Strength and stability of spherical-conical shell assemblies under external hydrostatic pressure

Abstract

Abstract Thin shells are increasingly finding new applications under the sea. In this study, we consider a thin-walled shell-of-revolution assembly comprising a deep spherical shell dome (deeper than a hemisphere) axisymmetrically and tangentially joined to a steep-sided conical shell, the whole being a closed shell structure intended for stationary deployment beneath the surface of the sea in relatively shallow water. The closed shell structure, which might serve as an underwater observatory, is intended to operate at a constant depth, anchored to the seabed against flotation forces, with the thin steel shell walls being required to withstand the external hydrostatic pressure of the surrounding water. We use shell theory to investigate the discontinuity stresses that occur at the junction of the spherical shell and the conical shell, and employ FEM to explore the buckling behaviour of the thin shell. While discontinuity stresses are relatively small, they may influence the lower buckling modes of the shell, which are found to be largely confined to the region of the cone that is adjacent to the junction. Considerations are extended to a doubly-curved variant of the cone in the form of a paraboloid of revolution. As expected, double curvature enhances buckling capacity and also influences the mode shapes.