NUMERICAL MODEL FOR THE SIMULATION OF THE PIPELINE-LAYBARGE INTERACTION IN PIPELAYING PROCEDURES

7/29/2019 NUMERICAL MODEL FOR THE SIMULATION OF THE PIPELINE-LAYBARGE INTERACTION IN PIPELAYING PROCEDURES

1/10

13

Abstract.Conventional offshore pipeline installation operations

in Brazil have been performed in an S-Lay procedure employing

the BGL-1 barge, owned by Petrobras. In this method, the

welded pipeline is supported on the rollers of the vessel andthe stinger, forming the over-bend. Then it is suspended in the

water all the way to seabed, forming the sag-bend. The over-

band and sag-bend form the shape of an S.

In this work, the focus concerns in the analysis of the interaction

between pipeline and lay barge on the over-bend region. This

analysis includes not only the contact between the pipeline and

the launching structure but also the tensioner behavior. Two

numerical models are proposed: (a) a rigorous contact model

that provides important information related to the consequences

of impact between pipeline and rollers. These consequences

can be dents to the pipe or tearing of the coatings; and (b)

a model for the simulation of the tensioner behavior. Thismodel includes a delay between the instant that the tensioner

is activated until it effectively starts working. It also considers

how fast the tensioner can recover the desired tension level in

the pipeline.

Simulations of actual operations are shown, in order to

illustrate the application of the proposed model.

Keywords: Numerical Methods, Offshore Pipeline, S-Lay

Installation Procedures

1 - INTRODUCTION

The installation of pipelines and owlines and theirconnection to platforms constitute some of the most challengingoffshore operations. Many methods of pipeline installationhave been employed such as S-Lay, J-Lay and Reel-Lay. Thesemethods are selected on the basis of environmental conditionsduring installation, availability and cost of equipment, length andsize of line, and constraints of adjacent lines and structures (Guo,2005; Kyriakides, 2007). Alternative installation procedureshave also been proposed (Silva, 2007).

The most common method of pipeline installationin shallow water is the S-Lay method. This method is so calledbecause the pipeline follows an S shaped curve as it moves from

the laybarge to the seabed as schematically shown in Fig. 1.

Figure 1 Schematic representation of S-Lay method.

In a S-Lay installation, the pipes are welded to each other inthe horizontal position on the barge and then the pipeline passes overan inclined ramp and stinger which gradually lowers the pipeline

into the water. This region of the S curve is known as the overbendand as the pipeline leaves the overbend region it is inclined almostvertically as it descends to the seabed, close to the seabed it onceagain returns to the horizontal position so that it eventually rests onthe seabed. This region is known as the sagbend region.

Usual pipelaying operation by S-Lay procedures inoffshore Brazil employ the BGL-1 barge (Fig. 2) owned byPetrobras. The BGL-1 is a second-generation laybarge that performsinstallation operations by moving forward using its own mooringlines. Basically, tug boats drop anchors at some predened positions;then the barge winches release the stern mooring cables, and collectthe mooring cables located at the bow.

Figure 2 The BGL-1 Pipeline Launching Barge.

INTERNATIONAL JOURNAL OF MODELING AND SIMULATION FOR THE PETROLEUM INDUSTRY, VOL. 3, NO.1, JUNE 2009

NUMERICAL MODEL FOR THE SIMULATION OF THE PIPELINE-LAYBARGE

INTERACTION IN PIPELAYING PROCEDURES

Danilo Machado Lawinscky da Silva, Mauro Henrique A. de Lima Jr., Breno Pinheiro Jacob

[email protected], [email protected], [email protected] Laboratory of Computational Methods and Offshore Systems

Department of Civil Engineering, COPPE/UFRJRio de Janeiro, RJ, Brazil


2/10

14 INTERNATIONAL JOURNAL OF MODELING AND SIMULATION FOR THE PETROLEUM INDUSTRY, VOL. 3, NO.1, JUNE 2009

In order to prevent the pipe from buckling in the regionsof maximum bending, the bend radius is controlled by keepingthe pipe under tension, so that the pipe actually follows a lazyS shape. The tension is applied to the pipe by tensioners onthe barge which are usually arrays of rubber wheels or beltswhich surround the pipe and apply an axial force to the pipe

through the friction generated between the tensioner and thepipe external coating as shown in Fig. 3.

