Some Results on the Analytical Solution of Cylindrical Shells With Large Openings

An analytical solution for cylindrical shells with large openings has been developed by the asymptotic method. In comparison with previous analytical solutions obtained by Eringen, Van Dyke and Lekkerkerker, the following three areas have been improved by the present method: 1) The modified Morley’s equation, which is applicable to $ro/RT≫1$⁠, is used instead of Donnell’s shallow shell equation. 2) The accurate expression of boundary curve of hole is expanded in terms of powers of ρ_o = r_o/R, while the previous approximate geometric description corresponds to the first term of the expansion. 3) The accurate boundary conditions for generalized forces are expanded in terms of powers of ρ_o and truncated after the terms of ρ_o³; the previous approximate boundary conditions correspond to the terms of order up to ρ_o, in the asymptotic expansions. The present solutions are in good agreement with Van Dyke’s solutions for small openings. The analytical results show that the error caused by the previous approximate boundary conditions is significant and has the order O(ρ_o); the error caused by the previous approximate geometric description of hole boundary has the order O(ρ_o²); and finally, the error caused by using Donnell’s shallow shell equation is very small for ρ_o ≤ 0.7. For openings with ρ_o > 0.25, say, noticeable differences exist between the present and the previous results. The stress analysis of cylindrical shells connected with nozzles has been developed by using the present solution. For increasing the accuracy of stress analysis in the nozzle, the exact description of the edge of nozzle is given and the near-edge boundary layer stress state in the nozzle is considered. The results obtained are in good agreement with those by Eringen for small openings and with those by F.E.M. and experiments for large openings.