Keywords: buckling, plastic buckling, circular cylinders, submarines, external pressure, design chart, ANSYS.

The paper presents new experimental results on the buckling of unstiffened circular cylinders suffering plastic non-symmetric bifurcation buckling under external hydrostatic pressure. In addition to an experimental analysis, theoretical analyses are also carried out. A closed-loop trivial solution is used, together with a finite element analysis using ANSYS. Comparison between ANSYS and the closed-loop trivial solution is good. A design chart is provided, which looks quite linear.

A Submarine pressure hulls consists of a combinations of circular cylinders, cones and dome ends. Under external hydrostatic pressure, the cylindrical and conical sections can fail through non-symmetric bifurcation buckling at a pressure, which might be a small fraction for the structure to fail under uniform internal pressure [1,2,3]. This mode of collapse is sometimes called shell instability or lobar buckling.

To increase the shell instability buckling resistance of these vessels, it is normal practice to stiffen these vessels with ring stiffeners in their flanks. If the ring stiffeners are not strong enough, the entire vessel can buckle bodily by a mode called general instability [1]. Another mode of failure is called axisymmetric deformation, where the body of the vessel implodes inwardly while retaining its circular form [1].

The buckling resistance of these vessels is further reduced if these structures have initial out-of-circularity. This is because as the external pressure is increased the initial out-of-circularity grows with increasing pressure until parts of the structure become plastic. This causes the tangent modulus to decrease and this further lowers the buckling resistance of these vessels until catastrophic failure takes place.

This study is limited to initially imperfect circular cylinders collapsing under external hydrostatic pressure. Twelve new vessels, together with the soldered models of Windenburg and Trilling [3] and the welded models of Reynolds [4] are investogated. A design chart, which could be used to design full-scale vessels, is provided.

1

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

2

R. von Mises, "Der Kritische Aussendruck für Allseits Belastete Zylindrische Rohre", Fest Zum 70. Geburtstag von Prof. Dr. A. Stodola, Zürich, pp. 418-30. Translated and annotated by D.F. Windenburg, 1936, Report No. 366, DTMB, Washington D.C, USA, 1929.

3

D.F. Windenburg and C. Trilling, "Collapse by Instability of Thin Cylindrical Shells Under External Pressure", Trans., ASME, 11, pp 819-825, 1934.

4

T.E. Reynolds, "Inelastic Lobar Buckling of Cylindrical Shells under External Hydrostatic Pressure", DTMB Report No. 1392, Aug., 1960.

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