Stability of combined imperfect conical tanks under hydrostatic loading

Liquid-containment shells of revolution: A review of recent studies on strength, stability and dynamics

“…Hafeez et al [54] investigated the buckling behaviour of such tanks under hydrostatic pressure, using a finite-element program. The influence of geometric design parameters on the buckling capacity of conical-cylindrical tanks, as well as the effect of geometric imperfections and residual stresses due to welding, were studied.…”

Equatorial bending of an elliptic toroidal shell

“…(14), (15), (17) and (18) respectively), and replacing r d 1 ϕ (for the curved meridian) by dx (for the cylindrical shell), one can transform the results for the elliptic-toroidal shell to those for a cylindrical shell. However, the cylindrical-shell model will not exactly replicate the behaviour of the toroid, since dx (parallel to the axis of revolution) is only an approximation for the real r d 1 ϕ, an approximation that is very good in the neighbourhood of /2 ϕ π = ± (errors are of the order of /6 2 ψ , where ψ is the angle from the edge), and that becomes better as r 1 becomes larger, and exact as r 1 approaches infinity.…”

“…Metal shells are particularly susceptible to buckling on account of their thin-ness (radius-to-thickness ratios typically in excess of 500). Numerical studies have been carried out on the buckling capacity of vertical cylindrical steel tanks [6][7][8][9][10][11], horizontal cylindrical and near-cylindrical vessels [12][13][14] and conical tanks [15][16][17]. The buckling capacity of multi-segmented shells under external water pressurisation has also been investigated [18], as has the elastic buckling of certain unusual mathematical forms for shells [19,20].…”

The ‘panel analysis’ technique in the computational study of axisymmetric thin-walled shell systems

“…These act as important reference 'base cases' to which the behaviour of more complex shell systems with circumferentially unsymmetrical loading is often related, making them deserving of thorough exploration and documentation. Perhaps surprisingly, despite their long-established presence in the classical mechanics literature, axisymmetric shell systems continue to be the focus of significant research study [2][3][4][5][6]. The review papers of Pietraszkiewicz and Konopińska [7] and Zingoni [8] offer further in-depth information on the history of advancements in shell theory, including the computational modelling of shells of revolution.…”