LifeFrequency Manual

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Table of Contents

LifeFrequency Users Manual Rev. 1 i Flexcom Version 7.7

Table of Contents

CHAPTER 1 - OVERVIEW ........................................................... 1

Introduction..........................................................................1

Manual Organisation ..............................................................1

Part A ................................................................................... 2

Part B ................................................................................... 2

Part C ................................................................................... 2

Operation .............................................................................3

Installation ...........................................................................4

Starting LifeFrequency............................................................4

Summary of Inputs ................................................................5

Top Menu Bar........................................................................7

File....................................................................................... 7

Run ...................................................................................... 7

Modules ................................................................................ 8

View..................................................................................... 9

Help ....................................................................................11

CHAPTER 2 - STAND-ALONE OPERATION .................................13

Introduction........................................................................13

Long Term Environmental Conditions......................................14

Wave Scatter Diagram ...........................................................14

Directionality ........................................................................16

Table of Contents

LifeFrequency Users Manual Rev. 1 ii Flexcom Version 7.7

Fatigue Data....................................................................... 16

LifeFrequency Analysis Procedure .......................................... 18

Two Special Cases ................................................................ 23

Jonswap Spectrum .............................................................. 24

A Note on Units................................................................... 25

Repeat Runs....................................................................... 26

References ......................................................................... 27

CHAPTER 3 - POSTPROCESSOR WITH STRESS SPECTRA

OPERATION.............................................................................29

Introduction ....................................................................... 29

Operation........................................................................... 30

Units ................................................................................. 31

CHAPTER 4 - POSTPROCESSOR WITH RAOS OPERATION.........33

Introduction ....................................................................... 33

Operation........................................................................... 33

Units ................................................................................. 35

CHAPTER 5 - REFERENCE.........................................................37

LifeFrequency – Reference.................................................... 39

Analysis Title........................................................................ 40

Name of Flexcom File ............................................................ 41

Units................................................................................... 43

PDF .................................................................................... 44

Table of Contents

LifeFrequency Users Manual Rev. 1 iii Flexcom Version 7.7

Hot Spot Sets – Define ...........................................................45

Properties – Stress ................................................................46

Fatigue Data – Properties .......................................................50

Log-Linear S-N Curve – Define ................................................53

Piecewise Log-Linear S-N Curve – Define ..................................55

Data Pairs for S-N Curve – Define ............................................57

Mode ...................................................................................58

Seastates .............................................................................59

Seastate Scatter Diagram – Selected Seastates .........................60

Seastate Scatter Diagram – One Seastate .................................66

Seastate Scatter Diagram – All Seastates..................................67

Spectrum .............................................................................68

Seastate Directions – Stand-alone Mode ...................................69

Seastate Directions – Postprocessor with Stress RAOs Mode ........72

Pre-run Analyses – Postprocessor with Stress Spectra Mode ........73

Pre-run Analyses with RAOs – Postprocessor with Stress RAOs Mode

..........................................................................................74

CHAPTER 6 - EXAMPLE DRILLING RISER FATIGUE ANALYSIS..77

Introduction........................................................................77

Environment .......................................................................77

Fatigue Data .......................................................................81

Results...............................................................................81

Example Files......................................................................85

Table of Contents

LifeFrequency Users Manual Rev. 1 iv Flexcom Version 7.7

CHAPTER 7 - EXAMPLE SCR FATIGUE ANALYSIS WITH STRESS

SPECTRA..................................................................................87

Introduction ....................................................................... 87

Model ................................................................................ 87

Environment....................................................................... 89

Fatigue Data....................................................................... 90

Results .............................................................................. 90

Example Files ..................................................................... 91

Input Data ......................................................................... 92

Riser Properties .................................................................... 92

Vessel ................................................................................. 93

Internal Fluid ....................................................................... 95

CHAPTER 8 - EXAMPLE SCR FATIGUE ANALYSIS WITH RAOS ..97

Introduction ....................................................................... 97

Environment....................................................................... 98

Fatigue Data....................................................................... 99

Results .............................................................................. 99

Example Files ....................................................................102

Chapter 1 - Overview

LifeFrequency Users Manual Rev. 1 1 Flexcom Version 7.7

CHAPTER 1 - OVERVIEW

Welcome to the Users Manual for LifeFrequency. LifeFrequency is an optional frequency

domain fatigue life prediction module to Flexcom. This chapter, ‘Overview’, provides an

introduction to LifeFrequency, and outlines the Users Manual layout. Specifically, ‘Overview’

is divided into the following sections:

− ‘Introduction’ describes in broad outline the operation of LifeFrequency.

