements typically up to polynomial order six.
For thin shells, hierarchical assumed strain elements with five degree
s-of-freedom (two rotations and three mid-plane translations) and six
degrees of freedom (three translations on the top and bottom surfaces
of the shell) per hierarchical mode have been formulated. Hierarchical
in-plane modes are adaptively selected on the basis of their ability
to reduce solution errors. For thick shells both in-plane and through-
the-thickness mode selection is controlled by the process of adaptivit
y. Numerical experiments have been carried out to test the usefulness
of assumed strain formulation in the framework of the p-method combine
d with selective polynomial escalation. The sensitivity to element dis
tortion and influence of super-parametric formulation on the rate of c
onvergence have been numerically assessed. (C) 1997 Elsevier Science L
td.