Buckling of cylindrical shells with general axisymmetric thickness imperfections under external pressure

This study focuses on the buckling of cylindrical shells under external pressure with general axisymmetric thickness imperfections. Firstly, the result of uniform thickness imperfection and recent study result of axisymmetric modal thickness imperfection are reviewed briefly. Secondly, asymptotic formulas of the buckling load, which are in terms of the thickness imperfection parameter up to arbitrary order, are determined through asymptotic analyses. The analyses are based on a system of linearized governing partial differential equations of perfect shells with variable thickness. Thirdly, the effects led by three patterns of thickness imperfections on the buckling of the laterally pressured cylindrical shells, which are uniform, axisymmetric modal and parabolic, are respectively investigated. Buckling loads of uniform and axisymmetric modal thickness imperfections coincide with the known results. In addition to the analytic investigation, numerical analyses and comparisons are also carried out. The analytical study results presented in the paper can be utilized to evaluate the stabilities of cylindrical shells under external pressure with general axisymmetric imperfections in thickness, once the thickness imperfection is known.