Design of submarine pressure hulls to withstand buckling under external hydrostatic pressure

Transcription

1 icccbe 2010 Nottingham University Press Proceedings of the International Conference on Computing in Civil and Building Engineering W Tizani (Editor) Design of submarine pressure hulls to withstand buckling under external hydrostatic pressure Carl T.F. Ross, Terry Whittaker & Andrew P.F. Little University of Portsmouth, UK Abstract The paper presents an investigation into various methods of calculating the theoretical collapse loads for a pressure vessel, under uniform external hydrostatic pressure; based on different design codes. The design codes used for the investigation were BS 5500, for vessels under external pressure and also, the design charts of Ross of the University of Portsmouth. It is the opinion of the present authors that the current design methodology, namely BS 5500 was difficult to use and gave inaccurate collapse pressures for some large-scale pressure vessels. Moreover, BS 5500 appeared to be too pessimistic for one mode of failure and too optimistic for another mode of failure. For the present study, a full-scale theoretical pressure vessel was used and the fore mentioned methodologies applied in its design to see if there were any similarities that each method may have had. From the results obtained, it became apparent that some methodologies were more accurate than others, depending on the mode of collapse. Moreover, it also became apparent that some of the methods themselves were outdated, user-unfriendly and in some cases, may have even been dangerous. Keywords: submarines, pressure hulls, hydrostatic pressure, structural design 1 Introduction Under uniform external hydrostatic pressure, a submarine pressure hull can buckle through shell instability or lobar buckling at a pressure (Ross, 1965; Ross, 2001), which may be a fraction of the same vessel to explode under uniform internal pressure, as shown in Figure 1.

2 Figure 1, Shell instability of a circular cylinder This mode of failure is undesirable, as it is structurally inefficient and one way of improving its structural inefficiency, is to ring-stiffen it with suitable sized ring stiffeners, spaced at suitable distances apart. If, however, the ring stiffeners are not strong enough, the entire ring-shell combination can buckle bodily in its flank, through a mode of failure called general instability, as shown in Figure 2. Figure 2, General instability If the ring stiffeners are very strong and the spacing between them is relatively small, then failure can take place through a mode of failure called axisymmetric deformation, where the circular cylinder keeps its circular form while imploding inwards, as shown in Figure 3. This mode of failure is more predictable and designers often prefer to design out the two instability modes of failure, so that if failure takes place, it fails through this more predictable mode of failure, called axisymmetric deformation. Figure 3, Axisymmetric collapse In this paper, we will design a full-scale model using BS 5500 and also, using Ross s (2001) codes.

3 2 The designs One full-scale structural design was considered, namely Submarine 1; details of which are given in Figure Submarine 1 Figure 4, Dimensions of the full-scale submarine The following parameters were used for Submarine 1: T = 2 = 50.8mm B = 1 = 25.4mm D = 8 = 203.2mm l = 27 = 685.8mm = 364 = mm R = 192 = mm Ε = Young s modulus = 3 e 07 Ksi = 2.07 e 05 GPa ν = Poisson s ratio = 0.3 σ = Yield stress = psi = 552 MPa Material of construction = HY80 Steel 2.2 Designing against shell instability In order to investigate shell instability, the section between adjacent frames was theoretically isolated and then the following two methods were employed to determine the collapse pressures due to shell instability: Design Chart of Ross et al (2009), which makes use of the Von Mises formula (1936), Design Chart of BS5500 (1980). The theoretical von Mises (1936) collapse pressure, for perfect circular cylinders was calculated using the computer program MISESNP.EXE (Ross, 2001). The computer program also calculates the Windenburg thinness Ratio (λ) (Windenburg & Trilling, 1934); this value will be used in conjunction with the design charts of Ross, to calculate the plastic knockdown factor, namely PKD and thus, the actual collapse pressure. The results from this program were as follows: λ= Thinness ratio = {(L/D) 2 /(T/D) 3 } 0.25 * (σ/e) 0.5 = Pcr = von Mises buckling pressure = 25 MPa with 14 lobes (n=14) Knowing λ, the required PKD has to be determined from the design chart of Ross et al (2009); see Figure 5.

