DAMPING AND HYSTERESIS EFFECTS ON THE BEHAVIOUR OF FLEXIBLE RISERS

Transcription

1 DAMPING AND HYSTERESIS EFFECTS ON THE BEHAVIOUR OF FLEXIBLE RISERS H.J.J, van den Boom Maritime Research Institute Netherlands G. de Boer Maritime Research Institute Netherlands SUMMARY Flexible risers have been used in many applications for several years now. The design of a flexible riser configuration in the first years was based on quasi-static calculations. At present the designer is supported with enhanced simulation software tools. For this purpose discrete element methods have been developed. Results from full scale measurements have indicated that the modelling of hydrodynamics and mechanical properties should be subjected to further research. This is not only relevant for extreme sea state analysis but also for fatigue analysis. Improved fluid load models have been derived from systematic model tests with full scale riser sections. Modelling of material damping and non-linear bending stiffness with hysteresis effects proved to be of significant importance. 1 INTRODUCTION The use of armoured hoses in offshore production is increasing rapidly. Flexible risers and flowlines have become key components in floating production. They allow the floater considerable freedom of motion and are easy to install. Several semi-submersible type platforms in a spread mooring and turret-moored ship-shaped vessels (Fig. 1) sometimes assisted by DP-systems will be in operation in the near future. Fig. 1 Flexible riser with FPS 1

2 With the floating production systems being deployed in deeper water and under more harsh weather conditions, specific attention has to be paid to the dynamic behaviour, ultimate strength and the service lifetime of flexibles. Besides the burst and collapse resistance, material wear and degradation, the capacity of the flexible hose with respect to the global loads in axial (tension), bending (curvature) and torsional directions is to be assessed. This has urged both basic riser material research and development of global behaviour analysis for flexibles under service conditions. In the design and development of a riser system, the global dynamic behaviour of the system is of critical importance. In extreme sea states both motions and loading of the system should be subjected to detailed analysis. Although the system is free to move, mutual interference between risers and contact with anchor lines should be prevented. This requires an integral dynamic analysis of the mooring system and the risers. For evaluation of the ultimate strength of risers the minimum bending radii and the maximum tensions in the riser and fittings are to be assessed. Reliable lifetime prediction is another important aspect in the design of the configuration and choice of materials. Components of the riser which are subjected to repeated, fluctuating or alternating stresses can exhibit fatigue. This can occur even when the stresses are below the ultimate strength or even yield strength levels. In general, fatigue is a product of many factors such as quality of material and surface finish, minor defects and chemical and thermal environment, as well as the global integrity of the structure. From the viewpoints of safety, environment and economics (inspection, downtime and replacement), fatigue analysis of risers is essential. Due to the complicated construction as well as the actual service of risers, assessment of the service lifetime is not straightforward. Besides failure mode analysis and material testing also the dynamic behaviour of the riser during the actual service has to be known. As outlined above, both for extreme and fatigue analysis of risers a general computational model of the motions and the responding internal loads is required. The dynamic behaviour of the riser is excited by external sources, viz. floater motions, waves and current and the response is governed by material properties and fluid reactive forces. A computational model should incorporate these aspects. Accurate prediction of riser motions, tensions, curvature and torsion is not only important for the extreme sea state analyses but also highly relevant for the lower sea states which may contribute significantly to the fatigue damage. Since the risers feature large changes in geometry and also non-linearities in material property and fluid loading, the dynamic behaviour of the riser is essentially non-linear. To describe this behaviour dedicated discrete element models in 2