Figure 3 BGL-1s tensioner.

The force on the pipeline is reacted at the seabed endof the pipeline by the dead weight of the pipeline and frictionbetween it and the seabed. Obviously the larger the force appliedby the tensioners to the pipeline, the more gradual will be thebending radius in the S portion of the laying curve. Also, as thepipe weight increases it is necessary to apply a greater forceto the pipe to maintain the desired bend radius and so preventbuckling, particularly in the sagbend portion of the curve asschematically shown in Fig. 4.

As individual pipe lengths are welded onto the growingpipeline, the barge is winched forward and the new sectionof pipeline passes over the stinger towards the seabed. In thecase of anchor positioned barges tugs are used to continuouslyreposition the anchors ahead of the barge so that the barge cankeep moving forward.

Pipelines in S-Lay installation operations are not easyto simulate numerically, since the contact mechanism betweenthe pipeline and the launching structure is complex, speciedonly in some points of the ramp and stinger.

Figure 4 Scheme of S-lay installation: Pipeline Loads; Propagating Buckle

from a Local Bending Buckle.

It is recognized that deepwater offshore oil exploitationactivities requires the use of sophisticated computational toolsto predict the behavior of oating offshore systems underthe action of environmental loads. These computationaltools should be able to perform coupled dynamic analyses,considering the non-linear interaction of the hydrodynamic

behavior of the platform with the structural/hydrodynamicbehavior of the mooring lines and risers, represented by FiniteElement models. The implementation of such analysis toolsconsiders the coupling of the equations of motion of the FEMmodel of the lines with the 6-DOF equations of motion of theplatform hull.

The use of such a sophisticated computational toolbecomes mandatory not only for the design of productionplatforms, but also for the simulation of offshore installationoperations. For instance, in the installation of submarinepipelines, the wall thickness design may not be governed bythe pressure containment requirements of the pipeline duringthe operation, but by the installation process, specically the

combined action of bending, tension and hydrostatic pressureacting on the pipeline, that is also submitted to the motions ofthe laybarge (Fig 4). Therefore, to predict the behavior of suchoffshore operations it is very important to use a computationaltool that not only considers the coupling of the pipeline withthe motions of the barge, but also that rigorously consider thecontact between the pipeline and its supports (laybarge, stinger,seabed).

Therefore, the objective of this work is to present atool that improves the coupled analysis model described above.Such tool represents, during the dynamic analysis, the contact ofthe pipeline and the laybarge, as well as the tensioner behavior

during installation procedures.

2 - CONTACT MODEL

A contact problem is a boundary-value problem, ora initial-boundary-value problem in which two bodies A andB interact according to the principles of the mechanics ofcontinuous media. The domains of the bodies are A0 and B0respectively, at a reference time t = 0, At and Bt at a time t.Thus the primary kinematic axiom of a contact problem is thatcongurations At and Bt ofA0 and B0, respectively, do notpenetrate each other, i.e.

(1)

The Eq. (1) is called the impenetrability condition.The intersection of the two bodies is the null set. In other words,the two bodies are not allowed to overlap, which can alsobe viewed as a compatibility condition. The impenetrabilitycondition is highly nonlinear for large displacementsproblems, and in general cannot be expressed as an algebraicor differential equation in terms of the displacements. Thedifficult arises because in an arbitrary motion it is impossibleto anticipating which points of the two bodies will contact(Belytschko, 2000).


3/10

15

The boundaries of the bodies are denoted by At andBt respectively and are dened as:

(2)

and

(3)

Where t is the total boundary, t;D and t;F areregions where displacements and surface forces are prescribed,respectively, t;C is the region where the contact interactionsoccur.

Figure 5 Contacting bodies.