− ‘Manual Organisation’ gives a summary of the chapters comprising this manual.

− ‘Operation’ outlines the different program modes of operation.

− ‘Installation’ is a guide to installing the software.

− ‘Starting LifeFrequency’ describes how to run the module and provides a basic

description of the LifeFrequency GUI

− ‘Summary of Inputs’ gives a brief overview of the program inputs.

− ‘Top Menu Bar’ describes the options in the top menu bar.

INTRODUCTION

LifeFrequency is an optional fatigue life prediction module to Flexcom. It incorporates the

frequency domain features of the Flexcom Analysis module. LifeFrequency is not just a

postprocessor to Flexcom. Instead, the program is built around Flexcom, and in the most

general case, a fatigue analysis with LifeFrequency includes one or more Flexcom random

sea analyses carried out under the control of LifeFrequency, without user intervention.

MANUAL ORGANISATION

This manual provides all of the information that you need to know about LifeFrequency

including user information, reference information, and information about the examples that

are provided with the module. The manual has three main parts as follows:



− Part A provides a comprehensive description of how to use the LifeFrequency

module.

− Part B provides comprehensive reference information about all user inputs to the

LifeFrequency graphical user interface (GUI).

− Part C describes the examples that are provided with the LifeFrequency module to

demonstrate the different modes of operation of LifeFrequency and the fatigue

analysis capabilities of the module.

Part A

Part A is comprised of four chapters as follows:

− Chapter 1 (this chapter), ‘Overview’, provides an introduction to LifeFrequency, and

outlines the Users Manual layout.

− Chapter 2, ‘Stand-alone Operation’ provides the theoretical background to the Stand-

alone mode of the program.

− Chapter 3, ‘Postprocessor with Stress Spectra Operation’ provides the theoretical

background to the Postprocessor with Stress Spectra mode of the program.

− Chapter 4, ‘Postprocessor with RAOs Operation’ provides the theoretical background

to the Postprocessor with RAOs mode of the program.

Part B

Part B is comprised of one chapter as follows:

− Chapter 5, ‘Reference’ provides a detailed reference for all of the windows and menus in

the LifeFrequency GUI.

Part C

Part C is comprised of three chapters as follows:



− Chapter 6, ‘Example Drilling Riser Fatigue Analysis’ illustrates the LifeFrequency

Stand-alone mode of operation in the fatigue analysis of a drilling riser.

− Chapter 7, ‘Example SCR Fatigue Analysis with Stress Spectra’ illustrates the

LifeFrequency Postprocessor with Stress Spectra mode of operation in the fatigue analysis

of an SCR.

− Chapter 8, ‘Example SCR Fatigue Analysis with RAOs’ illustrates the LifeFrequency

Postprocessor with RAOs mode of operation in the fatigue analysis of an SCR.

OPERATION

The LifeFrequency procedure for calculating the fatigue life at a point on a riser or tether is

based on generating a spectrum of combined bending and axial stress at that point, for each

combination of wave height, wave period and wave direction in the long term environmental

data for the location in question.

LifeFrequency has three modes of operation as follows, each mode differing in how these

stress spectra are produced:

− Stand-alone Mode

In the most general case, spectra are calculated by LifeFrequency based on the results

of one or more Flexcom random sea analysis, performed directly by LifeFrequency,

without user intervention. This mode of operation is termed the LifeFrequency Stand-

alone mode, because LifeFrequency performs all stages of the fatigue analysis directly.

