Numerical analysis of axisymmetric buckling of conical shells

Nonlinear boundary-value problems of axisymmetric buckling of conical shells under a uniformly distributed normal pressure are solved by the shooting method. The problems are formulated for a system of six first-order ordinary differential equations with independent rotation and displacement fields. Simply supported and clamped cases are considered. Branching solutions of the boundary-value problems are studied for different pressures and geometrical parameters of the shells. The nonmonotonic and discontinuous curves of equilibrium states obtained show that collapse, i.e., snap-through instability is possible. For a simply supported shell, multivalued solutions are obtained for both external and internal pressure. For a clamped thin-walled shell, theoretical results are compared with experimental data.