Keywords: submarines, pressure hulls, external pressure, axisymmetric, lobar buckling, ANSYS.

The paper presents for the first time, theoretical and experimental analyses of the buckling of seven thin-walled circular cylinders, together with that of a circular cone; all were tested to destruction under uniform external hydrostatic pressure. The mode of failure for three of the cylinders and the cone was plastic axisymmetric collapse, while four of the circular cylinders collapsed through non-symmetric bifurcation buckling or shell instability; also called lobar buckling. All the vessels collapsed under external hydrostatic pressure and in the case of the plastic axisymmetric failures, the vessels imploded inwards while keeping their circular forms throughout their collapse. In the case of non-symmetric bifurcation buckling, the failure mode of the vessels was lobar buckling or shell instability, where the vessel imploded inwards with evenly spaced waves spaced around its circumference. The theoretical analysis adopted the finite element method, where the commercial computer package, namely ANSYS was used. The theoretical work involved the inclusion of both material and geometrical non-linearity, using an incremental step-by-step method. About fifty incremental steps were used per model. Comparison between theory and experiment was good and this appeared to indicate that the method could be applied to full-scale vessels. The ANSYS computer analysis used the eight-node isoparametric shell element, namely Shell93; which was not axisymmetric. A typical submarine pressure hull consists of a combination of thin-walled circular cylinders, cones and domes. In this paper, we will consider both the thin-walled circular cylinder and the thin-walled circular cone. Now under uniform external pressure, such a vessel can implode through shell instability or lobar buckling [1], at a fraction of the pressure to cause the same vessel to explode under uniform internal pressure. This mode of failure is an undesirable mode owing to its poor resistance to withstand uniform external hydrostatic pressure. One method of improving its poor resistance to withstanding uniform external hydrostatic pressure is to ring stiffen it, with ring stiffeners spaced suitably apart. In this case, if the stiffeners are not strong enough, the vessels can collapse through general instability. Moreover, the vessel can still fail due to shell instability, if adjacent ring stiffeners are spaced too far apart, but if the stiffeners are strong and closely spaced together, the shell can fail through axisymmetric deformation. In the case of axisymmetric deformation the circular cylinder keeps its circular form while imploding inwards. It is for the reasons of these different modes of plastic failure, that the present study was carried out, where both geometrical and material non-linearity were considered for both shell instability and axisymmetric deformation.

1

C.T.F. Ross, "Pressure Vessels: External Pressure Technology", Horwood, Chichester, UK, 2001.

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