UDC: 531.01, 621.643.3

The deformation mechanics of interlock tubes by 2. Chen, Offtech Group, Global Engineering Ltd., Croydon, R. L. Reuben, Department of Mechanical Engineering, Heriot- Watt University, Edinburgh, and D. G. Owen, Department of Offshore Engineering, Heriot- Watt University, Edinburgh.

Interlock tubes are one of the key structural layers of most flexible pipes of composite construction for offshore oil and gas transmission and water injection applications. The design and manufacture of such a tube based on a good understanding of its deformation mechanics are undoubtedly of significance to the integrity and safety of flexible pipes and pipe systems. This paper describes a semi-empir ica l model f o r the evaluat ion of the deformations in the critical sections of the interlock tube as i t responds t o the overall p i p e loading and configuration. Results of a finite element analysis and radiographic tests are incorporated to verify and supplement the model.

Key words: Interlocking tubes, stainless steel, flexible pipes, flexible risers, integrity.

List of Symbols

strip thickness of interlock

depth of section of interlock

comer radius of interlock

pitch of interlock

interlock angle

radial intrusion pressure of elastomer into gaps

interface reaction forces between adjacent interlock

gaps interface friction forces between adjacent interlock

gaps pipe radius of curvature under bending

slip of turn l+i relative to i

deformation elongation of turn i

maximum strain at interlock fillet radius (p = microstrain)

global pipe elongation under tension

global pipe tension

axial deflection per unit load times pipe length

amount of slip per unit length of interlock under

bending

amount of slip per unit length of interlock under

tension

'Strain', August I992

Introduction

Flexible pipes are invariably of composite construction consisting of a number of concentric layers of various materials which may be bonded together or may be of unbonded structure (Fig. 1). A feature which both types of pipe share is the provision of a carcass whose primary function is to provide mechanical stability against buckling collapse. This carcass often takes the form of an interlock tube (also known as the flex or the interlock) which is cold formed from strip material (Fig.2). With the increasing use of flexible pipes in marine hydrocarbon exploitation, there is a need to gain knowledge on the long term integrity and performance of such pipes so that reliability estimates can be made for critical applications.

Fig 1. Schematic view of composition of bonded and unbonded flexible pipes

A

Fig 2. In situ and sectional views of interlock tube

Previous literature pertaining to flexible pipes has dealt mainly with the dynamic behaviour of flexible risers of various configurationsl-7.

A limited number of papers on the internal mechanics and service life prediction has also appeared since 1985 8-12.

However, none of these has treated the important action of the interlock tube, which is surprising given its importance in the flexible pipe construction. After a very large number

99

of cycles under conditions of severe strain there is a possibility that fatigue cracking in these interlocking tubes may be the first physical sign of damage in the entire pipe. Of course, a clear picture of the mechanism by which the interlock deforms and a knowledge of the magnitude of the deformation involved are essential before any fatigue analysis can be carried out.

In the present investigation, a 2-D analytical model, referred to as the deformation approach, will first be developed for the evaluation of the deformations which can result in fatigue cracking. Results of a finite element analysis and radiographic tests of full scale pipe samples are incorporated to validate and supplement this model. It should be pointed out that, since the work to be reported here has been part of a systematic investigation into the mechanical behaviour and fatigue performance of a bonded flexible pipe, this paper is particularly applicable to that type of pipe. However, with appropriate modifications, it is felt that the approach can also be useful for interlock tubes in unbonded pipes.

The deformation mechanics of the interlock tube

Description of the interlock tube functions Before starting to analyse the loading and deformation mechanisms of the interlock tube, it is useful to describe the functions which it is designed to fulfil. These are:

- to help prevent rupture of the elastomeric liner in the event of rapid internal depressurisation;

- to support the radial inwards loading resulting from the response of the reinforcement cable layers to overall tension, torsion or bending of the pipe;

- to resist point and distributed loads, including external pressure.

The tube is not intended to contain internal pressure, this function being fulfilled by the reinforcement layers. The gap between adjacent turns of the interlock is responsible for the necessary flexibility of the tube and the size of this gap is also a major factor in determining the minimum bend radius of the pipe. The adjacent turns are intended to slide with respect to each other, thus avoiding axial loading of the tube resulting from pipe tension or bending.