3 the time domain have been developed. An example of this is the lumped mass discrete element method as utilized by the program DYNFLX, which has proven to be capable of describing the full 3-D curvature of flexible risers as well as the governing mechanisms of their dynamic behaviour (see references [1] and [2]). Due to lack of material test data and full scale feedback, most riser analysis programs feature approximative fluid models and linear material properties. Considerable discrepancies were reported in a comparison between field data and stochastic time domain simulations by Otteren and Hanson in 1990 [3], in a recent Eureka research project Norsk Hydro, Shell, Statoil, SINTEF and MARIN have compared simulations and measured data from the Oseberg, Veslefrikk and Troll-West fields. As part of this work, the fluid loading and the modelling of the material properties of flexibles were investigated [4 ]. In the present paper the lumped mass finite element discretization for flexible riser analysis is reviewed together with a more detailed discussion of the fluid load modelling (Section 2). As the lumped mass discrete element method is computer efficient not only full non-linear simulations can be performed for extreme sea states, but also for fatigue analysis. In Section 3 practical computational procedures for both extreme sea state and and fatigue analysis are presented. The non-linear modelling of riser material properties such as damping and hysteresis effects is discussed in Section 4. 2 MATHEMATICAL MODEL 2.1 Discrete Element Method A flexible riser is extremely slender and its effect on the floater motions can be compared with the effect of an anchor line. The first order wave forces dominate the floater motions, the line just follows these motions without affecting them. The mean and low frequency motions at the top of the riser act more or less as a quasi-static pretension while the wave induced motions forced by the floater upon the riser top, excite dynamics in the riser system. These motions and relevant internal loads can be described by a spacewise discretization of the riser lumping the mass and all forces to a finite number of nodes [1], see Fig. 2. The governing equations of motions are obtained from Newton's law in global coordinates: [M j + mj(t)] Xj(t) = Fjtt) (1) 3

4 in which: j = node index t = time x = (x,y,z,t 0 M = segment mass matrix m = added mass matrix. Floater msm;mm;;mïïmm^mêmmïfkm Fig. 2 Lumped mass discretization The nodal force vector F contains all external and internal loads acting on the individual nodes in x,y,z, and torsional direction respectively. These forces can be functions of time and riser state variables such as nodal position, velocity and curvature of the riser. Components of this force vector are tension, buoyancy, weight, fluid loads, shear forces due to bending, torque and special loads due to e.g. buoys or tethers. When all these force components, together with the forced end position and orientation of the riser, are known, the accelerations, velocities and excursions of the nodes can be solved by a finite difference method and the simulation can be continued for the next time step. Flexible risers are in fact only flexible with respect to bending but can be quite stiff in axial and torsional direction. For that purpose DYNFLX maintains the axial tension and torque in the final solution set. Consistent tension-displacements and torque-twist values are provided by a Newton- Raphson iteration applied to the force-strain relations at each time step [1]. 4

5 This method has proven to be a powerful feature for solving problems with large geometrical non-linearities D Curvature Model The lumped mass discretization of a flexible riser features four degrees of freedom per node, i.e. stretching, bending in two directions and torsion. The geometry may be presented in nodal positions and Eulerian angles; two orientation angles and one torsion twist angle. To derive the internal load components (tension, two bending and torque respectively), according to slender rod theory the orientation of a finite segment with local axes (, *v, h) m ay be described in global coordinates by means of a rotation tensor Rij: (2) e i = {e K' e \>' fv = Ri i fj where e* is the fixed basis vector The curvature of the rod coincides with the angular velocity vector of the local triad, if its origin moves along the centre line S with unit velocity. The curvature vector K can thus be defined by: 3ei 3s = K x ei (3) The curvature components can then be expressed as functions of the space derivatives of the base vector e which can be related to the three Euler angles [2]. Using a first order difference scheme this approach can easily be adopted in the lumped mass discretization. In this way the full 3-D curvature of the riser is described in the element orientations derived from the nodal positions and the element torsion angle. The axial strain and curvature aire related to the tension and the moments in the cross-section by the constitutive equation: (T M K (EA GI P EI E 0 0 EI The derived tension and bending moments can be decomposed into nodal force components in the global system of coordinates. In this way the internal mechanical loads are accounted for in the right-hand side of equation 1. Results obtained with 3-D curvature model and the numerical solution technique have been verified with results from analytical solutions and large deflection experiments with PVC pipes [2]. (4 5

