Examples Manual - Academic Edition

Version 7.7

Academic Edition

Examples Manual

Version 7.7

July 2008

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Table of Contents

Chapter 1 Introduction ................................................................................................. 1 Overview .............................................................................................................................. 1

How to Use This Manual ................................................................................................... 2

Description of Examples .................................................................................................... 3

Example 1 – Single Catenary Riser ......................................................... 5 Overall Specification ........................................................................................................... 5

Finite Element Discretisation ............................................................................................. 5

Boundary Conditions ......................................................................................................... 6

Static Analysis ............................................................................................................. 6

Dynamic Analysis ....................................................................................................... 6

Applied Loads ..................................................................................................................... 6

Static Analysis ............................................................................................................. 6

Dynamic Analysis ....................................................................................................... 6

Miscellaneous ...................................................................................................................... 7

Results .................................................................................................................................. 8

Example Files ....................................................................................................................... 9

Input Data .......................................................................................................................... 12

Structure Properties .................................................................................................. 12

Environmental and Loading Data .......................................................................... 13

RAO Data ................................................................................................................... 13

Regular Wave Profile ................................................................................................ 14

Example 2 – Free Hanging Catenary Riser .......................................... 19 Overall Specification ......................................................................................................... 19

Finite Element Discretisation ........................................................................................... 19

Boundary Conditions ....................................................................................................... 20

vi

Static Analysis ........................................................................................................... 20

Current Analysis ....................................................................................................... 20

Dynamic Analysis ..................................................................................................... 21

Applied Loads ................................................................................................................... 21

Static Analysis ........................................................................................................... 21



Miscellaneous .................................................................................................................... 21

Results ................................................................................................................................ 22

Examples Files ................................................................................................................... 23

Input Data .......................................................................................................................... 26


Seabed Friction .......................................................................................................... 26


Current Profile ........................................................................................................... 27

RAO Data ................................................................................................................... 28


Example 3 – Steep Wave Riser ............................................................... 33 Overall Specification ......................................................................................................... 33

Finite Element Mesh Generation .................................................................................... 33


Static Analysis ........................................................................................................... 33



Applied Loads ................................................................................................................... 34

Static Analysis ........................................................................................................... 34



Miscellaneous .................................................................................................................... 35

vii

Results ................................................................................................................................ 36

Examples Files ................................................................................................................... 37

Input Data .......................................................................................................................... 40



Current Profile ........................................................................................................... 41


Vessel Initial Position ............................................................................................... 42

RAO Data ................................................................................................................... 42

Example 4 – API Drilling Riser Analysis ............................................ 49 Overall Specification ......................................................................................................... 49



Static Analysis ........................................................................................................... 50


Applied Loads ................................................................................................................... 50

Static Analysis ........................................................................................................... 50


Miscellaneous .................................................................................................................... 51

Results ................................................................................................................................ 52

Examples Files ................................................................................................................... 53

Reference ............................................................................................................................ 54

Input Data .......................................................................................................................... 57


Environmental Data .................................................................................................. 57

Miscellaneous Data ................................................................................................... 58

Current Profile ........................................................................................................... 58


RAO Data ................................................................................................................... 59

viii

Example 5 – TLP Tether Tow-Out and Installation ........................... 65 Overall Specification ......................................................................................................... 65



Tether Tow-Out ......................................................................................................... 66

Tether Installation ..................................................................................................... 66

Applied Loads ................................................................................................................... 66

Tether Tow-Out ......................................................................................................... 66


Miscellaneous .................................................................................................................... 67

Results ................................................................................................................................ 68

Examples Files ................................................................................................................... 68

Tether Tow-Out ......................................................................................................... 68


Input Data .......................................................................................................................... 72


Environmental Data .................................................................................................. 73


Example 6 – Analysis of a Jack-up Platform ....................................... 75 Overall Specification ......................................................................................................... 75



Applied Loads ................................................................................................................... 75

Static Analysis ........................................................................................................... 75



Miscellaneous .................................................................................................................... 76

Results ................................................................................................................................ 76

Examples Files ................................................................................................................... 77

ix

Input Data .......................................................................................................................... 80




Current Profile ........................................................................................................... 81


Chapter 1: Introduction

Examples Manual Rev. 1 1 Flexcom Version 7.7 Academic Edition

Introduction Welcome to the Examples Manual for Flexcom Version 7.7 Academic Edition. This manual incorporates examples that show some of the range of applications for which the academic edition of the software may be used.

This first chapter, ‘Introduction’, provides an overview of the manual layout. Specifically, ‘Introduction’ is divided into the following sections:

• ‘Overview’ gives a brief introduction to Flexcom. • ‘How to Use This Manual’ gives guidelines on running the examples

described in this manual and where the analysis input files for the examples can be located.

• ‘Description of Examples’ briefly describes the Flexcom analyses included in this manual.

Overview

Flexcom is a fully non-linear three-dimensional time domain finite element package for the analysis of a wide range of offshore structures. Static, quasi-static and full dynamic analysis capabilities are provided. A sophisticated and intuitive Graphical User Interface (GUI) ensures optimal productivity with minimal training.

The examples in this manual cover a wide range of program applications, including analysis of flexible risers, rigid risers, a TLP tether tow-out and installation, and mooring systems. Static, quasi-static and dynamic analyses are all described. The examples in this manual are intended to provide a representative sample of the capabilities of the program. There are, however, many program features that are not described in the examples and the range of application of the program is by no means limited to the type of structures described here.



How to Use This Manual

A total of six example Flexcom analyses are described in the following chapters. Each chapter presents a brief description of the structure being analysed, together with a description of the finite element discretisation used to model the structure. All relevant input data (structure properties, environmental data etc.) is presented in tabular format for ease of reference. The procedure used to perform the analyses is described, including the boundary conditions and loads that are applied in each step of the analysis. A brief discussion of some of the more pertinent results of the analysis follows, together with some sample plots.

All of the analysis input files required to run the examples may be found in the ‘Examples’ subdirectory of your Flexcom installation directory, provided that you installed the examples when you installed Flexcom. If you did not install the examples, you may do so at any time by running the Setup program.

A list of the files associated with each example is given in the relevant chapter of the manual.

It is recommended that, for examples that are of interest, you should first read the relevant chapter of this Examples Manual to familiarise yourself with the structure being analysed. You should then perform the various analysis steps in the order in which they are described in the manual. It is worth taking the time to examine the contents of the various menus in the GUI at each step. Context-sensitive on-line help is available for all of the menus in the analysis and postprocessing modules to further explain the function of each menu. You can of course alter the entries in the menus to examine the effect of, for example, changing structure properties, or you may wish to specify the generation of additional plots in the postprocessing modules. Remember, however, to save altered files under a new filename if you do not wish to overwrite the original example files.



Description of Examples As noted earlier, the examples in this manual are intended to provide a representative sample of the type of analyses that may be performed using Flexcom. The first three examples analyse flexible riser systems, starting with a simple single catenary riser, then progressing to a free hanging catenary (involving seabed contact), and finally a steep wave riser.

Example 4 deals with a rigid riser system. It analyses a rigid riser described in Bulletin 2J of the American Petroleum Institute (API), and compares results with those presented in the API publication.

The remaining two examples demonstrate some of the wide range of applications of Flexcom. Example 5 considers the tow-out and installation of a tension leg platform tether, while Example 6 analyses a jack-up platform subjected to static and dynamic loading (including wind, wave and current).



