Clamped torispherical shells under external pressure — some new results

Abstract

Perfect clamped torispherical shells subjected to external pressure are analysed in the paper using the BOSOR 5 shell buckling program. Various values of the knuckle radius-to-diameter ratio ( r/D) and the spherical cap radius-to-thickness ratio ( Rs/ t) were studied, as well as four values of σyp, the yield point of the material. Buckling/collapse pressures, modes of failure and the development of plastic zones in the shell wall were determined. A simple diagram is presented which enables the failure mode in these shells to be predicted. The collapse pressures, pc, were also plotted against the parameter Λs (√( pyp/ pcr)). When the controlling failure mode was axisymmetric yielding in the knuckle, the collapse pressure curves depended on the value of σyp, which is unusual. However, when the controlling failure mode was bifurcation buckling (at the crown/knuckle junction), the collapse pressure curves for the various values of σyp all merged, i.e., they were independent of σyp. This latter situation is the one which normally occurs with the buckling of cylindrical and hemispherical shells. A limited investigation was also made into the effects of axisymmetric initial geometric imperfections on the strength of externally-pressurised torispherical shells. When the failure mode was axisymmetric yielding in the knuckle, initial imperfections of moderate size did not affect the collapse pressures. In the cases where bifurcation buckling at the crown/knuckle junction occurred, small initial geometric imperfections at the apex did not affect the buckling pressure, but axisymmetric imperfections at the buckle location did influence it. With the other failure mode (i.e., axisymmetric yielding collapse at the crown of the shell), initial geometric imperfections caused a reduction in the torisphere's strength.