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 and curved shells without any assumption other than neglecting the transverse normal strain. The transverse shear is taken into account by using a function f depending on the thickness coordinate and which is introduced in the assumed kinematics. The boundary value problem is derived from the principle of virtual power. With the function f in the kinematics, all equations are directly applicable to Kirchhoff-Love, Reissner-Mindlin, Reddy theories and, obviously, our theory by using a certain sine function f. This latter is justified in plates from three-dimensional 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 addition, a new finite element is proposed to analyse axisymmetric semi-thick shells in elasticity and for small displacements. The element has three nodes and ten degrees of freedom, is of C-1 continuity for the transverse 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 surprises concerning the hard clamped edge, in comparison with a two-dimensional eight node isoparametric solid finite element model used in reference.