Chapter 2: Example 1 - Single Catenary Riser


Example 1 – Single Catenary Riser

Overall Specification

This example considers a single catenary riser subjected to static and dynamic loads. The riser is 350m in length and is sited in a water depth of 375m. The riser is filled with seawater. Motions of an attached vessel are applied to the riser from specified Response Amplitude Operators (RAOs). Fig. 2.1 shows a schematic of the installation. As is recommended in Chapter 15 of the Reference Manual, in the section entitled ‘Restarts’, the analysis is performed in two stages. The first stage consists of an initial static analysis, which is then followed in the second stage by a dynamic analysis restarted from the static.

Finite Element Discretisation

Fig. 2.2 shows the finite element discretisation of the riser. The key discretisation details are given in Table 2.1. The model comprises 50 elements and 51 nodes.

The end nodes of the riser (Nodes 1 and 51) are defined directly using the Nodes – Define Directly option. Between these end nodes, a cable is defined with the Cables – Define Cable option, and the intermediate nodes between Nodes 1 and 51 are generated along the cable profile using Cables - Generate Nodes. Elements are defined along the cable profile by directly defining Element 1 between Nodes 1 and 2, and then generating the remaining elements using Element 1 as the master element.

Table 2.1. Summary of Structural Discretisation.

Number of Nodes 51

Number of Elements 50

Number of Integration Points per Element 3



Boundary Conditions

Static Analysis

Node 1 is fixed in all translational degrees of freedom (DOFs 1-3) while being free in the rotational degrees of freedom (DOFs 4-6). Node 51 is specified as having attached vessel boundary conditions for the translational degrees of freedom. This is equivalent to a pin-joint between the top of the riser and the vessel. As this is a static analysis, the vessel does not move and so the location of the pin-joint is effectively fixed.

Dynamic Analysis

All translational degrees of freedom of Node 1 are fixed while the rotational degrees of freedom are set equal to their final values found from the static analysis. These values may be found by examining the Results section of the main output file (Example1–static.out). The boundary conditions at Node 51 remain the same. Because this is a dynamic analysis, however, the motion of Node 51 will be defined by the specified vessel RAOs.

Applied Loads

Static Analysis

The position of the riser is determined under gravity and buoyancy loads. The riser is filled with seawater to the MWL.

Dynamic Analysis

A regular wave is applied to the structure, details of which are given in the Input Data section. The motion of the vessel connection point, which is defined by the specified vessel RAOs, is applied to the top of the riser using the Boundary - Vessel option.



Miscellaneous

The Type - Static option is selected to specify a static analysis. For this analysis option, simulation time has only notional significance and the Time option is primarily used to indicate how the loads and displacements are to be applied to the structure. In this example, the static analysis can be completed in one step as the loads are already applied by the cable pre-static step. Therefore, the analysis goes from 0 to 1 seconds with a time step of 1 second. As the beam finite element solution iterates from the cable analysis, bending effects are taken into account and the riser settles into its final configuration.

During the dynamic step, loads are applied over a 55-second time interval from 1 to 56 seconds. The program variable time stepping procedure is used. This procedure selects the time step size by monitoring the ambient dominant period of the system response. The dynamic loads are ramped on over the first 11 seconds, that is over 1 wave period. An initial value of 0.1 seconds is suggested for the time step with upper and lower limits of 0.75 seconds and 0.05 seconds respectively. The Option - Restart menu is used to indicate that the dynamic analysis is to be restarted from the static, using the New Loads or BCs option.

The mass and stiffness damping coefficients are set at 0.0 and 0.13, respectively, for the dynamic analysis. This small level of damping helps to suppress high frequency noise in the structure response.

During the dynamic analysis, run-time timetraces of the vertical motion of the top node of the riser, the curvature at the lowest point on the catenary, and wave elevation are presented. A run-time structure view is also shown. You can add to, or change, the selection of parameters displayed at run-time using the Analysis – Run Time Settings option in the Analysis module top menu bar.



Results

Fig. 2.3 shows the configuration of the riser found from the static analysis. Figs. 2.4 to 2.6 plot respectively, the local-z bending moment distribution, the effective tension distribution along the riser, and the curvature distribution for the static analysis. On examination of the output file it will be noted that the vertical reactions at the support points sum to the total apparent weight of the structure. Table 2.2 shows the reaction values at the end nodes of the riser in the vertical (global-X) and horizontal (global-Y) directions at the end of the static analysis.

Table 2.2. Reactions at Riser End Nodes.

Node D.O.F Reaction (kN)

1 1 35.8

2 -12.0

51 1 91.5

2 12.0

The sum of the vertical reactions equals 127.3 kN, which is equal to the total apparent weight of the structure. The apparent weight of the structure may be calculated using the following formula:

eia wwww −+=

where: w = weight of structure = mlg

wi = weight of internal fluid = gld ii ρπ 24

we = weight of displaced fluid = gld eb ρπ 24

Note that: m = mass per unit length of structure

l = length of structure di = internal diameter



ρi = density of internal fluid

ρe = density of external fluid

db = buoyancy diameter

Note also that the horizontal reactions are equal and opposite.

For the dynamic analysis, effective tension envelopes are presented in Fig. 2.7, while Fig. 2.8 gives a timetrace of curvature at the lowest point of the catenary.

Example Files

The analysis input files for this example may be found in the ‘Examples\Example 1’ subdirectory of your Flexcom installation directory. The input files are as follows:

Example1-static.fl3 Initial static analysis file

Example1-dynamic.fl3 Dynamic analysis file

Example1.res Vessel response (RAO) file

Example1-dynamic.rts Dynamic analysis run-time settings file

Example1-static.ps3 Static analysis postprocessing file

Example1-dynamic.ps3 Dynamic analysis postprocessing file



Mean Water Line

Seabed

RISER

X

Z

Y

Fig. 2.1. Schematic of Riser Configuration.



Seabed

X

Z

Y

Key Nodal Co-ordinates

Node X Y Z

1 225.0 0.0 0.0 51 375.0 150.0 0.0

Element numbers are underlined.All elements have the same length.

51

50

49

50

49

1

23

12

Fig. 2.2. Finite Element Discretisation Details.



Input Data

Structure Properties

Component EIyy

(Nm2)

EIzz

(Nm2)

GJ

(Nm2)

EA

(N)

m

(kg/m)

p

(kgm)

dI

(m)

dd

(m)

db

(m)

RISER 20.96E3 20.96E3 2.5E6 1.538E9 57.5 0.2 0.2032 0.2582 0.2582

where: EIyy = Bending stiffness about local-y axis

EIzz = Bending stiffness about local-z axis

GJ = Torsional stiffness

EA = Axial stiffness

m = Mass per unit length

p = Polar moment of inertia of cross-section per unit length di = Internal diameter

dd = Drag diameter

db = Buoyancy diameter



Environmental and Loading Data

Parameter: Value:

Water depth (m) 375.0

Water density (kg/m3) 1025.0

Drag coefficient, Cd 1.0

Inertia coefficient, Cm 2.0

Internal fluid height (m) 375.0

Internal fluid density (kg/m3) 1025.0

RAO Data

Global Coordinates (X, Y, Z)

Vessel reference point initial position

(395, 175, 10)

DOF Magnitude Phase (°)

Heave 0.4 15.0

Surge 0.6 90.0

Sway 0.5 75.0

Yaw 0.05 -15.0

Roll 0.1 40.0

Pitch 0.2 20.0



Regular Wave Profile

Amplitude

(m)

Period

(s)

Direction

(º)

6.0 11.0 45.0

Note that the wave emanates from the origin of the global axes.