The governing equations for a multi-body contact

problem are the same as for a single body system, equationsof motion, constitutive equations, initial conditions, boundaryconditions, with the addition of the contact conditions (Hughes,1976). Thus the problem formulation is:

(4)

(5)

(6)

(7)

Where are the Cauchystress, material coordinates, body force, material density,acceleration, surface force, displacement, constitutive tensorand strain, respectively; nt1j are the components of the outwardsurface normal. Overbarred quantities mean prescribed values.A variety of methods for the treatment of contact constraintconditions have been introduced (Belytschko, Hunek, 1993;Wriggers, Laursen, 2002).

Traditionally, the numerical simulation of pipelinesin S-Lay installation operations considers contact modelsbased on generalized scalar element. This element consists oftwo nodes linked by a non-linear gap spring (Nielsen, 1978;

Grealish, 2005).

The contact model proposed here combines niteand discrete element methods. Its formulation is described asfollows.

2.1 - FEM DEM Formulation

The well-known nite element equation for dynamicproblems is:

(8)

Where Mat are the inertia forces, M is the mass matrix,at is the acceleration vector, Ftb are the body forces, Ftp are thesurface force, FtC are the contact forces, FtD are damping forces,Ftint are the internal forces. Each vector contains the assembly ofall elements contribution in the nite element mesh.

The only term in Eq. (8) that is not trivial is the vectorof contact forces FtC. Here, this vector is assembled according tothe discrete element formulation.

The discrete element modeling is a Lagrangian numericaltechnique used to solve problems that can be represented as aset of discrete bodies or particles. Such discrete elements can berigid or deformable and interact with one another through normaland shear contact forces (Oate, Munjiza, 2004). At the proposedmodel the elements are the rollers supporting the pipeline overthe laybarge ramp and singer and their positions in space andtime are associated to the rigid body motion of the laybarge.

Evaluation of Contact Forces

Once contact between a pair of elements has been

detected, the forces occurring at the contact point are calculated.The interaction between the two interacting bodies can berepresented by the contact forces Aqt and Bqt, which by theNewtons third law satisfy the following relation:

(9)

Taking and decompose qt into the normal andtangential components, and , respectively.

(10)

Where n is the unit vector normal to the contact surfaceat the contact point.

Several models that describe contact forces are foundin the literature. The model used combines the linear Force-Displacement Law (Hookes Law) with a viscous damping forcewhich is proportional to the relative velocities of particle elementsin contact. Then the normal contact force is decomposed intwo components: the elastic component, and the dampingcomponent, .

(11)

The elastic component is proportional to the normal

stiffness and to the interpenetrationg

SILVA et al.: NUMERICAL MODEL FOR THE SIMULATION OF THE


4/10


(12)

If g > 0, the Eq. (12) holds, if g 0, there is no interpenetration andthe normal component is zero.

The damping component reduces the oscillations of contact forceand dissipates kinetic energy during collision (Mendes, 2006). This componentis assumed viscous and is given by:

(13)

Where CN is the viscosity coefcient at normal direction and vN isthe relative velocity at normal direction.

Normal force magnitude is given by

(14)

The tangential component has a critical value,following the Coulomb friction Law, allowing sliding betweenelements.

The tangential force magnitude is given by

(15)

Where the integral of the relative velocity duringthe time of contact represents the elastic tangential energystored. CT is the viscosity coefcient at this direction. The totaltangential force is limited by Coulombs friction Law. Whenthis force reaches its maximum value of qtN, with beingthe friction coefcient, there is relative sliding and tangentialelastic energy storage is ceased.

The physical parameters CN and CT reect energydissipation during collisions, which is hard to evaluate directly.They can be taken as a fraction of the critical damping for thesystem of two rigid bodies i andj with mass mi and mj.

(16)

and

(17)

(18)

eN is the coefcient of restitution in the normaldirection. In a similar way CT can also be obtained.

Normal Stiffness

The discrete elements, the rollers of ramp and stinger,are assumed to be rigid. This means that the normal stiffnessneed to be chose large enough to prevent any interpenetrationduring the dynamic analyze.

Thus the normal stiffness should be, in principle, anarbitrarily large number. However, for computer calculations,it should be large enough to enforce the constraint condition,

but not so large that the governing equations become ill-

conditioned. On the other hand, too small a normal stiffnessparameter results in an unacceptable penetration of the pipelineinto the rollers and the overall response is disturbed.