6 2.3 Fluid Loads Flexible risers are subjected to complicated flow fields generated by directionally spread irregular seas and current and disturbed by wave diffraction caused by the neighbouring floater. The following frequency ranges in the motion response of the riser can be distinguished: * Low frequency (periods > 30 s) and more or less quasistatic response to horizontal floater motions, tide, etc. * Wave frequency motions (periods between 4 and 30 s) due to top motions and direct wave-forces. * High frequency motions (periods < wave periods) induced by vortex shedding, instabilities, operations, etc. Advanced numerical schemes solving the Navier Stokes equations for instationary viscous flow are available for simple geometries. Though promising for the future, complexity and computer power consumption of these methods are prohibitive for practical flexible riser analysis. Hence use has to be made of approximative semi-empirical formulations such as Morisons equation. The fluid forces acting on the submerged part of the riser originate from the water particle motions due to waves and current as well as the riser itself. These forces are approximated as function of the relative velocity (drag) and acceleration (inertia): F = kp C D DL u u + %npc J D 2 L ü (5) Since the inertia part of the fluid reactive forces is already accounted for in the left-hand side of equation (1)/ and the current velocity is assumed to be constant u only consists of the orbital acceleration due to waves. The relative velocity u is approximated by super position of the wave, current and structure velocities: u = v w + v c - x (6) Detailed diffraction analysis on a FPS-tanker have shown that the flow disturbances caused by the tanker do not significantly affect the response of the riser. Therefore the fluid loads on the riser may be computed for the undisturbed incoming waves. The instantaneous particle velocities and accelerations can be computed for arbitrary wave trains by FFT or impulse response technique (Volterra Series) utilizing small amplitude linear wave theory. Unlike in linear wave and ship motion theory where wave forces are computed below the calm water line, the fluid loads on flexibles have to be evaluated up to the instantaneous wave elevation. This has proven to be important especially for surface piercing risers. For this purpose 6

7 DYNFLX evaluates the wave crest kinematics according to the so-called 'Wheeler stretching' method. 2.4 Derivation of Fluid Force Coefficients Assuming a discretization with sufficient elements the fluid forces on each element can be approximated according to equation (5) using coefficients for 2-D cylinders. Taking advantage of the circular cross section and the slenderness of risers, the fluid loads may be decomposed in normal and tangential components. For the drag forces this yields: F Dn = hp C Dn DL (u C O S Q ) 2 F Dt = ** p C Dt DL (u sina > 2 (7) where a is the angle of the incident flow. The drag and inertia coefficients can be derived from forced oscillation tests with full scale riser sections. Alternatively the coefficients may be deduced from captive tests in waves. The coefficients are functions of velocity (Reynolds number) and frequency of oscillation (Keulegan-Carpenter number). It should be noted however that the added mass of the riser is normally small when compared to the risers own mass. Furthermore the riser diameter is small when compared to the wave length. Therefore stationary resistance tests with prototype scale riser sections provide a practical means to derive reliable drag coefficients. Such tests have been carried out in MARIN'S deep water basin in 1989 and 1990 [5], The test series comprised various riser section models (see Fig. 3) with a diameter of 0.11 m. Tests with artificial roughness showed that marine growth significantly increased the tangential drag coefficient but hardly affected the normal drag. Results of similar tests with various arrangements of buoyancy beads showed that the drag forces acting on such sections required a different formulation. Depending on the diameter, length and spacing, the beads produce significant cross-flow (lift) forces when the flow makes a small angle with the circular plane of the beads. When the flow is oriented along the riser, the beads are subjected to shielding effects. The following drag formulations for buoyancy bead sections were proposed: F Dnb = ^.Snb DL " 2 F Dtb " *P C Dtb DL u2 (8 in which: C Dnb = C nl 2n cosct /( 4 + n sina) C Dtb = C tl 2n s i nq /( 4 + n sina) + C.- sin(2a) C nl' C tl and C t2 are coefficients depending on bead shapes and distribution. 7

