CORRECT ASYMPTOTIC THEORIES FOR THE AXISYMMETRICAL DEFORMATION OF THIN AND MODERATELY THICK CYLINDRICAL-SHELLS

A refined shell theory is formulated for the elastostatics of long, mo derately thick cylindrical shells in axisymmetric deformation. This th eory corresponds to a two-term outer asymptotic expansion of the exact solution for small values of the dimensionless shell thickness parame ter. The complexity of the known exact solution for the three-dimensio nal elasticity problem has stimulated an interest in thin and thick sh ell theories to provide accurate approximate solutions in the shell in terior without any reference (or matching) to the inner asymptotic sol ution. The principal difficulty in developing a shell theory lies in t he determination of an appropriate set of two-dimensional boundary con ditions for the shell solution from the prescribed edge data of the th ree-dimensional theory. The derivations of boundary conditions for the thin shell theory and the refined shell theory constitute a main cont ribution of this paper. Correct boundary conditions obtained for the f irst time include (i) displacement edge conditions for thin shell theo ry, and (ii) stress and two types of mixed edge conditions for the ref ined shell theory. Several applications of the refined theory are give n to show that corrections to the thin shell solution can be important .