Keywords: general instability, plastic buckling, ring-stiffened cones, external pressure, ANSYS, finite elements.

The paper describes, for the first time, experimental tests carried out on three ring-stiffened circular conical shells that suffered plastic general instability under uniform external pressure. In this mode, the entire ring-shell combination buckles bodily in its flank. The cones were carefully machined from EN1A mild steel to a very high degree of precision.

The paper also provides three design charts using the results obtained from these three vessels, together with the results obtained for twelve other vessels from other tests. All fifteen vessels failed by general instability. One of these design charts was based on conical shell theory and two of the design charts were based on the general instability of ring-stiffened circular cylindrical shells, using Kendrick's theory, which were made equivalent to ring-stiffened circular conical shells suffering from general instability under uniform external pressure. The design charts allow for the possibility of obtaining plastic knockdown factors, so that the theoretical elastic buckling pressures for perfect vessels can be divided by the appropriate plastic knockdown factor, to give the predicted buckling pressure. The theoretical work is based on the solutions of Kendrick, together with the finite element program of Ross [1], namely RCONEBUR and the finite element package ANSYS. This method can also be used for the design of full-scale vessels.

Submarine pressure hulls usually take the form of ring stiffened circular cylinders and cones blocked off by dome ends. If a long thin-walled circular cylinder or cone is not ring-stiffened, its buckling resistance under uniform external pressure is abysmally poor, [1]. Such a vessel may fail by non-symmetric bifurcation buckling, or shell instability.

One method of greatly improving the buckling resistance of such vessels is to ring-stiffen them. If, however, the ring-stiffeners are not strong enough the entire ring-shell combination can collapse due to the application of uniform external pressure. This mode of failure is known as general instability.

Exact theoretical analysis of many of these structures has been defied, particularly for the less slender vessels that buckle plastically, as the slightest initial out-of-circularity causes the vessels to fail at buckling pressures that are much lower than predicted by theory. The reason for this is partly because the initial out-of-circularity is random and difficult to model. In practice this random initial out-of-circularity grows non-linearly with increase in uniform external pressure so that one part of the vessel becomes plastic. When this occurs, the tangent modulus of the vessel in the area that has gone plastic, decreases to quite a small value. This further complicates the deformation, and causes other parts of the structure to go plastic. The situation is then worsened and eventually the vessel suffers sudden and catastrophic failure. The paper presents several such design charts, which can be used for full-scale vessels.

1

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

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