4 Figure 5, Ross design chart for shell instability Now,. 1.4 Therefore, from Figure 5, PKD = 2.8 Now the von Mises theoretical buckling pressure for perfect vessels, namely Pcr, must be divided by PKD to give the actual predicted buckling pressure, namely Pcr (actual). P actual P = MP 8.9MPa 890m depth of water. PKD. From BS 5500 s design chart of Figure 6, the shell instability calculations were also carried out. Now K= P, P Where P m = the von Mises buckling pressure for perfect vessels & P y = 2σT/D = the pressure to cause axisymmetric yield. From Figure 6, P P = 0.56 Now P y = , therefore p 0.56 Py Converting to MPa MPa 10 Where p = actual buckling pressure, given by BS5500. From the above, it can be seen that a design depth of 472 m, by BS 5500 is too pessimistic, when dealing with shell instability, because Ross (2001) predicts a corresponding diving of 890m!

5 Figure 6, BS 5500 design chart 2.3 General instability To design against the general instability mode of failure, two methods below were used, namely Kendrick Part 1 (1953) 7 BS5500, as follows: Kendrick Part 1. BS 5500 which uses Bryant s formula (1954). The theoretical buckling pressure for Kendrick Part 1 was calculated by Ross computer program (2001). As the vessel that was analysed was of a ring stiffened nature, it was difficult to use Ross computer program, namely MISESNP (Ross, 2001), as MISESNP was intended for unstiffened circular cylinders. To overcome this problem, an equivalent shell thickness (T ), and equivalent vessel radius (Rf) were used to calculate the equivalent Windenburg s thinness ratio, namely λ (Windenburg and Trilling, 1934). From the design chart of Ross et al (2008); λ = 1.38, therefore: Hence, from Figure 7, PKD = 1.2. Figure 7, Ross design chart for general instability

6 From Ross computer program (2001), namely Kendrick Part1, Pcr (theoretical) = 6.2MPa (4 Lobes) Hence, the actual general instability buckling pressure, namely Pcr (actual) was calculated. Pcr Actual Pcr 6.2MPa 5.2MPa 520M PKD 1.2 From BS 5500, which was very difficult to use, we get, the lowest Pcr value to be: 6.46MPa, failing with 4 lobes; corresponding to a maximum diving depth of 646 m; which was positively dangerous, because Ross code gave a corresponding collapse diving depth of only 520m! 2.4 Axisymmetric deformation Using the Boiler Formula, Ross (1999), the collapse pressure= P = 5.7 MPa = 570m of water depth. We have no disagreement with using the Boiler Formula of BS5500! 3 Conclusions The findings from the results for Pressure Vessel 1 appear to show that BS 5500 is too pessimistic for shell instability, but worse still, too optimistic for general instability. The authors do not have any quarrel with BS 5500, as far as the axisymmetric mode of failure is concerned. Moreover, Ross design charts are much easier to use and in any case, their linear nature of Ross design charts make it easier for the designer to use. In contrast this; the design chart of BS 5500 is curved, making life difficult for the designer. Calculating the buckling pressures by BS 5500 is worsened because the calculations are very laborious, because they have to be done for every value of n, the number of circumferential waves that the vessel buckles into. This is necessary to obtain the minimum value of Pcr. References BRYANT, A.R., Hydrostatic pressure buckling of a ring-stiffened tube. NCRE Report No. R306, October. BSI, BS5500, British standards specification for unfired fusion welded pressure vessels. Issue 5. UK, British Standards Institution. ROSS, C.T.F., The collapse of ring-reinforced cylinders under uniform external pressure. Trans., RINA, 107, ROSS, C.T.F., The instability of ring-stiffened circular cylindrical shells under uniform external pressure. Trans., RINA, 107, ROSS, C.T.F., Mechanics of Solids, Chichester, UK, Horwood. ROSS, C,T.F., Pressure vessels: external pressure technology, Chichester, UK, Horwood. ROSS, C.T.F., OKOTO K.O. and LITTLE, A.P.F., Buckling by general instability of cylindrical components of deep sea submersibles. Paper 300 in Proceedings of the Ninth International Conference on Computational Structures Technology, B.H.V. Topping and M. Papadrakakis, (Editors), Civil-Comp Press, Stirlingshire, Scotland. ROSS, C.T.F., SPAHIU, A., BROWN, G.X. and LITTLE, A.F.P., Buckling of near-perfect thick-walled circular cylinders under external hydrostatic pressure. Journal of Ocean Technology, Vol.4., No. 2 pp VON MISES, R., USEMB Translation Report No. 366, Washington, DC, USA. WINDENBURG, D.F. and TRILLING, C., Collapse by instability of thin cylindrical shells under external pressure. Trans. ASME, 11,