Analytical Study on the Buckling of Cylindrical Shells With Arbitrary Thickness Imperfections Under Axial Compression

This paper presents an analytical study on the buckling of axially compressed cylindrical shells with arbitrary thickness imperfections (nonaxisymmetric and axisymmetric). First, the basic governing partial differential equations, which consider thickness imperfections, are obtained. Second, a unified method that combines the perturbation method and Fourier series expansion is developed to derive buckling load, radial displacement and stress function, that are expressed by triple series in terms of thickness imperfection parameter and buckling modes up to arbitrary order. Third, two patterns of nonaxisymmetric thickness imperfections, which are modal and exponential, are, respectively, investigated. These results are absolutely new to literature. When modal thickness imperfection becomes axisymmetric, the buckling loads degenerate to the known results. In addition to the analytical investigation, analyses and comparisons are also carried out.