Keywords: submarine pressure hulls, corrugated, ring-stiffened, finite elements, plastic buckling, ANSYS.

The paper describes a finite element investigation into the buckling, under uniform external pressure, of 4 submarine pressure hulls. Two of these submarine pressure hulls were traditional ring-stiffened types, but two of these hulls were in the form of corrugated circular cylinders. The latter design was based on an invention by the present author. The investigation found that the new design was quite structurally efficient and in the case of the smaller vessel, it was found to be more structurally efficient than the conventional design.

Another investigation, based on axisymmetric plastic buckling of the bellows' variety, was carried out on the two corrugated vessels, to determine if they were prone to collapse through the bellows' mode of failure. Neither of the two corrugated pressure hulls was found to fail through the bellows' mode of failure. The author, however, concludes that the bellows' mode of failure can occur if the cone angles were too large. Two of the finite element theories were based on the author's work, but the giant computer package ANSYS was also used to vindicate the author's earlier work. Thin-walled circular cylinders are often used to construct submarine pressure hulls. This is partly because circular cylinders make good pressure vessels and partly because a circular cylinder has a good hydrodynamic shape. Additionally, the designer may be able to obtain the required internal volume, because he/she can allow the cylinder to be of the appropriate length. However, under uniform external pressure, a circular cylinder can buckle [1,2], at a pressure which may only be a small fraction of that required to cause axisymmetric yield.

One method of vastly improving the buckling resistance of these vessels is to ring-stiffen them. If the ring stiffeners are not strong enough the entire ring-shell combination can buckle bodily; this mode of failure is known as general instability [3,4].

Ring-stiffened circular cylinders, however, have proven popular in the design and construction of submarine pressure hulls at the end of the 19th century and throughout the entire twentieth century, and they will continue to prove popular in the 21st century. In 1987, an alternative design to using the ring-stiffened circular cylinder for a pressure hull was presented by Ross [5], when he invented the corrugated circular cylinder, as shown in Figure 55.1.

Ross showed with the aid of two vessels, that the corrugated pressure hull was structurally more efficient than the ring-stiffened equivalent of the same volume and weight. Ross used the two vessels, namely Corrugated Vessels 1 & 2.

The results have shown that the corrugated pressure hull has much structural merit. Indeed for both Corrugated Vessels 1 & 2 the buckling pressures were much higher than their ring-stiffened equivalents.

For both of the chosen corrugated vessels, it appears that the axisymmetric bellows' type failure is extremely unlikely. However, the cone angles of the corrugated vessels must not be made too large as failure through axisymmetric bellows' buckling can take place at relatively low values of uniform external pressure.

1

Von Mises, R., Der Kritische Aussendruck für Allseits Belastete Zylindrische Rohre, Fest Zum 70, Gerburtstag von Prof. Dr. A. Stodola, Zürich, 418-30, 1929. (Also USEMB Translation Report No. 366, 1936).

2

Ross, CTF., Pressure Vessels : External Pressure Technology, Horwood, Chichester, UK, 2001.

3

Tokugawa, T., Model Experiments on the Elastic Instability of Closed and Cross-Stiffened Circular Cylinders under Uniform External Pressure, Proc. World Engng, Congress, Tokyo, Vol. 29, Paper No. 651, 249-79, 1929.

4

Kendrick, S., The Buckling under External Pressure of Circular Cylindrical Shells with Evenly Spaced Equal Strength Circular Ring Frames - Part 1, NCRE Report R211, 1953.

5

Ross, CTF., A Novel Submarine Pressure Hull, J. Ship Res, 31, 139-43, 1987.

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