The loading and deformation mechanisms

a ) The loading mechanism According to the design of the interlock tube, it should only experience the radial inwards loading created by the reinforcement layers when the pipe is tensioned or bent. However, a detailed analysis 13 has revealed that the interlock tube can be axially stressed while the pipe is under tenslon or bending. In extreme cases this can give rise to fatigue cracking at section A of the interlock (Fig. 2) . As a pipe is tensioned, the adjacent turns of the interlock

100

will tend to s l ide relative to each other and the reinforcement cable layers will generate a radial pressure on the elastomeric liner causing:

(i) the intrusion of the elastomer into the gaps between adjacent turns; and,

(ii) pressure between interfaces of adjacent turns.

As a result, the sliding action is impeded and the following loads are developed:

- radial pressure and intrusion pressure P, - interface reaction forces Pi - interface friction forces Fi

The resulting loading system is illustrated in figure 3.

I Rubber

Fig 3. Forces exerted by elastorneric liner on the interlock tube under global pipe tension

When a pipe is bent, the gaps between adjacent turns of the interlock on the convex side of the bend will tend to slide open and those on the concave side to slide shut. The loading mechanism for the interlock on one side would therefore be somewhat different from that on the other. However, for the purpose of the present work, it is considered sufficient to identify the loading system acting on the tension (convex) side of the interlock tube. On this side, one can expect a loading system similar to that seen in the case of tension. However, some differences do exist between the two cases mainly due to the fact that, in the case of bending, not only will the adjacent turns slide but they will also rotate relative to each other, resulting in a shift of the points of action of the interface reaction forces, Pi. The positions of these points of action will depend on the clearances between adjacent turns and the relative rigidities of different parts of the turn. Figure 4 depicts the loading system on a turn of the interlock tube when the pipe is under bending. As can be seen by comparison with figure 3, the points of action of the forces, Pi, have been shifted.

b) The deformation mechanism When a pipe is stretched, it will elongate (FigSa and Fig. 5b) and, in response to the global elongation of the pipe, the interlock tube will stretch by the same amount, i.e. AL. According to the loading mechanism described above, axial deformation of the interlock will occur. That is to

‘Strain’, August 1992

say, AL is actually a result of both the sliding action and the deformation of the turns. As illustrated in Figures 5a and 5b, the amount of slip of turn i+l relative to turn i, which is a rigid body motion, can be identified as si = gi - gIi. The deformatlon of a turn may be represented in the manner shown in Fig. 5c.

5c. It is thought that these represent two limiting cases of interlock compliance to the global curvature of the pipe and, for the purposes of the following discussion, these two cases will be referred to as ‘tensile’ and ‘bending’ modes ‘of interlock deformation. Slip is, of course, also possible during bending deformation.

Fig 4 Forces exerted by elastomeric liner on the interlock tube under global pipe bending

-I: I

-‘I4

Fig 5 Forces exerted by elastomeric liner on the interlock tube under global pipe tension

The resulting displacement of the turn in the axial direction due to deformation is given by

1 1 -6. +-6 . = 6. 2 ’ 2 l ’

Therefore one has

AL = Zsi + Z6i

It should be stressed here that both Csi and C6i are functions of the pipe global tension T. When the tension is small, the deformation Czi which depends largely upon the interface friction forces enhanced by the radial inwards loading, may be too small to cause fatigue problems. However, when the tension reaches a certain level, the deformation could be appreciable.

When the pipe is under bending, the mechanism becomes more complicated. According to the loads acting upon a turn of the interlock (Fig.4), it is possible for the turn to deform either as shown in figure 6 or as shown in figure

Fig 6. Bending mode of interlock deformation

When an interlock turn is considered to deform in the manner shown in figure 6, a ‘threshold bend radius’ can be identified and the critical strain can be calculated as a function of the applied bend radius of the pipe and some parameters relating to the interlock geometry. Details of this are provided elsewhere13 and it has been found that the theory based on this mechanism underestimates the critical strain by a factor of 4 and therefore is unlikely to be the mode which accounts for most of the deformation of the interlock.

On the other hand, since the interlock on the convex side of the pipe will be subjected to tension, it is natural to consider that the individual turns are deformed in a way similar to that described for the case of tension. That is to say, the interlock is deformed in a tensile mode. However, in this case the slip and elongation of the turn will not be circumferentially uniform. Moreover, the relative proportion of the slip and elongation which comprise the total axial extension, AL, of the interlock, is expected to be different from that for the case of tension. This is due to the difference in the loading mechanisms as described previously.