8 Dimensions in m * 'i-'.. ^ F -ip!» rt. 1 ". - ' : p. i * ".. ' : T. "F ' - ', " 3.30 Configuration I , f4,( ft , i, ' 55,[, _ 0.55 f[_ E Confiauration II Mifaai^*iiÉHa*^4iHMriHU , _L_ Configuration III rh 0 - fss ^^^^^ r4 ü i Fig. 3 Buoyancy bead sections for drag tests (dimensions in m) As illustrated by Fig. 4 the tangential drag component is sensitive for the shape and distribution of the buoyancy beads whereas the normal drag component is almost equal for the various configurations and only dependent on the angle of incidence of the flow. Unlike for the plain riser sections the drag on bead sections was not much affected by marine growth and flow velocity. The importance of the buoyancy bead drag formulation is illustrated by Fig. 5.

9 head config model test CDnb= Cnl " (HTTCOSO / (4 + 7rsina)) Cnl II o o Mi IV *-.o c Q O ANGLE OF INCIDENCE bead config model test CDtb= Ctl (27rsina/(4+rrsina)) + Ct2 sin(2a) II UI IV Ctl Ct2 o o + Q U Fig SO.O ANGLE OF INCIDENCE Fluid load coefficients for bouyancy bead sections 90.0

10 NEW FLUID LOAD MODEL CONVENTIONAL FLUID LOAD MODEL SNAPSHOT OF RISER MOTIONS ENVELOPES OF TORSION. TRANSVERSE DEFLECTION AND TENSION E. «1SION ( kn O X(m) o.o 4o.o «o.o izo.o LENGTH ALONG RISER ( m ) 4.0 e.o Ê o.o -Z.O' LENGTH ALONG RISER ( m ) ao.o 40.0 z O w z u eo.o o.o-l LENGTH ALONG RISER ( m ) Fig. 5 Effect of fluid load modelling 10

11 2.5 Wake Oscillator Model Both from model test and full scale observations it is well known that in stationary flow and undirectional waves under certain conditions risers exhibit significant cross-flow motions. This phenomenon is caused by oscillating lift forces due to periodic vortex shedding. The resonant motions occur when the frequency of vortex shedding 'locks in' with the natural frequency of the. transverse motions of the riser. This not only results in cross-flow motions but also in a significant increase of the in-line drag. To incorporate these effects in practical riser analysis, the use of a wake oscillator model for the drag forces has been proposed [5], In this approach the non-linear oscillator of the lift force is coupled to the equation of motion of the riser element. The vortex shedding frequency follows from the Strouhal relation and the natural frequency of the system. For the drag coefficient of the oscillating element the following empirical relations is used: C D = C D0 {1 + I ( y/ D ) "' 65 I + J sin(2ut) (9) in which: C D0 ~ stat i nar y drag coefficient a = standard deviation of cross flow displacement D y = riser diameter co = frequency of cross flow motion I,J = constants Implementation of this approach in DYNFLX for a simplified vertical riser section has produced in-line and cross-flow displacements as observed in model test [5]. 3 COMPUTATIONAL PROCEDURES 3.1 Extreme Analysis The discrete element model described in the previous section can be used for deterministic analysis of the dynamic behaviour of a flexible riser for a specific condition. For a chosen sea state and current condition, the floater motions are normally derived either from computations or model tests. Together with the synthetic or measured wave record the floater motions are then used as input to the riser analysis. Floater motions also contain low frequency components especially in the horizontal modes. Second order wave forces and wind gusts excite these motions only restored by the mooring system. These motions have a resonant character since the damping is mainly from viscous origin and therefore small. For these reasons it can be important to account for the damping and virtual stiffness of the mooring and riser systems in the computation of floater motions. This can be achieved by a coupled simulation of the floater, mooring and riser dynamics. 11

