A novel analytical study on the buckling of cylindrical shells subjected to arbitrarily distributed external pressure

Abstract A completely new analytical method to solve the fourth-order governing partial differential equations with variable coefficients is proposed for the buckling of cylindrical shells subjected to distributed external pressure. Unlike the present energy method in literatures, pressure distribution needs not be assumed beforehand and be simple, which is arbitrary in this manuscript. The present novel method makes the buckling analysis for the complicated external pressure distributions (including discontinuous loads) possible. Furthermore, general buckling load formulas related to geometrical sizes of the shell and pressure distribution functions are obtained by the combined perturbation method and Fourier series expansion for the first time. The first and second order asymptotic terms of buckling loads are directly given for the purpose of engineering application. Based on the presented method, three types of external pressure loads (namely, linear liquid pressure, wind type pressure and discontinuous stepwise external pressure)are considered. Validity and accuracy are demonstrated by comparing with the results in published literatures for linear liquid pressure and wind type pressure, and it is also the first time to derive the buckling load for a shell under discontinuous stepwise external pressure. Parametric discussion is also performed to investigate the effects of load distribution types and parameters on buckling resistance capacity.