The deformation approach

As is well known, a prediction of fatigue life using the Palmgren-Miner rule is not possible without a knowledge of the time histories of either the stresses or the strains in question. In the case of the inter lock tube under consideration, the stresses or strains causing fatigue cracking of sections A and B as shown in figure 5 must be evaluated as a function of the overall applied pipe loading or bend radius.

There seems to be no simple way of directly determining the stresses. For example, in order to calculate the stresses in sections A and B of figure 5 due to pipe tension, the pressures and forces shown in figure 3 must first be obtained. Of course, the radial pressure, P, , can be

‘Strain’, August 1992 101

evaluated using existing cable and wire rope theories 1 4 ~ 5

However, the determination of the intrusion pressure, Pri, the interface reaction forces, Pi, and friction forces, Fi , is by no means an easy task. The determination of Pri is complicated mainly because of the complex process of intrusion of the rubber and sliding action of adjacent turns of the interlock. The difficulties involved in finding the interface reaction forces and friction forces are largely due to the uncertainties about the points of action of forces Pi. From this example one can easily imagine how much more difficult and complex it would be to evaluate the stresses in the interlock due to pipe bending.

In order to avoid the above difficulties and complexities, a model, referred to as the deformation approach, has been developed as an alternative way of assessing the effect of fatigue loading imposed upon the interlock. As the name implies, this approach concerns the deformations (strains), instead of stresses, developed in critical sections of the interlock as it responds to the overall applied tension or bend radius. Three different cases, i.e. pipe under tension, pipe under bending and the combination of the two will be considered separately. Figure 7 gives the geometrical parameters of the interlock profile which will be useful in the following analysis.

Pipe under tension

Following the analysis of the deformation mechanism described previously the approach is to assume that the elongation 6i shown in figure 5 is known and then work out the strains in the critical sections corresponding to this elongation. Later on, the relationship between 6i and the applied tension will be established by considering the global pipe axial stiffness, the interlock geometry, and the amount of sliding motion. Finally, some interesting special cases will be discussed in conjunction with the formulae derived.

(a ) Strains corresponding to 6; Consider that a turn of the interlock would deform in the manner shown in figure 5. Because the radii of curvature at A and B are the same, the strains at these areas should be identical and thereafter it will suffice to analyse the strain at B.

To calculate the strain at B corresponding to an elongation 6i of turn i, the following assumptions have been made:

(i) The three dimensional problem of the tube may be treated as two dimensional.

(ii) The elongation is only due to the deformation of the central part of the turn.

(iii)The deformation at the central part may be characterised by the change of angle p shown in figure 7.

(iv) Deformations are small, sinAP = Ap, tanAP = A p and,

cos (p + Ap) = cos p.

Referring to figure 5, it can be seen that the elongation of the left half of the turn shown in figure 7 will be 0.56i and the change in angle p is given by:

A p = 6 , / A , ( 2 )

Having determined the angle change Ap, the strain in question can be given as (Figure 7).

(3)

where SSI is the length of the arc corresponding to angle (90 - p), that is

ss, = (90°-P). . 180" (4)

Finally, substituting equatlons (2) and (4) into equation (3),

. 180t nrA, (90' - p) E = ( 5 )

This equation gives the strain at the critical area of the interlock corresponding to an elongation ai of turn i. It demonstrates how the interlock geometry (thickness t, radius r, section depth A, and angle p) affects the strain and hence the fatigue performance of the interlock tube.

I

Fig 7. Key dimensions of the interlock section

(b) Relationship between 6; and applied pipe tension According to equation ( l ) , if the elongation, AL, of the pipe and the total amount of slip, Xsi, of the interlock are known, the summation of all the elongations of the individual turns can be determined by

The elongation of the pipe under tension T may be related to a pipe axial stiffness parameter, G, which is the axial deflection per unit load multiplied by length of pipe, L:

AL = T L/G (7)

G can be obtained either by theoretical analysis or from experiment.

The amount of slip of turn i +1 relative to turn i, (si = gi - gIi

102 'Strain', August 1992

as illustrated in Fig. 5a and Fig. 5b), is a function of tension T for a specific pipe. For different pipes, the geometry and clearances of turn i and turn i + l , the roughness (friction coefficients) of the interfaces and the positions of the leg ends of the turns, can all affect si. This makes it extremely difficult to evaluate theoretically the total amount of slip, Csi, in equation (11). For this reason, an experimental method has been developed to measure the slip function and this will be described briefly later. An empirical formula for Csi with the form

may then be establlshed for a particular size of pipe. It is easy to see that the meanlng of s,(T) is the amount of slip per unit length of the interlock tube, and that this is a function of tension T for a given pipe.