In fact, the choice of the normal stiffness is a crucialpart in contact-impact calculations.

The normal stiffness here is chose to be approximately

the same order of magnitude as the stiffness of the degree offreedom normal to the contact interface.

2.2 - Contact Detection

The rst stage in a contact algorithm consists inchecking if the bodies have interpenetrated. The algorithm works

by monitoring the position of nite elements of pipeline meshand comparing these to the instantaneous location of discreteelements of ramp and stinger at each solution iteration.

Of course to check all discrete elements of ramp andstinger against every nite element of the pipeline mesh is not ofinterest. Therefore, the discrete domain is split into cells as the

scheme shown in Fig. 6. Then the contact search is only amongelements belonging to the same cell. This procedure has a verylow cost and eliminates a lot of unnecessary computations.

Figure 6 Roller Box into a sub-cell.

In order to turn more efcient and to rene the searchfor the collision points, a cell hierarchy is created. This is madeputting the whole discrete domain into a rst level cell, which issubdivided into sub-cells at each roller box. Those sub-cells areveried independently, with that, when the contact is detectedin a sub-cell the other cells do not need to be veried. A cellhierarchy scheme for a ramp and stinger conguration is shownin Figure 7.

Figure 7 Cell hierarchy Scheme (rst level cell).


5/10

17

3 - TENSIONER MODEL

The tensioner model is based on the generalizedscalar element. This element consists of two nodes linkedby a nonlinear gap spring. Force-displacement or stiffness-displacement functions associated to each local direction are

dened, and the local coordinates systems can also be actualizedat each step during simulation.In the tensioner case, the objective is to control the

tension level in the pipeline during the pipelaying operation. Itshould keep the tension level in an operational range.The tensioner model is schematically shown in Fig. 8.

Figure 8 Tensioner Model.

An additional element is created at the pipeline topand to simulate the tensioner behavior its axial stiffness varieskeeping the tension level at the dened range. Varying theaxial stiffness implies change the scalar element length movingthe pipeline top back and ahead. This behavior simulates themovement of the pipeline induced by the tensioner.

Others characteristics of the tensioner behavior arealso incorporated to this model:

Operational Range denes a range in which the tensioneris not activated. This means that the tension level is near tothe desired tension;

Response Delay after the tension level leave theoperational range the tensioner is activated but there is adelay until it effectively starts working;

Response Velocity once effectively working, it isnecessary to set how fast the tensioner is capable of restorethe tension level;

Displacement Limit there is a limit in which thetensioner can move the pipeline ahead and back in order tocompensate its tension level.

4. - OUTPUT DATA

Some output data are of particular interest in pipelayingoperations, such as support separation and reactions. These dataare automatic calculated and printed.

4.1 - Support Separation

The separation is the distance, measured between thepipeline and the roller of the support. This distance is calculatedat the middle point of each discrete element of all roller boxeson the laybarge and stinger as schematically shown in Fig. 9.

Figure 9 Points for Separation Distance Output.

There is a plan for the three points at each rollerlevel in a roller box. The support separation and reactions arecalculated on this plan at the point of the pipeline that crossesit. This point is easily determined by simple vector calculation,as shown in Fig. 10.

Figure 10 Pipeline crossing the roller level plan.

Ifn1 ( v1 v2) > 0 and n2 ( v1 v2 ) 0 then thenite element crosses the plan of this roller level. The relationbetween the lengths of vectors n

1

and n2

dene the point in thenite element.

Then distances are given by the follow equations:

(19)

(20)

(21)

WhereDi, diand ni are shown in Fig. 11, and rPipe isthe pipeline external radius.



6/10


Figure 11 Separation Distance.

4.2 - Support Reactions

The support reaction is the force exerted on the pipelineby the roller boxes in the laybarge and stinger. The horizontal,vertical and lateral support reactions are also calculated foreach discrete element of all roller boxes on the laybarge andstinger.