-200 -150 -100 -50 0 50Local-3 Axis (m)

150

200

250

300

350

400

Loca

l-1 A

xis

(m)

Structure

Fig. 2.3. Static Configuration



0 50 100 150 200 250 300 350Curved Distance along Structure (m)

-0.7

-0.6

-0.5

-0.4

-0.3

-0.2

-0.1

0Lo

cal-z

Mom

ent (

kNm

)

Element set 1; B.M. about local-z axis

Fig. 2.4. Local-z Bending Moment Distribution.


1020

3040

5060

7080

9010

0E

ffec

tive

Tens

ion

(kN

)

Element set 1; Effective tension

Fig. 2.5. Static Effective Tension Distribution.




00.

005

0.01

0.01

50.

020.

025

0.03

0.03

5TT

L. C

urva

ture

(1/m

)

Element set 1; Resultant curvature

Fig. 2.6. Static Curvature Distribution.


025

5075

100

125

Eff

ectiv

e Te

nsio

n (k

N)


Fig. 2.7. Effective Tension Envelopes.



0 10 20 30 40 50 60Time (s)

0.02

90.

0292

50.

0295

0.02

975

0.03

0.03

025

0.03

050.

0307

5Cu

rvat

ure

(1/m

)

Elem. no. 15; Midpoint

Fig. 2.8. Curvature Variation at Lowest Point on Catenary.



Chapter 3: Example 2 – Free Hanging Catenary Riser


Example 2 – Free Hanging Catenary Riser


This example considers the behaviour of a free hanging catenary riser subjected to static and dynamic loads. The riser is 260m in length and is sited in a water depth of 120m. Motions of an attached vessel are applied to the riser from specified Response Amplitude Operators (RAOs). Fig. 3.1 shows a schematic of the riser configuration. This example demonstrates the use of a number of Flexcom features, including the Run Time Settings and the Summary Output File.


60 elements are used to model the 260m length riser. Fig. 3.2 shows the basic finite element discretisation for the riser model. Note that the vessel model is formed of so-called auxiliary elements and nodes. These are not part of the actual finite element discretisation and are included purely to illustrate the location of the vessel throughout the analyses. Table 3.1 summarises the structural discretisation.

The end-nodes of the riser (Nodes 1 and 61) are defined directly using the Nodes – Define Directly option. Between these end-nodes, a cable is defined with the Cable – Define Cable option and the intermediate nodes between Nodes 1 and 61 are generated along the cable profile using Cables – Generate Nodes. Elements are defined along the cable profile by directly defining Element 1 between Nodes 1 and 2, and then generating the remaining elements using Element 1 as the master element. Note that when using the cable pre-static step for a configuration that is partially lying on the seabed, the first node of the cable must always be the node on the seabed.




Number of Structural Nodes 61

Number of Structural Elements 60


Boundary Conditions

Static Analysis

Translational boundary conditions are applied to the bottom node of the riser (at the pipeline end manifold, or PLEM). For the static analysis, rotational boundary conditions are also applied at this point. Note that boundary conditions are applied by defining Node 101 as equivalent to Node 1 and then applying the boundary conditions to Node 101. The rotational boundary conditions are thus applied to Node 101 also. DOFs 4 and 5 are fixed at zero, while DOF 6 is fixed at 90°.

The top of the riser is specified as having attached vessel boundary conditions for the translational degrees of freedom while the rotational degrees of freedom are free. This is equivalent to a pin-joint between the top of the riser and the vessel. Note that it is not necessary to specify an RAO file for the vessel at this stage – it is sufficient that Flexcom knows the initial position of the vessel.

Current Analysis

The boundary conditions are unchanged from the static analysis.



Dynamic Analysis

The boundary conditions themselves are again unchanged from the initial static analysis, however an RAO file is now specified for the vessel. Hence, the motions of the top node of the riser are defined by the motions of the attached vessel, which are calculated from the specified RAOs.

Applied Loads

Static Analysis

The equilibrium position of the riser (which is assumed to be full of air) is determined under gravity and buoyancy loads.

Current Analysis

In this analysis a cross current is applied to the riser. The current varies piecewise-linearly with depth, and its profile is given in the Input Data section of this chapter. The direction of the current is constant and is at 90 degrees (anti-clockwise) to the global Y-axis.

Dynamic Analysis

An in-line regular wave is applied to the structure, causing vessel motions and hydrodynamic loading on the riser. Details of the wave are given in the Input Data section. The wave direction is at 180 degrees anti-clockwise relative to the global Y-axis. Note that the wave emanates from the origin of the global axes.

Miscellaneous

For the static analysis the Type-Static option is selected. The analysis is run from 0 to 1 second in a single step. Similarly for the current analysis the Type-Static option is selected and the analysis is run from 1 to 2 seconds in a single step. The current analysis is restarted from the initial static analysis.



The dynamic analysis is run for a 55-second time interval from 2 to 57 seconds, which is equivalent to five wave periods. The wave loads are ramped on to the structure over the first 11 seconds (one wave period) of the analysis. The dynamic analysis is restarted from the current analysis. All analyses include the effect of anisotropic seabed friction.

Run-time timetraces of the vertical motion of the top of the riser, the effective tension at the top of the riser and the wave elevation are displayed during the dynamic analysis. A run-time structure view is also shown.

Results

A snapshot of the configuration in its static equilibrium position (before current loading is applied) is shown in Fig. 3.3. The effective tension distribution along the riser in this position is given in Fig. 3.4. A plan view of the configuration subject to the cross current loading, which clearly shows the deflection of the riser in the direction of the current, is shown in Fig. 3.5.

Results from the dynamic analysis of the system are presented in Figs. 3.6 and 3.7. These show respectively max/min. envelopes of vertical position and max./min. envelopes of the effective tension distribution in the riser. Noteworthy in these results is that although the applied vessel motions are relatively small, the variation in the effective tension is large. Also a relatively large section of the riser lifts off the seabed. These results are typical of the free hanging riser configuration.

This example also illustrates the use of the Summary Output File. The contents of this file are specified using the Summary Output File Settings window, which may be accessed from either the Analysis or Database Postprocessing modules. In this example, a summary output file is generated automatically at the end of the dynamic analysis. The example summary output file is shown in Table 3.2.



Examples Files


Example2-static.fl3 Initial static analysis file

Example2-current.fl3 Static current analysis file


Example2.res Vessel response (RAO) file

Example2-dynamic.spt Dynamic Summary Output Settings file

Example2-dynamic.rts Dynamic analysis run-time settings file

Example2-static.ps3 Static analysis postprocessing file

Example2-current.ps3 Current analysis postprocessing file

Example2-dynamic.ps3 Dynamic analysis postprocessing file



MWL

120 m

PLEM

Support Vessel

Riser

Seabed

Fig. 3.1. Schematic of Riser Configuration.



X

Y

Key Nodal Coordinates

Node

161

X Y Z

0.140.

0.160.

0.0.

