ON A REFINED MODEL IN STRUCTURAL MECHANICS - FINITE-ELEMENT APPROXIMATION AND EDGE EFFECT ANALYSIS FOR AXISYMMETRICAL SHELLS

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.