− Postprocessor with Stress Spectra Mode

In the LifeFrequency Postprocessor with Stress Spectra mode, your fatigue analysis is

preceded by a series of Flexcom frequency domain random sea analysis runs that you

perform directly in Flexcom, to find the dynamic response for each combination of

wave period, wave height and wave direction in the scatter diagram. The input to

LifeFrequency is then a list of Flexcom output files, from which LifeFrequency

reads in turn the stress spectra required to complete the fatigue life estimation. In this

case, the LifeFrequency module can be considered a simple Flexcom postprocessor.



Chapter 3 describes the LifeFrequency Postprocessor with Stress Spectra mode in greater

detail.

− Postprocessor with RAOs Mode

This mode is similar to the Postprocessor with Stress Spectra mode, in that your fatigue

analysis is preceded by a range of Flexcom frequency domain random sea analyses.

The difference is that you run analyses for selected combinations of wave height,

period and direction only, and you postprocess these to generate RAOs of effective

tension and bending moment (or stress). These RAOs then become the

LifeFrequency inputs, and the program uses these to transform wave spectra in the

scatter diagram for which you did not do a dynamic analysis, into stress spectra. The

LifeFrequency Postprocessor with RAOs mode is described in detail in Chapter 4 of this

manual.

INSTALLATION

LifeFrequency is automatically installed with Flexcom. However the software is only

activated if you are a licensed LifeFrequency user; otherwise the LifeFrequency button on the

Flexcom Modules Sidebar will be inaccessible (“greyed out”). If you are not a LifeFrequency

user but are interested in finding out more about becoming one, contact MCS.

STARTING LIFEFREQUENCY

You run LifeFrequency by clicking on the LifeFrequency button on the Flexcom Modules

Sidebar. When you click on the LifeFrequency button the Working Area changes to that for

LifeFrequency, as shown below.



In addition to the above, there are a number of options on the top menu bar associated with

performing a LifeFrequency analysis. These top menu bar options are described later. The

next section summarises the LifeFrequency inputs in the above screen.

SUMMARY OF INPUTS

As you can see from the picture above, data input to LifeFrequency is divided into nine

sections; Run Details, Options, Hot Spot Sets, Fatigue Data, S-N Curves, Mode of Operation,

Environment and Postprocessor. The inputs in each section are now briefly summarised.

The Title dialog is used to associate a descriptive title with the LifeFrequency run, which will

subsequently appear on all graphical and tabular output. The Flexcom File dialog is used to

specify the name of the file containing the structure model data in the Stand-alone mode.



The Units drop-down list is used to specify the units employed in inputting the

LifeFrequency data. The PDF drop-down list is used to specify the probability density

function to be used in calculating fatigue life estimates from stress spectra.

The Hot Spots Sets – Define dialog is used to define the locations on the structure for which

fatigue life estimates are required. The Properties – Stress dialog is used to assign effective

structural properties to hot spot sets for use in calculating bending and axial stresses.

The Fatigue Data – Properties dialog is used to assign properties specific to fatigue life

calculations to each hot spot set. It allows you to specify the S-N curve, stress concentration

factor, whether the analysis is to be based on combined stress or bending stresses only, and

whether or not thickness effects are to be considered.

The S-N Curve dialogs are used to define S-N curves to be used in the fatigue analysis. These

may be log-linear, piecewise log-linear, or user defined.

The Mode drop-down list is used to choose between the three LifeFrequency modes of

operation. The operation of each mode is discussed in Chapters 2-4. Only some of the dialogs

in the Environment and Postprocessor sections will be available, depending on which mode you

select.

The Environment section relates to the Stand-alone and Postprocessor with Stress RAOs modes of

operation. The Seastates drop-down list is used to choose between formats for inputting the

seastate scatter diagram. The Seastate Scatter Diagram dialog is used to input the wave scatter

diagram, group the seastates into blocks, and nominate a reference seastate for each block.

The Seastate Directions dialog is used to specify long-term directionality data. The Spectrum drop-

down list is used to specify which wave spectrum type to use.