Element numbers are underlined All elements have the same length

61

60

1

1

Seabed




Input Data


Component EIyy

(Nm2)

EIzz

(Nm2)

GJ

(Nm2)

EA

(N)

m

(kg/m)

p

(kgm)

dI

(m)

dd

(m)

db

(m)

RISER 20.0E3 20.0E3 2.5E6 350.0E6 100.0 1.4133 0.2 0.27 0.27

where: EIyy = Bending stiffness about local-y axis

EIzz = Bending stiffness about local-z axis

GJ = Torsional stiffness

EA = Axial stiffness

m = Mass per unit length

p = Polar moment of inertia of cross-section per unit length di = Internal diameter

dd = Drag diameter

db = Buoyancy diameter

Seabed Friction

Longitudinal Coefficient of Friction 0.1

Transverse Coefficient of Friction 0.5




Parameter: Value:





Current Profile

Height above Mudline (m)

Velocity

(m/s)

Direction

(º)

0.0 0.1 90.0

20.0 0.9 90.0

100.0 1.4 90.0

120.0 1.8 90.0



RAO Data


Vessel reference point initial position

(140, 200, 0)

DOF Magnitude Phase (°)

Heave 0.4 10.0

Surge 0.5 120.0

Sway 0.0 0.0

Yaw 0.0 0.0

Roll 0.0 0.0

Pitch 0.15 180.0


Amplitude

(m)

Period

(s)

Direction

(º)

6.0 11.0 180.0




Table 3.2. Example Summary Output File. _______________________________________________________________________________________

F L E X C O M Version 7.7.2

3D Non-linear Time Domain Finite Element Analysis

(c) MCS 2008 _______________________________________________________________________________________ Example 2 - Free Hanging Catenary - Dynamic

Summary of results from analysis: Example2-dynamic

_______________________________________________________________________________________

Variable Minimum Maximum Range Standard

Deviation

_______________________________________________________________________________________

(1) Motions

-----------

Riser Top Motions - DOF 1 (m) 138.215 141.785 3.569 1.260

- DOF 2 (m) 157.006 163.000 5.994 2.123

(2) Angles

----------

True Angle between Riser & Vessel 153.707 168.635 14.929 4.971

(3) Reactions

-------------

Reaction @ PLEM - DOF 1 (kN) 0.878 0.878 0.000 0.000 *

- DOF 2 (kN) -19.387 1.500 20.887 5.685 *

- DOF 3 (kN) -0.005 -0.003 0.002 0.001 *

(4) Forces

----------

Effective Tension @ Riser Top (kN) 62.807 91.913 29.106 9.146

(5) Force Envelopes

-------------------

Effective Tension Distribution (kN) 1.210 91.913 90.703 12.310 *

Curvature Distribution (kN) 0.000 0.098 0.098 0.000 *

(6) Seabed parameters

---------------------

Length on Seabed 82.333 99.667 17.333 5.456

_______________________________________________________________________________________

Notes:

------

(1) Parameters calculated over time interval 13.071 to 57.237



-175 -150 -125 -100 -75 -50 -25 0Local-3 Axis (m)

-25

025

5075

100

125

150

Loca

l-1 A

xis

(m)

Structure

Fig. 3.3. Free Hanging Riser Configuration.

0 50 100 150 200 250 300Curved Distance along Structure (m)

010

2030

4050

6070

80Ef

fect

ive

Tens

ion

(kN)


Fig. 3.4. Effective Tension Distribution in Riser.



-75 -50 -25 0 25 50 75 100Local-3 Axis (m)

-175

-150

-125

-100

-75

-50

-25

0Lo

cal-1

Axi

s (m

)

Structure

Fig. 3.5. Plan View of Riser – Cross Current Applied.


-25

025

5075

100

125

150

Vert

ical

Mot

ion

(m)

Element set 1; DOF 1

Fig. 3.6. Envelopes of Riser Vertical Motion.




010

2030

4050

6070

8090

100

Effe

ctiv

e Te

nsio

n (k

N)


Fig. 3.7. Envelopes of Effective Tension Distribution.

Chapter 4: Example 3 – Steep Wave Riser


Example 3 – Steep Wave Riser


This example investigates a steep wave riser configuration, subject to loads from waves and current. The riser is 430m in length and is sited in 300m of water. It is filled with oil and attached to a vessel for which Response Amplitude Operators (RAOs) are specified. Fig. 4.1 shows a schematic of the configuration. The analysis is performed in three stages. The initial static analysis then applies gravity and buoyancy forces, while the second static analysis applies current loading. Finally, the dynamic analysis finds the response of the structure to vessel motions and wave loading.

Finite Element Mesh Generation

Fig. 4.2 shows the location of the principle connections. The model consists of a steep wave configuration, modelled using three cable sections. The locations of the connections at each end of the buoyant section are not important. Simply place them anywhere that is physically reasonable. The actual position of the connections will be found when the analysis is performed.

Boundary Conditions

Static Analysis

Node 1 is fixed to zero in all translational degrees of freedom, while Node 87 is attached to the vessel. The initial position of the vessel is specified with an undisplaced orientation of 50 degrees to the global Y-axis in the YZ plane. Note that, attaching Node 87 to the vessel is equivalent to setting all translational degrees of freedom to zero, since the vessel does not move in this analysis.



Current Analysis

Nodes 1 and 87 are fixed to zero in all translational degrees of freedom together with the components of rotation in the global X and Y directions. The global Z-component of rotation at Node 1 is set at 13.09° and the global Z-component of rotation at Node 201 is set at 3.68°; these two values are obtained at the end of the first static analysis, from the main output file. Note that Node 87 and 201 are equivalent and the boundary conditions can be applied to either. However, only data for Node 87 is written out to the output files.

Dynamic Analysis

The boundary conditions from the previous analysis apply here also. They need not be specified again since it is a restart analysis.

Applied Loads

Static Analysis

The position of the riser is determined under gravity and buoyancy loads. The riser is filled with oil at a pressure of 18.008 MPa to the top of the riser.

Current Analysis

In this analysis, a cross current is applied to the riser. The current varies piecewise-linearly over the depth, and its profile is given in the ‘Input Data’ section. The direction of the current is constant with depth and is at 90 degrees (anti-clockwise) to the global Y-axis.

Dynamic Analysis

A regular wave is applied to the structure. The wave direction is at 230 degrees anti-clockwise relative to the global Y-axis. The input values are given below in the section ‘Input Data’. We also specify a Response Amplitude Operator (RAO) file



for the vessel. The movement of the vessel determines the displacement of Node 87.

Miscellaneous The first two analyses are static analyses and use the Type-Static option. The dynamic analysis employs the Type-Dynamic option. The program assumes all analyses to be non-linear by default. The first static analysis requires only one step since the cable pre-processor has applied all the loads. The analysis goes from 0 to 1 second with a 1-second time-step. The second analysis involves the application of the cross current over a nominal 1-second interval, from 1 to 2 seconds, in a single step.

The dynamic analysis begins at the end of the cross current analysis and continues for a further 50 seconds, which is five wave periods. The use of the Option-Restart menu is necessary to specify a restart analysis. The Time-Variable option is selected and the step size is determined mainly by the instantaneous value of the current period, as described in the Flexcom Reference Manual. The step size can vary between the minimum and maximum user-specified values of 0.05 and 0.5 seconds respectively. The maximum value of 0.5 is selected on the basis that it is one twentieth of the wave period of 10 seconds. The dynamic loads and displacements are ramped on over 10 seconds of the analysis (1 wave period).

The complete dynamic analysis of this steep wave flexible riser with three-dimensional wave and current loads has been achieved in three steps. Namely, a first static step with gravity and buoyancy loads, a second static step to apply the cross current load, and the final dynamic step to apply wave loads and vessel motions. In general, it is recommended that this strategy be used to analyse all flexible riser systems.



Following the guidelines given in the ‘Restarts’ section of Chapter 15 of the Reference Manual, we carry out a first static step with buoyancy, gravity and applied mechanical loads. This enables you to do a number of simple analytical checks on the model to see if it is properly set up. For example, the algebraic sum of the vertical reactions should be equal and opposite to the sum of the vertical applied loads and the total apparent weight of the riser.

