M. Touratier et Jp. Faye, ON A REFINED MODEL IN STRUCTURAL MECHANICS - FINITE-ELEMENT APPROXIMATION AND EDGE EFFECT ANALYSIS FOR AXISYMMETRICAL SHELLS, Computers & structures, 54(5), 1995, pp. 897-920
A two dimensional kinematics is proposed for moderately thick plates a
nd curved shells without any assumption other than neglecting the tran
sverse normal strain. The transverse shear is taken into account by us
ing a function f depending on the thickness coordinate and which is in
troduced in the assumed kinematics. The boundary value problem is deri
ved from the principle of virtual power. With the function f in the ki
nematics, all equations are directly applicable to Kirchhoff-Love, Rei
ssner-Mindlin, Reddy theories and, obviously, our theory by using a ce
rtain sine function f. This latter is justified in plates from three-d
imensional elasticity theory. The corresponding theory has been found
efficient in statics (buckling) and in dynamics (free vibrations) for
composite structures without needing shear correction factors. In addi
tion, a new finite element is proposed to analyse axisymmetric semi-th
ick shells in elasticity and for small displacements. The element has
three nodes and ten degrees of freedom, is of C-1 continuity for the t
ransverse displacement and C-0 for the membrane displacement and the '
membrane-shear' rotation. Finally, an introduction to the edge effects
for axisymmeric shells is presented. The study has shown some surpris
es concerning the hard clamped edge, in comparison with a two-dimensio
nal eight node isoparametric solid finite element model used in refere
nce.