12 Numerical solution of motions and peak loads, certainly for stiff configurations and slack/snap conditions, requires small time steps. Combining this with a sufficient duration of the simulation needed to resemble the statistics of the combined high and low frequency motions, this results in a significant (computer) time consumption. In practical engineering therefore the following computational procedures can followed: 1. Computation of floater motions taking into account the quasi-static load excursion characteristics of the mooring and the damping provided by the mooring and riser system. 2. Regular wave analysis of the mooring and riser system; assuming linear ship theory, input of floater motion RAO's is then sufficient. These analyses give a first impression of the dynamic effects and are normally sufficient for concept development. 3. Bi-harmonic analysis of riser and mooring system; in this case the low frequency motion of the vessel is approximated by a harmonic motion and then superimposed on regular wave motions- This analysis provides insight in the most critical stages of the low frequency oscillation. 4. Irregular wave analysis for 'fixed' low frequency positions such as the 'near', 'mean', 'far' situations. As the simulation of the riser and mooring accepts the input of arbitrary irregular floater motion records together with the instantaneous wave elevation history, computational analysis of risers and mooring can be combined with model testing for the floater motions. This is of particular importance for deep water. As each time simulation results in time series of motions, tensions and curvatures for each of the nodes/elements, interpretation of the results (e.g. mutual interference of risers) is often laborious. For this purpose the animation program VISUAL was developed. This package visualizes the 3-D motions of the floater, mooring system and the risers together with the instantaneous loads and further relevant data. 3.3 Service Life Assessment Besides the response to extreme sea states, the durability of flexible risers and flow lines is more and more a subject of research and engineering. An important aspect of the lifetime prediction is the fatigue analysis of flexible risers. As stated earlier flexible risers with their specific construction and end-fittings require a thorough fatigue life assessment. Such an analysis basically requires input from: a. Durability testing of material. b. Loading information for the specific application. Due to the complicated construction, use of various materials and the loading of flexible risers, much effort was (and is) required for material testing and failure mode analysis. Recently several large test rigs, such as at KSEPL in Rijswijk, 12

13 have become operational. Scaling of material and construction properties is complicated and therefore the tests are normally carried out with sample sections of the actual pipe. This implicates that the tests are carried out at real time which makes the testing extremely time and cost consuming. The results of the tests, however, are product related and can therefore be used for arbitrary configurations and situations. Once the fatigue capabilities of a given type of pipe are available from schematic loading histories, the analyses for the specific field application can be carried out. For this purposes the actual long-term loading of the pipe is to be provided. As the curvature and tension are the governing parameters for the fatigue analysis, this implicates that dynamic analysis have to be carried out for all conditions which are expected to be encountered. Already in 1986 for this purpose MARIN and Shell co-operated in the development of a computer package (DYNAFA) capable of such analysis. Because of the non-linearities involved it was decided to evaluate the behaviour in the time domain. For this purpose the the 2-D version of DYNFLX was used as kernel. The computational approach is a loop of simulations over all relevant sea states of a wave scatter diagram which is input to the program. Having derived the curvature and tension histories at selected nodes, a load cycle counting procedure is carried out. For. this purpose a 'peak to trough counting' (Range Mean) method for curvature changes, average curvature and average tension is applied. Occurrences are registered in separate predefined classes. The cumulative occurrences in e.g. one year, can then be computed taking into account the duration of each simulation and thé percentage of occurrence of each sea state in the wave scatter diagram. 4 MATERIAL PROPERTIES For the sake of simplicity, most flexible riser analyses so far have been carried out assuming linear stiffness properties whilst neglecting material damping. With an increasing number of applications of flexible risers in harsh environments (such as the North Sea) and an increasing design life, the mechanical properties of the pipe play more and more a significant role. To keep up with the requirements for flexible riser analysis, non-linear stiffness, hysteresis and damping have to be included. A mathematical model for these properties will be given in Section 4.2. In the next section the effect of the damping and the hysteresis on the behaviour of a typical steep wave riser will be discussed. 13