With AL and Csi being expressed as in equations (7) and (8) respectively, the relationship between 6i and applied pipe tension can be given by

6i =-C6, n 1 = ( A L - C s i ) / n = [F -- s , (T) .L]/n (9)

where n is the number of turns in length L of the interlock tube, which can be found by knowing the interlock pitch, P, and the length of the pipe, i.e.

n =L/P (10)

Therefore

which gives the elongation per interlock turn corresponding to the applied pipe tension.

(c) Relationship between

This relationship can be obtained simply by substituting equation (1 1) into equation (5)

and overall pipe tension T

E, = m A i (90 - p)

Using this equation along with fatigue data for the interlock tube, it is possible to assess the effects of the interlock geometry and pipe tension upon the tensile fatigue resistance of the pipe.

Pipe under bending

Similar procedures to those in the preceding section will be employed to describe the deformation approach for calculating the interlock deformations while the pipe is under bending.

As the relationship between the critical strain and the elongation of the turn has already been established, it is necessary to develop the formulae for zi and E

corresponding to the applied bend radius. i

I Interlock on the tension side

_--- Interlock on

the compressive rid

NA = Neutral Axis GA = Geometric Axis

F@ 8. Geometry of the interlock tube in pipe under bending

(a ) Relationship between 6i and applied bend radius Assume a pipe of length L is bent to a radius R, as shown in figure 8. It can easily be seen that

L = [ R + (OD/2) + b] . 8 (13)

L, = [R + (OD/2) + (ID + 2t)/2] . 8 (14)

Also, the tube has extended, so

AL= L, - L = [(ID + 2t)/2 - b] . 8

And, since 8 = L/ [R + (OD/2) + b] then:

ID + 2t - 2b AL = L . 2R + OD + 2 b

Combining the above equation with equations (6), (8) and (10) an expression similar to equation ( 1 1 ) for is obtained:

(17) 6i =[ ID+ 2t - 2 b 2R + O D + 2 b

where the slip function sb(R) has a similar meaning to s,(T) used in the case of tension but is a function of bend radius R instead of tension T. As can be seen from the above formula, the elongation of the turn is not only dependent upon the applied bend radius, but is also a function of the posit ion of the neutral axis of the bent pipe. The determination of sb(R) and the location of the neutral axis have, again, to rely on experiment.

(b ) Relationship between The relationship between the critical strain and the corresponding bend radius can be obtained simply by

and applied bend radius

‘Strain’, August I992 103

substituting equation (17) into equation (3, which gives

- s b (R)] ID+ 2t - 2b

(18) 2R + OD+2b mA (90 - p)

180t.€’.[ E, =

Deformation of the interlock under combined tension and bending

In practical applications of flexible pipes, it is more often than not the case that the pipe is both tensioned and bent. Naturally, the question arises as how the deformation approach, which has been developed for either tension or bending, can be applied to the case of combination of the two loadings.

Clearly, interaction between the two deformation mechanisms will occur. The degree of such interaction will be largely dependent upon which of the two loading cases is dominant. (or, to be precise, upon the relative levels of the tension and bending.) Nevertheless, the three cases discussed in the following paragraphs may be considered to cover the range of possible situations.

(a ) Tension dominant As is often the case with the top end region of a flexible riser, dynamic analysis gives a dominant tension along with a very small bend curvature for the pipe. To simplify the problem, one may reasonably ignore the effect of bending and evaluate the critical strain by equation (12).

(b ) Bending dominant This case can, for instance, occur at the sag bend area of a Lazy-S flexible riser configuration and is the opposite extreme from the ‘tension dominant’ case. The critical strain may be evaluated by equation (1 8) of the preceding section.

( c ) Both tension and bending appreciable In this case, neither of the two effects should be neglected. However, the theory may be made applicable by assuming that the pipe is first tensioned and then bent. Thus the strain due to tension, E,, can be calculated by equation (12) since the slip function will be the same as that for tension alone. For the strain due to bending, &b, equation (18) can still be used but, since the pipe has been tensioned, the position of the neutral axis will be changed and the slip function is also expected to be different from that for the case of pure bending.

