Correct asymptotic theories for the axisymmetric deformation of thin and moderately thick cylindrical shells

Abstract

A refined shell theory is formulated for the elastostatics of long, moderately thick cylindrical shells in axisymmetric deformation. This theory corresponds to a two-term outer asymptotic expansion of the exact solution for small values of the dimensionless shell thickness parameter. The complexity of the known exact solution for the three-dimensional elasticity problem has stimulated an interest in thin and thick shell theories to provide accurate approximate solutions in the shell interior without any reference (or matching) to the inner asymptotic solution. The principal difficulty in developing a shell theory lies in the determination of an appropriate set of twodimensional boundary conditions for the shell solution from the prescribed edge data of the threedimensional theory. The derivations of boundary conditions for the thin shell theory and the refined shell theory constitute a main contribution of this paper. Correct boundary conditions obtained for the first time include (i) displacement edge conditions for thin shell theory, and (ii) stress and two types of mixed edge conditions for the refined shell theory. Several applications of the refined theory are given to show that corrections to the thin shell solution can be important.