14 4.1 Structural Damping Model The right-hand side force vector of the motion equation given in Section 2.1 contains several contributions (e.g. external damping due to the relative motion between riser and water particles). The main contributions are the nodal forces related to the axial strain and curvature of the riser. The magnitude and direction of these nodal forces are given as a function of the nodal motions: (T ] [E ] = Tj K KJ KJ,,\) V with: T l' T 2 = transrormat i n matrices K = stiffness matrix. This model corresponds with an internal static equilibrium. For damping of eigen frequencies related to the riser modelling the numerical integration scheme depends fully on external fluid damping. A commonly used (simplified) structural damping model is the proportional damping model of Rayleigh. By neglecting the mass proportional damping this model can be introduced by adding a damping term in equation (1): F = T l K f 2 (x + a x) (11) with: a = damping coefficient x = nodal velocity vector. For practical purposes the selection of a damping coefficient should result in realistic energy dissipation and reduction of eigen frequency amplitudes. 4.2 Hysteresis The results of laboratory tests of flexible risers as presented by B. Skallerud [6] show a significant hysteresis effect for the bending mode. The hysteresis in the bending moment effectively acts as a damper, dissipating energy. The hysteresis effect for the bending mode originates from the friction between the different layers of a riser. In practice this friction results in a higher (holding) bending stiffness. Up to a certain point the friction is able to prevent slip between layers. With increasing bending moment slippage starts gradually till full slip of the layers occurs. In that case the (sliding) bending stiffness is formed by the resistance of the individual layers. After reversal of the load the friction acts in the opposite direction and thus resulting in a hysteresis effect. In Fig. 6 a schematization of the bending hysteresis is given. 14

15 Bending moment Curvature (1/m) Fig. 6 Bending hysterises model The mathematical formulation of the stress-strain relation-is more complicated than given in equation (4). For the bending moment the equation is: (EI s (K(t)-K Fr ) + EI H K Fr > K s + K Fr M y (t) = i EI s K s (t) + EI H (K(t)-Kg(t) < I K s ±K Fr I (12) EI s (K(t)+K Fr ) " EI H K < K Fr - K Fr with: K FR " M Fr /EI H M_ = friction moment EI = sliding bending stiffness EI^ = holding bending stiffness K = curvature slip. In this equation the influence of the bending hysteresis is expressed by the curvature slip which represents the accumulated slip of the layers. Although usually the hysteresis for torsion and axial load is not of the same magnitude (see Skallerud [6]), a similar expression for torsion and axial load can be formulated. 4.3 Computations In this section some results obtained from computations with both material models will be presented. The cases concern a water surface piercing steep wave riser (160 m long in 100 m water depth) subjected to wave forces only. Both end terminations of the riser are clamped vertically and are of the 15

16 bending stiffener type. The purpose of the computations was to investigate the effect of both material models on the curvature variation at two locations, near the top of the riser (node 22) and in the hog top (node 8). The input for computations was kept constant except for the wave amplitude (2.0 and 5.0 m) and the wave frequency (ranges from 0.5 to 1.5 rad/s). For the structural damping model a coefficient of 0.02 was used. For the other material model only bending hysteresis was incorporated using friction moments of 0.5 and 1.0 knm (which is a realistic value, depending on internal pressure and riser fabrication). For the holding bending stiffness a value 10 times the sliding stiffness has been taken. For the linear and the structural model the sliding stiffness was used. All computations were started with a swell period (in which wave forces gradually were applied) from a static equilibrium situation. The simulation was extended until the curvature showed a periodic pattern. For the comparison of the models the curvature range (peak to trough value) was used as this value is of importance for the determination of the service life. In Fig. 7 the results for the computations of the linear material model and the structural damping model are given. A significant reduction of the curvature range was obtained for both locations. For node 8 an irregular response curve was obtained for the linear model which completely disappeared with the damping model. Obviously the fluid damping does not damp eigen mode vibrations of the riser sufficiently. The results for the hysteresis model are given in Fig. 8 (5.0 m wave amplitude) and Fig. 9 (2.0 m wave amplitude). For the regular wave with a frequency of 0.5 rad/s and 5.0 m amplitude a reduction of the curvature range was obtained. In-Fig. 10 this reduction is illustrated. Computed bending moments are given as a function of the curvature in time. The curves for a friction moment of 0.5 knm shows a clear hysteresis effect. The friction moment of 1.0 knm gave a larger reduction in the curvature range although the hysteresis effect has reduced. In Fig. 10 the moment is also plotted against curvature for 0.9 rad/s. Values are plotted from the start. The hysteresis loop for a friction moment of 500 Nm has reduced. For a friction moment of 1.0 knm no hysteresis loop is noticed. The variation of the bending moment amounts to 1.5 knm, which is smaller than the friction momemt. For node 22 no change in curvature range is obtained (both for 2.0 and 5.0 m wave amplitude). In Fig. 11 the bending moment is plotted versus curvature, showing that hysteresis does occur but has no effect on curvature range. Motions near the top are not affected by the hysteresis material model but are dominated by the global behaviour of the riser. 16