The current and wave loads could be applied together in one subsequent dynamic analysis. However, this could be very inefficient as the size of the time step would be governed by the wave period, but the riser may not fully respond to the applied current for a considerable number of wave periods. Hence, a lot of simulation time could be wasted. The best approach is to apply the current loads in a static analysis and then add the waves in a subsequent dynamic analysis. Furthermore, the full application of the current can generally be achieved with one or a small number of steps in a static analysis.

The vessel motions are specified using the RAO file, which is named in the Boundary-RAO File menu option. Note that in the RAO file, no wave heading is specified and therefore the program assumes that the vessel response is the same at all wave headings. Also, because only one frequency is specified, it must be within 1% of the wave frequency for vessel motions to be applied. The user indicates the nodes of the riser that are connected to the vessel by the use of the Boundary-Vessel option. In this case, all degrees of freedom at Node 87 are specified as attached to the vessel.

Results

From the initial static analysis, the in-plane static configuration of the riser is shown in Fig. 4.3 and the local-z bending moment distribution is shown in Fig. 4.4. From the restart with current, the out-of-plane static configuration of the riser with cross current is given in Fig. 4.5. Effective tension and curvature distributions



along the riser are presented respectively in Fig. 4.6 and Fig. 4.7. Sample dynamic results are given in Fig. 4.8 through to Fig. 4.12. Figs. 4.8 and 4.9 plot respectively timetraces of reaction and rotation at the vessel connection, while Figs. 4.10 and 4.11 show max/min envelopes of torque and curvature, computed over the last three wave periods. Finally, the effective tension envelope is plotted in Fig. 4.12.

Examples Files

The analysis input files for this example may be found in the 'Examples\Example 3' subdirectory of your Flexcom installation directory. The input files are as follows:

Example3-static.fl3 Static analysis file

Example3-current.fl3 Current analysis file


Example3.res RAO file

Example3-dynamic.spt Dynamic Summary Output Settings file

Example3-dynamic.rts Dynamic Run Time Settings file

Example3-static.ps3 Static Postprocessing file

Example3-current.ps3 Current Postprocessing file

Example3-dynamic.ps3 Dynamic Postprocessing file



X

Y

Z

RISER

Mean Water Line

Seabed

FOAMRISER

Fig. 4.1. Schematic of Steep Wave Riser Configuration.



Key Connection Coordinates

Connection X Y Z

C1 0 0 0

C2 290 120 0


Node

Node Node

C2

C1 Seabed Y

Z X

Node



Input Data


Component EIyy

(Nm2)

EIzz

(Nm2)

GJ

(Nm2)

EA

(N)

m

(kg/m)

p

(kg.m)

di

(m)

dd

(m)

db

(m)

RISER 30.0E3 30.0E3 1.1E6 495.0E6 80.0 0.525 0.1 0.25 0.25

FOAM 30.0E3 30.0E3 1.1E6 495.0E6 163.67 2.699 0.1 0.52 0.52

where: EIyy - Bending Stiffness about Local y Axis

EIzz - Bending Stiffness about Local z Axis

GJ - Torsional Stiffness

EA - Axial Stiffness

m - Mass per Unit Length

p - Polar Inertia of Cross-section per Unit Length di - Internal Diameter

dd - Drag Diameter

db - Buoyancy Diameter




Parameter: Value:





Internal fluid height (m) 290.0

Internal fluid density (kg/m3) 880.0

Internal fluid pressure (MPa) 18.008

Current Profile

Height Above

Seabed (m)

Velocity

(m/s)

Direction

(º) 0.0 0.0 90.0

160.0 0.4 90.0 300.0 1.0 90.0


Amplitude

(m)

Period

(s)

Direction

(º)

5.0 10.0 -130.0




Vessel Initial Position

Global Co-ordinates (X, Y, Z) Undisplaced Orientation (o)

(305, 120, 10) 50

RAO Data

Degree of freedom

Magnitude Phase (°)

Heave 0.3 0.0

Surge 0.2 -90.0

Sway 0.0 0.0

Yaw 0.0 0.0

Roll 0.0 0.0

Pitch 0.6 90.0



-100 -50 0 50 100 150 200 250Local-3 Axis (m)

-25

2575

125

175

225

275

325

Loca

l-1 A

xis

(m)

Structure

Fig. 4.3. Static Riser Configuration.

0 100 200 300 400 500Curved Distance along Structure (m)

-3-2

-10

12

3Lo

cal-z

Mom

ent

(kNm

)


Fig. 4.4. Local-z Bending Moment - Static.



-150 -100 -50 0 50 100 150 200Local-3 Axis (m)

-25

2575

125

175

225

275

325

Loca

l-1 A

xis

(m)

Structure

Fig. 4.5. Out-of-plane Configuration – Cross Current.


010

2030

4050

6070

Eff

ectiv

e Te

nsio

n (k

N)


Fig. 4.6. Static Effective Tension Distribution.




00.

050.

10.

150.

20.

25C

urva

ture

(1/

m)


Fig. 4.7. Static Curvature Distribution.

0 10 20 30 40 50 60Time (s)

5055

6065

7075

80V

ertic

al R

eact

ion

(kN

)

Node no. 87; DOF 1

Fig. 4.8. Vertical Reaction at Vessel Connection.



0 10 20 30 40 50 60Time (s)

2.5

33.

54

4.5

55.

56

6.5

Rota

tion

(Deg

rees

)

Node no. 87; DOF 7

Fig. 4.9. Magnitude of Rotation at Vessel Connection.

0 100 200 300 400 500Curvilinear Distance along Structure (m)

1.48

1.49

1.5

1.51

1.52

1.53

Torq

ue (k

Nm)

Element set 1; Torque

Fig. 4.10. Torque Envelope.




00.

050.

10.

150.

20.

250.

30.

35Cu

rvat

ure

(1/m

)


Fig. 4.11. Curvature Envelope.


010

2030

4050

6070

80E

ffec

tive

Tens

ion

(kN

)


Fig. 4.12. Effective Tension Envelope.



Chapter 5: Example 4 – API Drilling Riser Analysis


Example 4 – API Drilling Riser Analysis


This example considers the analysis of a 1520 ft drilling riser located in a water depth of 1500 ft. The riser is subjected to static and current loads, vessel offset, and dynamic regular wave loading. Comparison is made with similar analyses reported in Bulletin 2J of the American Petroleum Institute (API) [1]. The riser is fixed to the seabed via a ball joint and LMRP. It is also attached to a floating vessel 50 ft above the MWL. A schematic of the system is shown in Figure 5.1. The excitation and response are 2D (the riser is constrained to remain in the global XY plane), so no value is required for the Shear Modulus G (a nominal value of 1 is specified in the actual input data).

The codes used in the API bulletin for the analyses in this example are as follows:

1500-B-2-S Static analysis, current load and vessel offset applied.

1500-40-2-D Dynamic analysis, regular wave and vessel motions applied in addition to static loads.

Finite Element Discretisation The lower marine riser package (LMRP) and the lower ball joint (LBJ) are not included in the finite element model of this system. The riser is instead assumed to be pinned at the vertical height of the LBJ, which is 30 ft above the mudline. The model continues to the upper ball joint (UBJ), which is likewise not explicitly included in the model – the riser is again pinned at this point. A schematic of the finite element model is presented in Fig. 5.2. Details of the finite element discretisation are given in Table 5.1 below.




