An analytical solution to the buckling of cylindrical shells under arbitrarily distributed axial loads

Abstract This paper presents an analytical study on the buckling of cylindrical shells under arbitrarily distributed axial loads. It has three main innovation points. First, different from the previous studies, the axial loads need not be assumed to be specific forms beforehand and be simple ones such as cosine type, which are arbitrary in this paper (including continuous and discontinuous distributions). Second, combining the separation of variables and perturbation methods, it develops a novel general method to solve the fourth-order partial differential equations with unknown variable coefficients for cylindrical shells under distributed axial loads. Last, it derives the asymptotic formula of buckling loads with respect to shell geometry sizes and load functions for the first time. Using the presented formula, two continuous axial load distributions are analyzed first and the results show a good agreement with previous studies and those by the Bubnov-Galerkin method. Furthermore, one discontinuous axial load distribution is investigated. Comparative study on effects of load distribution parameters and types is also performed. The study has sufficient accuracy and significant engineering application value.