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Civil-Comp Proceedings
ISSN 1759-3433
CCP: 85
PROCEEDINGS OF THE FIFTEENTH UK CONFERENCE OF THE ASSOCIATION OF COMPUTATIONAL MECHANICS IN ENGINEERING
Edited by: B.H.V. Topping
Paper 75

Design Charts for the Plastic General Instability of Ring-Stiffened Conical Shells under External Hydrostatic Pressure

C.T.F. Ross, A.P.F. Little, R. Allsop, C. Smith and M. Engelhardt

Department of Mechanical and Design Engineering, University of Portsmouth, United Kingdom

Full Bibliographic Reference for this paper
C.T.F. Ross, A.P.F. Little, R. Allsop, C. Smith, M. Engelhardt, "Design Charts for the Plastic General Instability of Ring-Stiffened Conical Shells under External Hydrostatic Pressure", in B.H.V. Topping, (Editor), "Proceedings of the Fifteenth UK Conference of the Association of Computational Mechanics in Engineering", Civil-Comp Press, Stirlingshire, UK, Paper 75, 2007. doi:10.4203/ccp.85.75
Keywords: general instability, plastic buckling, ring-stiffened cones, external pressure.

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

The paper also provides a design chart, using the results obtained from these three vessels, together with the results of nine other vessels obtained from other tests. All 12 vessels failed by overall general instability. The design chart allows the possibility of obtaining a plastic knockdown factor, so that the theoretical elastic buckling pressures for perfect vessels can be divided by the plastic knockdown factor, to give the predicted buckling pressure. 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 reinforced (ring-stiffened), its buckling resistance under uniform external pressure is abysmally poor [1]. One method of greatly improving the buckling resistance of such vessels is to ring- reinforce 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 so far 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.

References
1
C.T.F. Ross, "Pressure Vessels: External Pressure Technology", Horwood, Chichester, United Kingdom, 2001.

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