Number of Nodes 61

Number of Elements 60


Boundary Conditions

Static Analysis

For all analysis stages Node 1 is held in all translational degrees of freedom (DOFs) and in rotational DOF 4. A vessel boundary condition is applied at Node 61 in the horizontal DOF 2. The vessel reference point is initially at the same elevation as the top of the riser, as per the API specification, and an offset of 45 ft is specified. The name of the vessel RAO file is also input at this static analysis phase. The RAOs are interpolated from the data in the API bulletin.

Dynamic Analysis

There is no specification of boundary conditions required for the dynamic phase. Dynamic motions calculated from the motions of the attached vessel are automatically applied at Node 61 in DOF 2 using the RAO data specified in the static analysis.

Applied Loads

Static Analysis

In the static analysis gravity, buoyancy, top tension and current loads are applied. The top tension of 600 kips is applied directly as a point load at the top of the riser (Node 61). Internal fluid, which is mud with a density of 2.7888 slugs/ft3 (12 ppg), is included in the analysis.



Dynamic Analysis

The dynamic analysis restarts from the static analysis, with a regular wave included. In the Options - Wave Kinematics menu the Extend MWL to Wave Surface option is invoked. This is one of a number of options in Flexcom for calculating Airy wave kinematics – you are referred to the Flexcom Reference Manual for further details.

Miscellaneous

The riser properties are specified in the static analysis input data using the Rigid Riser format. How a number of the values are calculated from the API specification is now briefly discussed.

The values for do and di are straightforward and taken directly from the API data. In the API bulletin the weight in air (denoted W) of a 50 ft joint is given as 8800 lb. From this the mass density ρ is calculated as follows:

32222 slugs/ft452.24)6667.175.1(*50*2.32

8800*4)(

4=

−=

−==

ππρ

io ddLgW

ALgW

where L is the joint length and g is the gravitational constant.

The API bulletin gives a value of 7660 lb for the weight in water of a 50 ft joint – this represents the weight of the joint full of seawater. This means the buoyancy force or uplift B experienced by the joint is (8800-7660) = 1140 lb. From this figure the effective buoyancy diameter db is calculated using the relation:

'8.16667.1*50*2.32*9876.1

1140*44)(4

2222 =+=+==>−=ππρ

πρ iw

bibw dLg

BdddLgB

where ρw is the mass density of seawater and remaining symbols are as previously.



Finally, the effective drag diameter dd reflects the API specification that the riser is oriented so that the choke and kill lines are broadside to current and waves. The value for dd of 2.4167 ft (29”) is the sum of the riser OD (21”) and the OD of the choke and kill lines (both 4”).

The static analysis uses the Type - Static option. One step only is required, so the analysis goes from 0 to 1 second with a 1 second time-step.

The dynamic analysis employs the Type - Dynamic option. The analysis begins at the end of the static analysis and continues for a further 64 seconds, which is five wave periods. Dynamic loads and vessel motions are ramped on over the first wave period. Options - Restart is used to specify that the dynamic analysis is restarted from the static run.

The data files provided with the software for this analysis include a run time settings file for the dynamic phase. This generates run time display of the angles at the LBJ and UBJ, to which is added a run time display of the wave elevation by default.

Results

Results from the static analysis of the drilling riser are presented in Table 5.2 below, and in Figs. 5.3 to 5.6 attached. Table 5.2 also shows results from the API bulletin. The Flexcom results compare favourably with the reported API values. Note that the location of the maximum bending stress is measured from the LBJ.

Fig. 5.3 plots the static distribution of rotation along the riser, while Fig. 5.4 shows the static distribution of effective tension, which is everywhere positive as required. Fig. 5.5 and 5.6 plot respectively the distribution of bending and von Mises stresses. The maximum von Mises stress is approximately 18.75 ksi, which is comfortably below the steel yield strength.



Results from the dynamic analysis of the riser are presented in Figs. 5.7 to 5.10, all of which plot response statistics calculated over the last two wave periods (that is, from 39.4 seconds to 65 seconds). Fig. 5.7 shows max/min envelopes of horizontal displacement while Fig. 5.8 shows corresponding envelopes of rotation. The maximum rotation at the LBJ is approximately 5o. Figs. 5.9 and 5.10 both present dynamic stress envelopes, of bending and von Mises stress respectively. The maximum von Mises stress throughout the dynamic run is just over 20 ksi, which is again satisfactory. Figs. 5.7 and 5.9 compare favourably with corresponding plots in the API bulletin.

Table 5.2. Results from Static Analysis of Drilling Riser (1500-B-2-S).

Solution Variable Units Flexcom API Values

Values Mean Range

Angle at UBJ (°) 0.37 0.36 0.06

Angle at LBJ (°) 3.12 3.12 0.08

Max. Bending Stress (ksi) 1.02 1.00 0.35

Location (ft) 127 121 20

Examples Files

The analysis input files for this example may be found in the 'Examples\Example 4' subdirectory of your Flexcom installation directory. The input files are as follows:

Example4-Static.fl3 Static analysis file

Example4-Dynamic.fl3 Dynamic analysis file

Example4-Dynamic.rts Run time settings file for dynamic analysis



Drill Ship.res RAO file

Example4-Static.ps3 Postprocessing file for static analysis

Example4-Dynamic.ps3 Postprocessing file for dynamic analysis

Reference

[1] American Petroleum Institute, "Comparison of Marine Drilling Riser Analyses", API Bulletin 2J, 2nd Edition, 1985.



MWL

Seabed

Support Vessel

1500 ft.

Lower Marine RiserPackage (LMRP)Lower Ball Joint (LBJ)

Wave, Currentand OffsetDirections

Rigid Riser

Fig. 5.1. Schematic of API Riser Configuration.




Node

161

X Y Z

30.1550.

0.0.

0.0.

61

60

Rigid Riser

X

Z

1

1Y

Element numbers are underlined

Seabed




Input Data


Component E

lb/ft2

do

ft

di

ft

ρ

slugs/ft3

dd

ft

db

ft Riser 4.32 x 109 1.75 1.6667 24.452 2.4167 1.8

E - Young’s Modulus

do - External Diameter

(Diameter of steel, not including choke/kill lines) di - Internal Diameter

ρ - Mass Density (Mass/Unit Volume) dd - Drag Diameter


Environmental Data

Water Depth: 1500ft

Water Density: 1.9876 slugs/ft3

Drag Coefficient: 0.7

Inertia Coefficient: 1.5

Internal Fluid:

Height: 1550ft

Density: 2.7888 slugs/ft3



Miscellaneous Data

Description Units Magnitude

Vessel Static Offset (ft) 45

Top Tension (kips) 600

Current Profile

Height Above

Seabed (ft)

Velocity

(ft/s)

30 0.6675

1500 3.3760


Amplitude

(ft)

Period

(s)

20.0 12.8



RAO Data


Vessel Reference Point –

Initial Position

(Corresponding to vertical riser)

(1500, 0, 0)

Heave RAO Phase (°)

Heave 0.0 0.0

Surge 0.6675 90.0

Sway 0.0 0.0

Yaw 0.0 0.0

Roll 0.0 0.0

Pitch 0.0 0.0



0 0.5 1 1.5 2 2.5 3 3.5Rotation (Degrees)

025

050

075

010

0012

5015

0017

50Di

stan

ce a

bove

LB

J (f

t)


Fig. 5.3. Static Rotations.