The reactions are the perpendicular components of theforce on the roller box surface. Their values come from thecontact model at the end of the iterative process in each timestep. The resultants are printed at the same points as the supportseparation distance, Fig. 12.

In ideal situations all rollers components make contactwith the pipe reducing/redistributing the applied local forces. Inreal situations, under dynamic loading conditions some of therollers may miss the pipe contact, resulting in more concentratedforces on a fewer number of rollers, as schematically shown inFig. 13. These situations are easily identied in the proposedmodel.

Figure 12 Reactions on the pipeline.

Figure 13 Reactions on the pipeline.

5 - NUMERICAL EXAMPLE:

S-LAY INSTALLATION

The proposed contact model has been incorporated intothe SITUA-Prosim system, a computer program that performs

the coupled static and dynamic analysis of oating offshore

systems. The SITUA-Prosim system has been developed since1997 (SITUA, 2005), in cooperation by Petrobras and LAMCSO(Laboratory of Computational Methods and Offshore Systems,at the Civil Eng. Dept. of COPPE/UFRJ, Federal Univ. of Riode Janeiro).

A module for pipeline installation simulation is

incorporated into SITUA-Prosim. This module, calledPETROPIPE, integrates a graphic interface to the numericaltools proposed here. It can easily generate numerical modelsfor pipeline installation procedures.

Several small preliminary problems have been runto test the validity of the algorithms. A variety of examplesinvolving complex congurations and nonlinear boundaryconditions were also analyzed.

5.1 - BGL-1 Data

The basic operations of the laybarge during pipelayingcan be outlined as it follows: (a) The laybarge is positioned on

its 8 anchors holding it aligned with the pipeline route; (b) Theanchors are progressively moved forward as the laying takesplace. Each anchor is lifted clear of the bottom and set in itsnew position.

The laybarge is restrained from lateral motion by themooring lines and it is moved periodically one pipe lengthahead. The mooring lines are kept under tension by the winches.These tension varies cyclically due to the long-period sway plussurge built up by the waves, storing energy in the wire lines asthe barge gradually moves to one extreme of its lateral range.The mooring lines must provide the horizontal restraint againstwave drift, wind drift, and current drift. They also react against

one another and especially must counter the tension on thepipe, which in effect is like a mooring line of relatively equaltension, leading directly astern.

The simulations performed here do not considerthe laybarge mooring line system. Since the focus is on thepipeline-laybarge interaction, the units are represented simplyby motion RAOs.

The geometrical and hydrodynamics characteristicsof BGL-1 were provided by Petrobras and are summarizedbelow:

Figure 14 BGL-1 Geometry.


7/10

19

Table 1. Main geometric characteristics of BGL-1

Propriety Values (real scale)

Drought 5.182 m

Height 9 m

Beam 30 mLength 120 m

5.2 - Ramp and Stinger Data

The local ramp-stinger coordinates system has itsorigin on the stern shoe, X-axis positive direction from bowto stern and Z-axis is vertical with positive direction upwards,Fig. 15.

The geometric data of ramp and stinger are presentedin Tables 2 and 3.

Figure 15 Ramp/Stinger Local Coordinates System.

Table 2. Ramp radius 150 m

Element X (m) Z (m) Length (m)

Tensioner -48.900 1.404 -

Roller Box 1 -39.030 1.146 3.0

Roller Box 2 -26.860 0.762 3.0

Roller Box 3 -18.290 0.036 3.0

Roller Box 4 -9.470 -1.240 3.0

Roller Box 5 -0.452 -3.089 2.5

Table 3. Stinger radius 150 m

Element X (m) Z (m)Offset

(m)Length

(m)

Roller Box 1 5.230 -4.578 0.449 5.415

Roller Box 2 9.077 -5.278 0.456 4.000Roller Box 3 12.879 -6.995 0.476 4.000

Roller Box 4 16.363 -8.371 0.510 4.000

Roller Box 5 20.348 -9.858 0.555 4.000

Roller Box 6 24.016 -11.454 0.612 4.000

Roller Box 7 27.643 -13.163 0.712 4.000

Roller Box 8 31.224 14.780 0.861 4.000

5.3 - Pipeline Data

The physical and geometric properties of the pipeline

are presented in Table 4.

