Buckling of the axially compressed cylindrical shells with arbitrary axisymmetric thickness variation

This paper focuses on the buckling of cylindrical shells under axial compression with small arbitrary thickness variations in the axial direction. General asymptotic formula of the buckling load, which is in terms of the thickness variation parameterεup to arbitrary order, is first derived by the perturbation expansion. Then effects led by three patterns of thickness variations on the buckling of axially compressed cylindrical shells, which are axisymmetric modal, local and stepwise variable, are, respectively investigated. Buckling loads of thin shells with axisymmetric modal thickness variation obtained from general analyses coincide with the Koiterʹs results. Particularly, an analytical study on the buckling of cylindrical shells with stepwise variable thickness is carried out, because these thin-walled structures are widely used in actual engineering. In addition to the analytic investigation, numerical analyses and comparisons are also performed.