250 300 350 400 450 500 550 600 650Effective Tension (kips)

025

050

075

010

0012

5015

0017

50D

ista

nce

abov

e LB

J (f

t)


Fig. 5.4. Static Effective Tensions.



0 0.25 0.5 0.75 1 1.25Bending Stress (ksi)

025

050

075

010

0012

5015

0017

50Di

stan

ce a

bove

LB

J (f

t)

Element set 1; Bending stress

Fig. 5.5. Static Bending Stress.

10 11 12 13 14 15 16 17 18 19von Mises Stress (ksi)

025

050

075

010

0012

5015

0017

50D

ista

nce

abov

e LB

J (f

t)

Element set 1; von Mises stress

Fig. 5.6. Static von Mises Stresses.



-10 0 10 20 30 40 50 60Horizontal Motion (ft)

025

050

075

010

0012

5015

0017

50Di

stan

ce a

bove

LB

J (f

t)


Fig. 5.7. Horizontal Motion Envelopes.

-2 -1 0 1 2 3 4 5 6Rotation (Degrees)

025

050

075

010

0012

5015

0017

50D

ista

nce

abov

e LB

J (f

t)


Fig. 5.8. Rotation Envelopes.



-5 -4 -3 -2 -1 0 0.999997 2 3 4 5Bending Stress (ksi)

025

050

075

010

0012

5015

0017

50Di

stan

ce a

bove

LB

J (f

t)

Element set 1; Bending stress

Fig. 5.9. Bending Stress Envelopes.

10 12.5 15 17.5 20 22.5von Mises Stress (ksi)

025

050

075

010

0012

5015

0017

50D

ista

nce

abov

e LB

J (f

t)

Element set 1; von Mises stress

Fig. 5.10. von Mises Stresses.



Chapter 6: Example 5 – TLP Tether Tow-Out and Installation


Example 5 – TLP Tether Tow-Out and Installation


This example considers the tow-out and installation of a tension leg platform (TLP) tether. The tether is 298m in length and is installed in water depth of 355m. The tow-out of the tether at a velocity of 1.8m/s is simulated with a reverse uniform current. For the installation analysis of the tether, the boundary conditions at one end are removed and that end then descends towards the seabed. A schematic of the tether during tow-out is shown in Fig. 6.1.

Finite Element Discretisation Two separate finite element models are used for the analysis of the tether tow-out and installation. For the tow-out analysis the following are included in the model: the tether, tow and guide cables, the tether buoy, two support buoys, two support buoy cables and a clump mass. A schematic of the finite element model for the tether tow-out is given in Fig. 6.2. In total, 54 elements and 55 nodes are used in the model. These include four flex joint elements that attach the tow and guide cables and the support buoy cables to the tether. The flex joints are given a nominal rotational stiffness of 1 Nm/o, to prevent Flexcom reporting that the model is statically indeterminate. This stiffness has no effect on the solution.

For the installation analysis, the following are included in the finite element model: the tether, the tow cable, the tether buoy and the clump mass. In total, 38 elements and 39 nodes are used in this model. In both models, the clump mass is modelled as a point mass at Node 39.



Boundary Conditions

Tether Tow-Out

Initial Static Analysis Nodes 1 and 55 are fixed in all translational degrees of freedom (DOFs). All other nodes are free.

Tow-Out Analysis The boundary conditions are unchanged from the static analysis, except that i) a constant displacement of 6m in DOF 2 is also applied at Node 1, and ii) Nodes 43 and 47 (which are the top of the support buoys) are restrained in DOF 4. This is done only to prevent spurious (numerical) rotations of the buoys about their longitudinal axes. Because the excitation and response are 2D, these BCs have no effect on the solution, other than to provide numerical stability.

Tether Installation

Static Analysis All translational DOFs are fixed at Nodes 1 and 39.

Installation Analysis DOFs 1 and 2 at Node 39 are freed. However, DOF 3 remains restrained, and BCs are applied in DOFs 4 and 5. These are only to prevent spurious or numerical out of plane motions, and have no effect on the tether planar response.

Applied Loads

Tether Tow-Out

Initial Static Analysis Static loads due to gravity and buoyancy are applied.



Tow-Out Analysis A uniform reverse current of 1.8m/s is applied to the structure. This simulates a tether tow-out speed of 1.8m/s.

Tether Installation

Static Analysis Static loads due to gravity (including the clump mass) and buoyancy are applied.

Installation Analysis The tether is allowed to drop towards the seabed under its own apparent weight and the weight of the clump mass.

Miscellaneous

Both phases of the tow-out analysis use the quasi-static solution type, which is invoked by choosing Type – Quasi-static in the Solution Parameters window. As explained in the Reference Manual, a quasi-static analysis is a damped dynamic analysis in which the applied loads and displacements are constant after an initial ramping on period. The damping increasingly dissipates inertia effects and the final solution achieved is a static one. A quasi-static analysis is required in a small number of sensitive cases when a genuine static analysis cannot be readily performed. The system under consideration here constitutes one such sensitive case, due mainly to the presence of the large diameter surface piercing buoys.

A static analysis of this system would fail to converge in many cases if the initial position (the initial wetted length) of the buoys was not close to the actual final static condition. This is because successive analyses could have, say, firstly a large excess of buoyancy over gravity, then in a next iteration a large excess of gravity over buoyancy, then back to buoyancy over gravity, and so on, with the solution diverging rapidly from the actual final position. This does not happen in a quasi-static analysis because the inertia of the system prevents unrealistic fluctuations of the solution about the static configuration.



The tow-out initial static goes quasi-statically from 0 to 100 seconds, with buoyancy and gravity ramped on over the first 10 seconds, and a damping coefficient of 2 specified for both stiffness and mass damping. A maximum time-step value of 5 seconds is reached and maintained after approximately 50 seconds. In the actual tow-out analysis, the start and end times are respectively 100 and 300 seconds, and the current loading and offset are ramped on over the first 50 seconds.

For the initial static analysis of the tether installation, the Type - Static option is selected – since the surface-piercing cylinders are now absent, there are no numerical difficulties with convergence in this case. Therefore, the static loads are applied in a single step from 0 to 1 second. The installation analysis is restarted from the initial static analysis and the Type - Dynamic option is selected. This analysis runs for a simulation period of 400 seconds, by which time the tether reaches an equilibrium position vertically below the tow vessel.

Results

Results from the tow-out and installation analyses of the TLP tether are presented in Figs. 6.3 and 6.4. Fig. 6.3 shows snapshots of the configuration at initiation of tow-out and at steady state towing conditions. Snapshots of the tether at various times during the installation are shown in Fig. 6.4.

Examples Files

The Flexcom input files for these analyses are included in the ‘Examples\Example 5’ subdirectory of the Flexcom installation directory. They are as follows:

Tether Tow-Out

Example5–InitialStatic.fl3 Initial static tow-out analysis file

Example5–Quasi-static.fl3 Quasi-static tow-out analysis file

Example5-Quasi-static.ps3 Postprocessing file for tow-out analysis



Tether Installation

Example5– Static.fl3 Static analysis file for installation

Example5–Dynamic.fl3 Dynamic analysis file for installation

Example5–Dynamic.rts Run time settings file for dynamic analysis

Example5–Dynamic.ps3 Postprocessing file for dynamic analysis



MWL

Tow Cable Guide Cable

Guide Vessel Tow Vessel

Vertical Buoyancy Modules

TLP Tether

Clump Mass Tether Buoy

Fig. 6.1. Schematic of TLP Tether Configuration.