The Postprocessor section relates to the Postprocessor with Stress Spectra and Postprocessor with RAOs

modes of operation. For the former, you specify the names of Flexcom random sea analyses

and corresponding percentage annual occurrences. In the latter case, you specify the names of

Flexcom random sea analyses for every combination of reference seastate in the scatter

diagram and every direction with a non-zero percentage occurrence.



TOP MENU BAR

The picture below shows the LifeFrequency top menu bar and toolbar.

There are five options in the menu bar, namely File, Run, Modules, View and Help. Each of these

is now briefly discussed. The toolbar options are described with their corresponding

commands from the menu bar.

File

The menu you get when you invoke the File option is shown below. The first four File menu

items are for manipulating input files in the standard ways. The first three icons in the toolbar

correspond to the first three items of the menu respectively.

Run

The Run menu is used to actually run a LifeFrequency analysis. When you click on Run, the

drop-down menu shown below appears.

The only option on the Run menu, LifeFrequency, actually instructs LifeFrequency to perform

the fatigue analysis. The fourth icon on the toolbar performs the same task.

When you do run a LifeFrequency analysis, one check is performed which is specific to the

fatigue program. The section 'Repeat Runs' of Chapter 2 describes how it is possible to rerun a



stand-alone fatigue analysis, varying only fatigue specific data such as S-N curve data or SCFs.

In such a case it is not necessary for the program to rerun all of the associated Flexcom

frequency domain random sea analyses, since the results of these analyses are unaffected by

changes in the fatigue data. What actually happens is the following. When you click on Run in

the LifeFrequency top menu bar, the program checks for the existence of a file with the

current job name but with the extension sto. This is a LifeFrequency data storage file with

contents as described in Chapter 2. If this file exists, LifeFrequency prints the following

message:

If you click on Yes, LifeFrequency will proceed to the fatigue calculations proper using the

data in the storage file, without rerunning any Flexcom analyses. On the other hand if you

click on No, then LifeFrequency will proceed to do a full fatigue analysis with one or more

Flexcom random sea runs as usual. In this latter case the data in the storage file is

automatically updated during the LifeFrequency run.

Modules

The Modules menu bar option provides a list of all the modules in Flexcom, and allows you to

select one as you would from the Modules Sidebar. This is intended to aid in mouse-free GUI

navigation. When you click on Modules, the drop-down menu shown below appears. Clicking

on any of the options naturally launches the corresponding module.



View

The View menu bar option allows you to examine various files associated with a

LifeFrequency fatigue analysis run by opening them in the Viewer application. Viewer is

discussed in more detail in Chapter 4 of the Flexcom Reference Manual.

Table 5.1 below tabulates the various files produced in a LifeFrequency analysis.



Table 1.1. LifeFrequency Files.

File Name Description

jobname.lf3

jobname.sea

jobname.fat

jobname.ver

jobname.lif

jobname.t01.mpt

jobname.sto

GUI data file.

Analysis input file (1) – Fatigue seastate data.

Analysis input file (2) – Remaining data.

Verification file.

Output file.

Plot file of minimum fatigue life v distance along hot spot set (nominally a timetrace plot file).

RAO storage file (for repeat Stand-alone mode analyses – see Chapter 2 for more details)

Of these seven files, four can be examined via the Viewer application. The GUI data file is

naturally opened using LifeFrequency itself. The significance of the RAO storage file was

outlined earlier; this file is for internal program use only and is not intended to be accessed by

users. The significance of the other file, the plot file, is briefly discussed here for completeness.

Each LifeFrequency analysis generates a plot of the minimum fatigue life at each hot spot

plotted against distance along the hot spot set. Figure 1.1 shows an example of such a fatigue

life plot. The distance on the X or horizontal axis is measured from the first element of each

hot spot set. The Y or vertical axis actually displays the fatigue life (note the logarithmic scale).

If there are two or more the user-defined hot spot sets in the fatigue run, a curve is generated

for each, and LifeFrequency automatically superimposes these curves. You can view this plot

in the usual way with the Plotting module; fatigue life plots are arbitrarily assigned the same file

extension as timetrace plots.



