Andrew P.F. Little

Collapse of composite tubes under uniform external hydrostatic pressure

This paper describes an experimental and a theoretical investigation into the collapse of 22 circular cylindrical composite tubes under external hydrostatic pressure. The investigations were on the collapse of fibre reinforced plastic tube specimens made from a mixture of three carbon and two E-glass fibre layers. The theoretical investigations were carried out using an in-house finite element computer program called BCLAM, together with the commercial computer package, namely ANSYS. It must be emphasised here that BS 5500 does not appear to exclusively cater for the buckling of composite shells under external hydrostatic pressure, so the work presented here is novel and should be useful to industry. The experimental investigations showed that the composite specimens behaved similarly to isotropic materials previously tested, in that the short vessels collapsed through axisymmetric deformation while the longer tubes collapsed through non-symmetric bifurcation buckling. Furthermore it was discovered that the models failed at changes of the composite lay-up due to the manufacturing process of these models. These changes seemed to be the weak points of the specimens.

The buckling of a corrugated carbon fibre cylinder under external hydrostatic pressure

A theoretical and an experimental investigation was carried out, where a carbon fibre corrugated circular cylinder was tested to destuction under external hydrostatic pressure. The theoretical investigation was via the finite element method, where the structure was modelled with several orthotropic axisymmetric thin-walled shell elements. The experimental observations were aided with strategically placed strain gauges. Comparison between theory and experiment showed that the experimentally observed buckling pressure was a little lower than the theoretical prediction. This may have been due to the fact that the model had slight initial geometrical imperfections in the circumferenential direction.

Plastic General Instability of Ring-Stiffened Conical Shells under External Pressure

The paper describes experimental tests carried out on three ring-stiffened circular conical shells that suffered plastic general instability under uniform external pressure. The cones were carefully machined from EN1A mild steel to a very high degree of precision. The end diameters of the cones, together with their thicknesses were the same, but the size of their ring stiffeners was different for each of the three vessels. In the general instability mode of collapse, the entire ring-shell combination buckles bodily in its flank. 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 15 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 allowed the possibility of obtaining plastic knockdown factors, so that the theoretical elastic buckling pressures, for perfect vessels, could 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, namely RCONEBUR and the commercial finite element package ANSYS. This method can also be used for the design of full-scale vessels.

The vibration of a large ring-stiffened prolate dome under external water pressure

The paper presents a theoretical and an experimental investigation into the free vibration of a large ring-stiffened prolate dome in air and under external water pressure. The theoretical investigation was via the finite element method where a solid fluid mesh with an isoparametric cross-section was used to model the water surrounding the dome, and a truncated conical shell and ring stiffener were used to model the structure. Good agreement was found between theory and experiment. Both the theory and the experiment found that as the external water pressure was increased the resonant frequencies decreased. # 2003 Elsevier Ltd. All rights reserved.

Buckling of ring stiffened domes under external hydrostatic pressure

The paper reports on the buckling of three ring-stiffened prolate domes under external hydrostatic pressure. The study was partly theoretical and partly experimental, where in the case of the latter, the finite element was used. Comparison between experiment and theory was good. The effect of ring stiffening the domes was to increase their buckling resistances by factors varying from 4.43 to 5.72.

BUCKLING OF A LARGE RING STIFFENED PROLATE DOME UNDER EXTERNAL HYDROSTATIC PRESSURE

The paper reports on the buckling of a ring-stiffened hemi-ellipsoidal prolate dome under external hydrostatic pressure. The study was partly theoretical and partly experimental, where in the case of the latter, the finite element method was used. Comparison between experiment and theory was good. The effect of ring stiffening the dome was to increase its buckling resistance by a factor of 2.05.

Buckling by General Instability of Cylindrical Components of Deep Sea Submersibles

This paper reports on theoretical and experimental investigations into the buckling characteristics of a series of six ring-stiffened circular cylinders that experienced general instability when subjected to external hydrostatic pressure. Each study used between 3-5 designs with the same internal and external diameters, but with different numbers and sizes of ring-stiffeners. Four used designs that were machined to a high degree of precision from steel, while the other two were machined from aluminium alloy. The theoretical investigations focused on obtaining critical buckling pressure values, namely Pcr, for each design from the well-known Kendrick’s Part I and Part III theories, together with an ANSYS finite element prediction. The thinness ratio λ1, which was originally derived by the senior author, was calculated together with a dimensionless quantity called the plastic knockdown factor (PKD), for each model. The plastic knockdown factor was calculated by dividing the theoretical critical buckling pressures Pcr, by the experimental buckling pressures Pexp. The thinness ratio was used because vessels such as these, which have small but significant random out-of-circularity, defy “exact” theoretical analysis and it is because of this that the design charts were produced. Three design charts were constructed by plotting the reciprocal of the thinness ratio (1/ λ1) against the plastic knockdown factor (Pcr / Pexp), using results from Kendrick Part I, Kendrick Part III, and ANSYS. Comparison of the results obtained using Kendrick’s theories and experimentally obtained results was good.

