On the imperfection sensitivity and design of tori-spherical shells under external pressure

Abstract Tori-spherical shells are often used as enclosures of pressure vessels in ocean and civil engineering. When subjected to external pressure, these thin-walled shells are prone to buckling. The corresponding critical buckling pressure heavily depends on deviations from the ideal shell shape, but also the yield strength as well as the knuckle radius. This article summarizes and analyzes all known experimental results for tori-spherical shells under external pressure. A detailed numerical elastic-plastic buckling analysis of a tori-spherical bulkhead is presented including details regarding non-linear material model, finite-element modeling and solver settings. In addition, a wide variety of empirical design and numerical geometric imperfection approaches for tori-spheres are presented, applied and validated. Among the geometric imperfection approaches are realistic measured geometric imperfections, dimple imperfections, flat patch imperfections and reduced stiffness methods. Large scale parametric imperfection amplitude analyzes are performed in order to determine which imperfection concept delivers in general the best fit to experimental results. New design factors for different tori-spherical shell geometry configurations are consequently developed and validated with experimental results. The new design factors lead to significantly improved critical load estimations in comparison to lower-bounds obtained empirically.