17 0.05 node 8 circular frequency (rad/sec). No Damping H> 0.02 Damping node \ \- & 0.02 a u I h M circular frequency (rad/sec) No Damping -<>0.02 Damping Fig. 7 Rayleigh damping model 17

18 0.07 node 8 / 5.0 m & 0.04 et 0: OJOI circular frequency (rad/sec) _^Mfr = 0. -^Mfr = o-mfr = node 22 / 5.0 m circular frequency (rad/sec) _^Mrr = 0. -^Mfr = D -Mfr= Fig. 8 Hysterises model (5.0 m) 18

19 0.03 node 8 / 2.0 m circular frequency (rad/sec) -^Mfr = 0. -*-Mfr = omfr=1000. node 22/2.0 m circular frequency (rad/sec) -*-Mfr = 0. -^Mfr=500. -o-mfr=1000. Fig. 9 Hysteresis model (2.0 m) 19

20 2500 node 8 I 0.5 rad/sec ^_ 57 Mfr= Nm S u E I W» C ffi //^ irp Mfr«500Nm - Jf' "" Thoutindths curvature (1/m) 2500 node 8 I 0.9 rad/sec? 2000 C O bo 1000 Mfr= Nm Mfr Nm Mfr^O.ONm c 4) Thousandths curvature (1/m) Fig. 10 Influence of friction moment 20

21 1000 node 22 I 0.9 rad/sec e g, I bo C Mfr«0.0Nm Mfr = Nm Jy/jfflw ^^Jfff Mfr Nm I Thousandths curvature (1/m) Fig. 11 Influence of friction moment 5 CONCLUSIONS Lumped mass discrete element method is suitable for 3 D nonlinear flexible riser analysis, both for extreme sea state and fatigue life assessments. Fluid load modelling is of prime importance for the prediction of riser motions and loads. Structural damping and non-linear stiffness in the bending mode should be incorporated in the mathematical model. Hysteresis effects in the stiffness do not necessarily reduce riser motions and loads. REFERENCES [1] Boom, H.J.J, van den, Dekker, J.N. and Elsacker, A.W. van; 'Dynamic Aspects of Offshore Riser and Mooring Systems', Offshore Technology Conference, May 1987, Houston. [2] Boef, W.J.C., Lange, F.C. and Boom, H.J.J, van den; 'Analysis of Flexible Riser Systems', Fifth International Conference on Floating Production Systems, December 1989, London. 21

22 [3] Otteren, A., Hanson, T.D.; 'Full Scale Measurement of Curvature and Motions on a Flexible Riser and Comparison with Computer Simulations', Offshore Mechanics and Arctic Engineering Conference, 1990, Houston. [4] Sodahl, N. et al. 'Influence from Nonelastic Material Modelling in Computer Simulation of Flexible Risers Verified by Full Scale Measurements', Offshore Technology Conference 1992, Houston. [5] Boom, H.J.J, van den, and Walree, F. van; 'Hydrodynamic Aspects of Flexible Risers', Offshore Technology Conference, Paper No. 6438, May 1990, Houston. [6] Skallerud, B.; 'Stiffness Properties and Damping Behaviour of Flexible Risers', International Seminar on Flexible Pipe Technology, February 1992, Trondheim. 22