Table 4. 16 Pipeline data

Parameter Value Unit

Outside Diameter 0.40640 m

Wall Thickness 0.011125 m

Yield Stress 414000 kN/m2Modulus of Elasticity of steel 207000 MPa

Axial Stiffness (EA) 2859694.14 kN

Flexional Stiffness (EI) 55894.90 kN*m2

Poisson Coefcient 0.3 -

Density of steel 77 kN/m3

Corrosion Coating Thickness 0.0032 m

Corr. Coating Weight Density 9.32 kN/m3

Concrete Coating Thickness 0.0381 m

Concrete Coating Weight Density 21.974 kN/m3

Hydrodynamic Diameter 0.489 mTube Length 12 m

Field Joint Length 0.6 m

Joint Fill Weight Density 10.065 kN/m3

Weight in Air 2.255935 kN/m

Weight Submerged 0.368493 kN/m

5.4 - Environmental Loads

The barge azimuth is 90o (point to east). It means thatthe current load, Table 5, act obliquely on the system. The waveload is presented in Table 6.

Table 5. Current Prole

Depth (m)Velocity

(m/s)Going to Azimuth (o)

0 1.02 N 0

20 1.02 N 0

70 0.45 N 0

84 0.39 N 0

89 0.00 N 0

Roller Box 5 -0.452 -3.089 2.5

Table 6 Irregular Wave (Jonswap)

Hs (m) Tp (s) Coming from Azimuth (o)

4.0 12.9 S 180

5.5 - S-Lay Model

The initial equilibrium conguration of the pipeline is generatedusing dynamic relaxation techniques as proposed by Silva(2005). The top tension in the pipeline is the parameter that

denes the S shape.



8/10


The generated S-Lay conguration is shown in Fig.16.Details of the pipeline on the overbend region are shown inFig.17.

Figure 16 S-Lay Conguration.

Figure 17 Stinger.

The geometry of the initial conguration is plotted

in Fig. 18. In this Figure, and in the follows, the results arerst shown for the whole pipeline and then for the overbend(laybarge-stinger) region.

Figure 18 Initial Conguration.

5.6 - Results

Some results of performed analyses are shown ingures that follow.

Figure 19 Tension (static).

Figure 20 Bending Stress (static).

Figure 21 Von Mises Stress (static).

Figure 22 Von Mises Stress (dynamic).

5.7 - Tensioner

The result for an analysis in which the tensioner isactivated is shown in Fig. 23: blue tenisioner not activated;green tensioner activated. This result is obtained applying aregular wave (H = 1.2m, Tp = 12s, E) to the model previousdescribed. The desired tension is set 250kN and the operationalrange 240kN to 260kN.

It should be noted a transient part of response beforethe tensiner has been completely activated. This progressiveactivation of the tensioner element follows the same strategiesas the application of environmental loads.

The pipeline movement due the variation of the

tensioner element length is shown in Fig. 24.


9/10

21

Figure 23 Tensioner Response.

Figure 24 Pipeline Movement at the Tensioner.

6 - FINAL REMARKS

This work presented a tool intended to improve theapplicability and accuracy of analysis of pipeline installationoperations, making the simulations more realistic. Such toolrepresents, during the dynamic analysis, the contact betweenthe pipeline and the laybarge as well as the tensioner behavior.

The generalized contact model presented here avoidssome limitations of the computational tools traditionally usedfor the static and dynamic analysis of pipeline installation.Also, this tool provides the engineer with several relevantinformation at preliminary design stages.

In summary, the presented model was shown to be quiteefcient and robust, and comprises an important contribution tothe analysis and design of pipeline installation operations. Theresulting numerical tool is able to provide valuable knowledgefor the design of safe offshore operations.

Acknowledgements

Finally, the authors would like to acknowledge theactive support of Petrobras, the Brazilian state oil company.Petrobras is internationally acknowledged as pioneer andleader in deep water exploitation activities, and has been

boosting research activities in this area and encouraging theuse of innovative numerical tools in real-life design situations.