A design chart for the plastic collapse of corrugated cylinders under external pressure

The paper presents a theoretical and an experimental investigation into the plastic collapse of circular steel corrugated cylinders under external hydrostatic pressure. The experimental investigation gives a detailed study of 9 steel corrugated cylinders which were tested to destruction. Six of these cylinders failed by plastic non-symmetric bifurcation buckling and three failed by plastic axisymmetric deformation. The results of these tests were used, together with the results obtained from previous tests, to present a design chart for the plastic collapse of these vessels. The design chart was obtained by a semi-empirical approach, where the thinness ratios of the vessels were plotted against their plastic knockdown factors. The process of using the design chart is to calculate the theoretical elastic instability pressure for a perfect vessel by the finite element method and also to calculate the thinness ratio for this vessel. Using the appropriate value of the thinness ratio, the plastic knockdown factors are obtained from the design chart. To obtain the actual collapse pressure of the vessel, the theoretical elastic instability pressure for a perfect vessel is divided by the plastic knockdown factor. This work is of importance in ocean engineering. A large safety factor must also be introduced.

Collapse of Glass/Carbon Fibre Circular Cylinders under Uniform External Pressure

This paper describes an experimental and an analytical and numerical investigation into the buckling behaviour of cylindrical composite tubes under external hydrostatic pressure. The investigations concentrated on fibre reinforced plastic tube specimens made from a mixture of three carbon and two E-glass fibre layers. The lay-up was 0°/90°/0°/90°/0; the carbon fibres were laid lengthwise (0°) and the E-glass fibres circumferentially (90°). The theoretical investigations were carried out using a simple solution for isotropic materials, namely a well-known formula by “von Mises” and also by finite element analyses using ANSYS. The experimental investigations showed that the composite specimens behaved similarly to isotropic materials tested by various other researchers. The specimens failed by the common modes associated with this study, namely due to elastic buckling, inelastic buckling and axisymmetric yield failure. Furthermore it was discovered that the specimens failed at changes of the composite lay-up due to the manufacturing process of these specimens. These changes seem to be the weak points of the specimens. For the theoretical investigations two different types of material properties were used to analyse the composite. These were calculated properties derived from the properties of the single layers given by the manufacturer and experimentally obtained properties. Two different approaches were chosen for the investigation of the theoretical buckling pressure, a program called “MisesNP”, based on a well-known formula by von Mises for single layer isotropic materials, and two finite element analyses using the famous computer package called “ANSYS”. This latter analyses simulated the composite with a single layer orthotropic element (Shell93) and also with a multi layer element (Shell99). It was found out that the results obtained with ANSYS predicted questionable buckling pressures that could not be reproduced logically. Nevertheless this report provides Design Charts for all approaches and material types. These Design Charts allow the possibility of obtaining a ‘plastic knockdown factor’. The theoretical buckling pressures obtained using MisesNP or ANSYS can then be divided by the plastic knockdown factor, to give predicted buckling pressures. This method can be used for the design of full-scale vessels.

Formulation of design charts for composite submarine pressure hulls

This paper describes an experimental and a theoretical finite element (FE) numerical investigation into the collapse of 44 circular cylindrical composite tubes under external hydrostatic pressure. The results for these 44 tubes are from earlier investigations carried out by Ross et al. (2007, 2008), with the resulting design charts building upon earlier work by Ross et al. (1999) and is now presented in a new format for the first time in this paper. The investigations carried out concentrated upon fiber-reinforced plastic tube models, manufactured from a mixture of three carbon and two E-glass fiber layers. The material lay-up was 0° / 90° / 0° / 90° / 0° with the carbon fibers being laid lengthwise (0°) and the E-glass fibers being laid circumferentially (90°). The theoretical investigations were carried out using a simple solution for isotropic materials, namely the well-known von Mises Formula, together with FE solutions of a numerical solution. The earlier investigations also used a numerical solution using the software program ANSYS (Canonsburg, PA), however the results of this work were found to be disappointing. The experimental investigations carried out showed that the composite models behaved similarly to isotropic materials previously tested, such that short models suffered collapse through axisymmetric deformation, whilst the longer tubes collapsed through nonsymmetric bifurcation buckling. Additionally, it was discovered that the models suffered failure at changes of the composite lay-up due to the manufacturing process of these particular models and these changes at which failure occurred give the appearance of being the weak points of the models. To carry out the theoretical investigations, two different types of material properties were used for the composite analysis. First, the material properties of the single layers, as supplied by the manufacturer and second, a set of material properties derived experimentally within the engineering laboratory. So as to verify the previously obtained experimental and theoretical results, the identical approach was chosen, in that MisesNP (Portsmouth, UK) was used, which is a program based on the von Mises Formula for single layer isotropic materials. The second theoretical method used two finite element analyses, using the commercial software package ANSYS. Specifically, the ANSYS analyses simulated the composite with a single layer orthographic element (Shell 93) and secondly with a multilayer element (Shell 99). Although the results from Shell 93 and Shell 99 agreed with each other, their predicted buckling pressures were, in general, higher than those predicted by the von Mises analytical method. With respect to the longer models, the von Mises solution produced a more consistent set of results, with the failure mode being elastic instability; this being highlighted when the experimentally obtained material properties were used. Hence the conclusion drawn was that the results obtained via finite element analyses produced buckling pressures that are questionable. This report provides design charts for all 44 models, using all of the theoretical approaches previously adopted, with both theoretically obtained material properties and those material property values obtained experimentally. The resulting design charts have not been previously published for all 44 models combined. These resulting design charts allow the possibility of obtaining a Plastic Knockdown Factor (PKD) for the models under investigation. Once the theoretical buckling pressures have been obtained, using either MisesNP or ANSYS, the theoretical buckling pressures can then be divided by the PKD via the design charts, so as to obtain the predicted buckling pressures. Work has been carried out by Sonardyne International Limited of Yateley, Hampshire, UK, using the design charts of Ross et al. (2007, 2008), in preference to BS5500 (British Standards Institution 2000), with substantial weight savings being made for their pressure vessels.