Finite element analysis and radiographic measurement of the interlock deformation

In the above analysis, equation (5) (i.e. the relationship between the critical strains and the corresponding deformations &) has been obtained using a number of simplifying assumptions and without taking into account

the effect of the interlock strip thickness reduction due to manufacturing. Also, the slip functions, s,(T) and sb(R), have been defined and remained undetermined. Therefore, a 2-D finite element (FE) analysis and radiographic tests on full scale pipe samples were carried out in order to gain a further insight into the deformation mechanics of the interlock tube. A brief description of the analysis and the experimental technique is given below.

The elements utilised in the FE analysis were eight noded isoparametric curvilinear quadrilateral elements and the typical mesh employed is shown in Figure 9. The way in which loading is applied to an interlock turn is also shown in Figure 9, the ratio of T, to T2 being selected so that maximum strain was induced in the critical area. The cases studied were:

- interlock with design dimensions, - effect of radius r; - effect of angle p; - effect of local cross section thickness reduction A;

where the variable dimensions r, p, and A are illustrated in figure 7.

Fig 9. Typical mesh (top) and loading system (bottom) applied to interlock turn in finite element stress analysis

Results of this FE analysis were utilised as a basis for verifying and modifying the strain-deformation formula, equation (5). It has been found that this equation overestimates the strain by an average factor of 2.3 and this is considered to be attributable to the assumption that elongation of the turn is only due to the deformation of its central part (assumption b). This discrepancy is consistent across the sizes of interlock tube and can be accounted for by a correction factor.

The experimental method developed for the determination of the slip functions ‘and the neutral axis position is basically to employ the technique of radiography and to produce images of the metallic parts of the pipe under different prescribed loading conditions. By studying and processing these images, useful information about the deformations of the interlock tube and other movements of components which take place within the pipe construction can be obtained. A description of this methodology and some results for bending and tension of a 102 mm diameter

104 ‘Strain’, August 1992

pipe are given elsewhere 16 and only a very brief summary of the method follows. Figure 10 shows a typical radiographic image in which the interlock and associated gaps as well as the cross-wound reinforcements can be seen. The slip functions can be determined by direct measurement of radiographs a s load is applied incrementally. During bending, the movement of the neutral axis can be followed by making radial measurements between reference posit ions on the radiograph.

This means that the interlock tube accomodates all the elongation, AL = (T/G)L, of the pipe by the sliding action and the individuaLturns are not axially deformed. This is in effect the intended ideal condition of the interlock design.

Case b: No slip, s,(T) = 0

Equations (1 6) and ( 17) yield

T G

6 . = & = - . p I imax

This corresponds to the condition when the sliding action is completely impeded and the interlock tube has to accomodate all the pipe elongation by axial deformation of the individual turns. This case may be avoided by quality control of the manufacturing process of the pipe.

Case c: Both deformation and slip take place, Fig 10. Example of radiograph of 102 mm flexible pipe

st (T) = 17. T/G, 0 c c 1

Equation ( 16) and (1 7) give Discussion

An analytical model of the interlock tube deformation has been developed in conjunction with the results of a finite element analysis and radiographic tests. The output of this model, i.e. the strain in critical sections of the interlock tube is essential before any fatigue analysis can be carried out. The main reason for the discrepancy between the geometric and finite element estimates of the critical strain is thought to be that the former confines all deformation to the central portion. The finite element analysis provides stress concentration factors which are consistent with those suggested by strain-gauged fatigue tests 17.

As pointed out earlier, the exact forms of the slip functions, s,(T) and sb(R), which have been defined as the amount of slip per unit length of the interlock tube, have to be determined by experiment for each size of pipe. This may seem to be a disadvantage, particularly when it is recognised that the function may be different for different sizes of pipes and, even within one size, production variations may cause s,(T) and sb(R) to vary. However, the following discussion (for the case of pipe under tension) shows that the theory is still very useful in evaluating the interlock deformations even when the empirical formula for the slip function is not available..

Case a: No deformation, s,(T) =T/ G

Equations (1 6) and (17) become

&, = o

T 6i = - - P ( l - q ) G

This can be any intermediate case between the above two extremes (q = 1 in case a and 7 = 0 in case b). Now the interlock tube accomodates the pipe elongation by both the sl iding action and deforming itself axially. This is considered to be the very mechanism which occurs within the pipe and which may cause fatigue problems of the interlock tube when the pipe is in severe dynamic servim, corresponding to very large numbers of cycles (greater than about 108) of large amplitude (close to minimum bend radius, for example).