REFERENCES

BELYTSCHKO, Ted, YEH, I.S., The Splitting Pinball Methodfor Contact-Impact Problems, Comput. Methods Appl. Mech.Engrg., vol. 105, pp. 375393, 1993.

BELYTSCHKO, Ted, LIU, Wing Kam, MORAN, Brian,Nonlinear Finite Elements for Continua and Structures.Chichester, John Wiley & Sons, 2000.

GREALISH, F., LANG, D., CONNOLLY, A., LANE, M.,Advances in Contact Modelling for Simulation of Deepwaterpipeline Installation, Rio Pipeline Conference & Exposition,October 17-19, Rio de Janeiro, Brazil, 2005.

GUO, B., SONG, S., CHACKO, J., GHALAMBOR, A.,

Offshore Pipelines, United States, Elsevier, 2005.

HUGHES, T.J.R., TAYLOR, R.L., SACKMAN J.L., CURNIERA., KANOKNUKULCHAI W., A Finite Element Method fora Class of Contact-Impact Problems, Comput. Methods Appl.Mech. Engrg., vol.8, pp. 249276, 1976.

HUNK, I., On Penalty Formulation for Contact-ImpactProblems, Computers & Structures, vol.48, pp. 193203,1993.

KYRIAKIDES, S., CORONA, E., Mechanics of OffshorePipelines, Volume 1: Buckling and Collapse, Slovenia, Elsevier,

2007.

LAURSEN, T.A., Computational Contact and ImpactMechanics. Berlim, Springer, 2002.

MENDES, R.B., ALVES, J.L.D., SILVA, C.E., Simulationof Torpedo Pile Launching by Coupled Discrete and FiniteElement Analysis. Procs of the XXVII Iberian Latin-American Congress on Computational Methods in Engineering CILAMCE, September 3-6, Belm, Brazil, 2006.

MUNJIZA, A., The Combined Finite-Discrete Finite Element

Method. Chichester, John Wiley & Sons, 2004.

NIELSEN R., PENDERED, J.W., Some Aspects ofMarine Pipeline Analysis, Numerical Methods in OffshoreEngineering, John Wiley & Sons, New York, 1978.

OATE, E, ROJEK, J., Combination of Discrete Element andFinite Element Methods for Dynamic Analysis of GeomechanicsProblems, Comput. Methods Appl. Mech. Engrg., vol.193, pp.30873128, 2004.

SILVA, D. M. L., Generation of initial stable congurations ofexible lines by Dynamic Relaxation Methods (In Portuguese).M.Sc thesis, COPPE/UFRJ, Rio de Janeiro, RJ, Brazil, 2005.

SILVA, D. M. L., JACOB, B.P., RODRIGUES, M.V., Implicitand Explicit Implemetation of the Dynamic Relaxation Methodfor the Denition of Initial Equilibrium Congurations ofFlexible Lines. Procs of the 25st International Conference onOffshore Mechanics and Arctic Engineering OMAE, June4-9, Hamburg, Germany, 2006.

SILVA, D. M. L., BAHIENSE, R.A., JACOB, B.P., TORRES,F.G.S., MEDEIROS, A.R., COSTA, M.N.V., NumericalSimulation of Offshore Pipeline Installation by Lateral

Deection Procedure. Procs of the 26st International



10/10


Conference on Offshore Mechanics and Arctic Engineering OMAE, June 10-15, San Diego, USA, 2007.

WRIGGERS, P., Computational Contact Mechanics. Chichester,John Wiley & Sons, 2002.

__, SITUA-Prosim Program: Coupled Numerical Simulationof the Behavior of Moored Floating Units User Manual, ver.3.0 (in Portuguese), LAMCSO/ PEC/COPPE, Rio de Janeiro,2005.

NUMERICAL MODEL FOR THE SIMULATION OF THE PIPELINE-LAYBARGE INTERACTION IN PIPELAYING PROCEDURES

Documents

Transcript of NUMERICAL MODEL FOR THE SIMULATION OF THE PIPELINE-LAYBARGE INTERACTION IN PIPELAYING PROCEDURES