Analytical buckling load formulas for cylindrical shell structures with variable thickness under non-uniform external pressure

The novel contribution of this paper is to develop a quadratic perturbation method to derive general analytical buckling load formulas for cylindrical shell structures with varying wall thickness under non-uniform lateral pressure loads for the first time. Arbitrary thickness and lateral pressure loads are skillfully described and governing differential equations are derived. A quadratic perturbation method is developed to derive buckling load formulas, which establishes the relation among buckling loads, thickness, and load functions. The presented formulas are adequately validated by comparing with recent results for variable wall thickness or non-uniform external pressure, and exhibit a great advantage in determining buckling loads. For the purpose of engineering application, buckling of a cylinder with linear thickness under linear liquid pressure and wind load is deeply studied by the presented formulas. This study can provide a highly efficient method for buckling load computation, and a guide to design the thickness of the shell under non-uniform lateral loads.