Conclusions

A model is presented for the prediction of the maximum strain in an interlocking tube as a function of global tension and bending of the composite pipe of which it forms a part. The model apportions the accommodation of the global pipe deformation between deformation of the interlock itself and slippage between the turns of the interlock requiring a critical strain - global deformation relationship for the individual turns and a ‘slip function’ to determine the relative amounts of slip and interlock deformation.

The critical strain - global deformation relationship was found to disagree with a finite element calculation of the stress concentration factor but this was sufficiently consistent over the sizes considered t c a!low the

‘Strain’, August 1992 105

incorporation of a correction factor. The situation is complicated by the uncertain nature of the loading in the interlock tube which may be further influenced by the

(6) O’Brien, P.J. and McNamara, J.F., “Significant characteristics of three-dimensional f lexible riser analysis”, Engineering Structures, 11, 4, (October 1989),

presence of the rest of the pipe. 223-233.

The slip functions and the position of the pipe neutral axis need to be determined by experiment. However, once camed out, this does not need to be repeated provided that the range of possible manufacturing variables is considered along with any variations in these for a given nominal size. Even without a knowledge of the slip functions, a ‘worst (8) Feret, J.J., Bournazel, C.L. and Rigaud, J., case’ fatigue analysis is possible if no interlock slippage is “Evaluation of flexible pipe’s life expectancy under permitted. dynamic conditions”, Houston, Texas, OTC 5230, (1986).

(7) O’Brien, E.J., Joubert, P., Kristofferson, B.R., Delecolle, D. and Quin, R., “Sea test of large high pressure flexible pipe”, OTC 4379, Houston, Texas, (May 1984).

(9) Out, J.M.M., “On the prediction of the endurance Acknowledgement strength of f lexible p ipe” , Offshore Technology

Conference, OTC 6165, Houston, Texas, (May 1989). The authors wish to acknowledge with thanks the kind cooperation of Dunlop Armaline Ltd in the experimental (10) D~ 0l iviera , J .G., ~ ~ t ~ , y. and Okamoto, T., work and the permission of the management to publish this “Theoretical and methodological approaches to flexible paper. pipe design and application”, Offshore Technology

Conference, Houston, Texas, OTC 5021, (1985).

( 1 1) Goto, Y., Okamoto, T., Araki, M. and Fuku, T., “Analytical study on the mechanical strength of flexible pipes”, Proceedings of the First OMAE Specialty, (1986).

References

(1) Bourgat, J.F., Dummy, J.M. and Glowinski, R., “Large displacement calculation of flexible pipelines by finite element non-linear programming methods”, Computational Methods in Non-linear Mechanics, ODEN, J.J. ed., North-Holland Publishing Company, (1980), 109-

(12) Feret, J.J. and Bournazel, C.L., “Calculation of stresses and slip in structural layers of unbonded flexible pipes”, Proceedings of the First OMAE Specialty, (1986).

(13) Chen, Z., “The mechanical behaviour and fatigue 175.

analysis of f lexible pipes”, PhD thesis, Heriot-Watt University, Edinburgh, U.K., (1990). (2) Owen, D.G. and Qin, J., “Model tests and analysis of

f lexible riser systems”, 5th International Offshore Mechanics and Arctic Engineering Symposium, Tokyo, Japan, (April 1986). (14) Hruska, F.H., “Radial forces in wire ropes”, Wire and

Wire Products, 27, (1952), 459-463.

(3) Owen, D.G. and Qin, J., “Nonlinear dynamics of f lexible risers by the f ini te element method”, 6th International Offshore Mechanics and Arctic Engineering Symposium, Houston, Texas, (March 1987).

(4) Vogel, H. and Natvig, B.J., “Dynamics offlexible hose riser systems”, 5th International Offshore Mechanics and Arctic Engineering Symposium, Tokyo, Japan, (April 1986)

(15) Knapp, R.H., “Structural modelling of undersea power cables”, Offshore Mechanics and Arctic Engineering, OMAE, Houston, Texas, (Feburary 1988).

(16) Chen, Z., Reuben, R.L. and Owen, D.G., “Determination of flexible pipe internal deformations”, to be published in Nondestructive Testing and Evaluation, volume 6,4, (1992).

(17) Chen, Z., Reuben, R.L. and Owen, D.G., “Fatigue testing of interlocking stainless steel”, to be published in Strain.

(5) McNamara, J.F. and O’Brien, P.J., “Nonlinear analysis of f lexible risers using hybrid f ini te elements”, 5th International Offshore Mechanics and Arctic Engineering Symposium, Tokyo, Japan, (April 1986).

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106 ‘Strain’, August 1992