Analytical study on the buckling of cylindrical shells with stepwise variable thickness subjected to uniform external pressure

This article focuses on the buckling of cylindrical shells with stepwise variable thickness subjected to uniform external pressure. First, combining the method of separation of variables, perturbation method, and Fourier series expansion, an analytical method for the buckling analysis of cylindrical shells with axisymmetric thickness variation subjected to external pressure is established. The method is verified by comparing with the previous results. Then, the stepwise variable thickness of cylindrical shells is described exactly by the arc tangent function. Finally, using the presented method, a general formula for the critical buckling load of cylindrical shells with stepwise variable thickness subjected to uniform external pressure is derived. This general formula is compared and discussed with some empirical formulae in the current design standards. This study lays a theoretical foundation for the calculation of the buckling load of cylindrical shells with stepwise variable thickness subjected to uniform external pressure. Moreover, it provides a reference and guidance for the further revision of related standards.