1

Articulation elements

Element numbers are underlined

Key Nodal CoordinatesNode X Y Z

1 8,9,40

39,44,48 43 47 55

358. 317. 317. 360. 360. 358.

400. 350.

50. 350.

50. 0.

0. 0. 0. 0. 0. 0.

1

43

42

40

89

8

39

9

47

46

44

43

3839

44

48

48

55

54

TLP Tether

Buoy B Buoy ATow Cable

Guide Cable

MWL

47

X

Y




Input Data


Component EIyy

Nm2

EIzz

Nm2

GJ

Nm2

EA

N

m

kg/m

p

kg.m

di

m

dd

m

db

m

Tether 5.64E9 5.64E9 4.48E9 33.8E9 1299.4 435.0 0.0 1.2 1.2

Tow/Guide Cables

6.0E3 6.0E3 6.0E3 1.6E9 15.62 0.1 0.0 0.05 0.05

Buoy Cables

5.64E9 5.64E9 4.48E9 33.8E9 15.62 0.1 0.0 0.05 0.05

Buoy A 7.0E9 7.0E9 2.1E10 33.8E9 1850.0 1.0E3 0.0 2.0 2.0

Buoy B 7.0E9 7.0E9 2.1E10 33.8E9 1200.0 1.0E3 0.0 2.0 2.0

Tether Buoy

5.64E9 5.64E9 2.1E10 33.8E9 2965.2 1.0E3 0.0 2.0 2.0

EIyy - Bending Stiffness about Local y Axis






dd - Drag Diameter




Environmental Data

Water Depth 355.0 m

Water Density 1025.0 kg/m3

Normal Drag Coefficient 0.7

Tangential Drag Coefficient 0.01

Inertia Coefficient 2.0

Water Depth: 1500.0 ft

Miscellaneous Data


Clump Mass (kg) 5096.84

Tow-out Speed (m/s) 1.8

Relative Displacement of Tow and Guide Vessels at Start of Tow-out

(m) 6.0



-550 -450 -350 -250 -150 -50 50Local-3 Axis (m)

010

020

030

040

050

060

0Lo

cal-1

Axi

s (m

)

Structure at 100sStructure at 400s

Fig. 6.3. Snapshots at Start and End of Tow-out Analysis.

-500 -400 -300 -200 -100 0Local-3 Axis (m)

-50

5015

025

035

045

0Lo

cal-1

Axi

s (m

)

1s50s

100s

150s200s250s

300s350s450s

Fig. 6.4. Snapshots of Tether during Installation.

Chapter 7: Example 6 – Analysis of a Jack-up Platform


Example 6 – Analysis of a Jack-up Platform


This example considers a Jack-up Platform subjected to static and dynamic loading, which includes wind, wave and current loads. A schematic of the configuration is shown in Fig. 7.1. The Jack-up is sited in a water depth of 110m. The overall height is 153m with the deck at a height of 135m above the seabed. In addition to other features this example demonstrates the use of the program in modelling 3D frame-type rigid structures, such as Jack-up platforms.


A schematic of the finite element discretisation used for the Jack-up model is shown in Fig. 7.2. In total, 72 elements and 57 nodes are used in the model. This includes six articulation elements that connect the deck of the Jack-up to the three support legs. In each of the legs 13 rigid beam elements are used, with each leg connected to the deck at two nodes as shown in Fig. 7.2. This model of the Jack-up allows the non-linear p-δ effect to be accounted for.

Boundary Conditions

The boundary conditions are the same for all three analyses in this example. The seabed nodes of the three legs (nodes 1, 15 and 29) are fixed in all the translational degrees of freedom (DOFs) and rotational DOF 4.

Applied Loads

Static Analysis

Gravity and buoyancy loads are applied to the Jack-up.



Current Analysis

In addition to the initial static loads, wind and current loads are applied to the structure. The current profile is listed in the ‘Input Data’ section. The wind forces are applied as point loads of 200 kN each, in the horizontal Y direction, at the top node of each of the four legs.

Dynamic Analysis

In addition to the above loads a regular wave seastate is applied to the Jack-up. Details of the wave profile are given in the ‘Input Data’ section.

Miscellaneous

For both the static and current analyses the Type-Static option is selected. Both analyses run in a single step, with the current analysis restarting from the static analysis. For the dynamic analysis the Type-Dynamic option is selected and the analysis restarts from the current analysis. This analysis is run for 48 seconds, which is four wave periods. The wave loads are ramped on over the first 12 seconds of the analysis, that is, the first wave period.

Results

Results from the dynamic analysis of the Jack-up are presented in Fig. 7.3 to 7.5. A snapshot of the Jack-up from a 3D viewpoint is shown in Fig. 7.3. A timetrace of the horizontal motion at the top of Leg 1 is given in Fig. 7.4. Presented in Fig. 7.5 are max./min. envelopes of the local-z bending moment distribution in Leg 1.



Examples Files


Example6-static.fl3 Static analysis file

Example6-current.fl3 Current analysis file


Example6-dynamic.ps3 Postprocessing file



MWL

Deck

Seabed

Fig. 7.1. Schematic of Jack-up Platform Configuration.



29

1

15

39,49

40,50

41,51

42

14

13,45

12,44

11,43

28

27,48

26,47

25,46

27

1

14

26

13

28

47

50

53

Seabed

Leg 3

Leg 1

Leg 2

Articulation elementsElement numbers are underlined


Node X Y Z

111,4312,4413,45

1415

25,4626,4727,48

2829

39,4940,5041,51

42

0.125.135.145.153.

0.125.135.145.153.

0.125.135.145.153.

0.0.0.0.0.0.0.0.0.0.

-57.2-57.2-57.2-57.2-57.2

0.0.0.0.0.

66.66.66.66.66.33.33.33.33.33.




Input Data


Component EIyy

(Nm2)

EIzz

(Nm2)

GJ

(Nm2)

EA

(N)

m

(kg/m)

p

(kg.m)

di

(m)

dd

(m)

db

(m)

LEGS 5.0E12 5.0E12 8.0E11 2.0E11 5.0E3 1.0E4 0.0 2.5 1.0

DECK 5.0E13 5.0E13 8.0E12 2.0E12 19.0E3 1.0E4 0.0 2.5 1.0

Where: EIyy - Bending Stiffness about Local y Axis






dd - Drag Diameter





Parameter: Value:





Miscellaneous Data


Wind Load (Total) MN 2.4

Current Profile

Height Above

Seabed (m)

Velocity

(m/s)

Direction

(º) 0.0 0.0 0.0

110.0 1.75 0.0




Amplitude

(m)

Period

(s)

Direction

(º)

12.5 12.0 0.0


-62.5 -37.5 -12.5 12.5 37.5 62.5 87.5 112.5 137.5Local-3 Axis (m)

-50

-25

025

5075

100

125

150

Loca

l-1 A

xis

(m)

Structure

Fig. 7.3. Snapshot of Jack-Up Platform Configuration.



0 10 20 30 40 50Time (s)

-0.5

-0.2

50

0.25

0.5

0.75

1H

oriz

onta

l-Y M

otio

n (m

)

Node no. 14; DOF 2

Fig. 7.4. Timetrace of Horizontal Motion at Top of Leg 1.

-600 -500 -400 -300 -200 -100 0 100 200Local-z Moment (kNm)

025

5075

100

125

150

175

Dis

tanc

e al

ong

Leg

1 (m

)


Fig. 7.5. Envelopes of Local-z Moment in Leg 1.



Documents

Examples Manual - Academic Edition