0 250 500 750 1000 1250 1500 1750 2000Distance Along Hot Spot Set (m)

1010

010

0010

000

1000

00M

in. F

atig

ue L

ife (Y

ears

)

Fatigue Life - SCR

Fig. 1.1 LifeFrequency Fatigue Life Plot

Help

The final top menu bar option, Help, is used to either display on-line help (Help Topics) or

information about the LifeFrequency/Flexcom version number and licence details (About

Flexcom…). These are standard Windows facilities.

Chapter 2 - Stand-alone Operation


CHAPTER 2 - STAND-ALONE OPERATION

This chapter provides the background to the program Stand-alone mode of operation in the

following sections:

− ‘Introduction’ gives an overview of the program Stand-alone mode.

− ‘Long Term Environmental Conditions’ describes the input of the long-term

environmental conditions, in terms of seastates and directions.

− ‘Fatigue Data’ summarises the program options for specifying data specific to the fatigue

damage calculations.

− ‘Analysis Procedure’ discusses how this data is used in performing a LifeFrequency

analysis.

− ‘Jonswap Spectrum’ describes how LifeFrequency calculates parameters for the

Jonswap spectrum.

− ‘A Note on Units’ discusses how units for forces, stresses etc. are handled by the various

components of the LifeFrequency package.

− ‘Repeat Runs’ describes how analyses can in some cases be repeated with a much-

reduced computing time.

− ‘References’ presents a number of appropriate references.

INTRODUCTION

The operation of LifeFrequency is best described by first detailing the required program

inputs, and then describing how LifeFrequency uses these inputs to produce fatigue life

estimates.

The input data required for the fatigue analysis using LifeFrequency can be grouped under

three headings or categories as follows:

Category i): Structure finite element model and general environmental data (water

depth and density, mud density, and so on).



Category ii): Wave scatter diagram and long-term directionality data.

Category iii): Fatigue-specific data such as hot spot locations, stress concentration

factors and material S-N curves.

LifeFrequency reads the required data in Category (i) from a Flexcom input file. You input

and save this data via the Flexcom Analysis module, and then in the LifeFrequency GUI

you simply specify the Flexcom file name you used when saving the data. The data should

include all of the inputs you would normally specify for a Flexcom random sea analysis,

except that no wave data is required. The reason for this is explained later in this chapter.

LONG TERM ENVIRONMENTAL CONDITIONS

Wave Scatter Diagram

Category (ii) above relates to the long-term environmental conditions at the location in

question. The first element of this is the wave scatter diagram, which is input via a window in

the LifeFrequency GUI. A blank Seastate Scatter Diagram window is shown in Figure 2-1.

A detailed discussion of this window is provided in Chapter 4. However, it is briefly

discussed here as part of the description of the LifeFrequency theory. The window for

inputting the scatter diagram very much reflects how the actual wave scatter diagram is

usually presented. Each cell of the window represents a particular combination of Hs and Tz,

and you input into a cell the number of occurrences (typically the number of “three-hour

intervals”) of that particular combination during, say, a 10 or 20-year period. You can

alternatively specify the scatter diagram in terms of Hs and Tp, the wave spectrum peak

period.



Figure 2-1: Blank Seastate Scatter Diagram Window

In principle, a fatigue analysis should involve performing a Flexcom random sea analysis for

each seastate in the scatter diagram for each direction of wave approach, and then using the

results to calculate fatigue damage as described in the section ‘LifeFrequency Analysis

Procedure’ later in the chapter. You can certainly do this in LifeFrequency; however, this

might be expensive in computer time notwithstanding the speed of Flexcom. Alternatively,

when you are inputting the scatter diagram, as well as inputting individual numbers of

occurrences, you can also divide the scatter diagram into a small number of “blocks”, and

nominate a seastate (a particular combination of Hs and Tz) within each block as the

representative or “reference” seastate for that block. An example of a wave scatter diagram

input in this way is shown in Figure 2-2. Here the scatter diagram is divided into 12 blocks

(not all fully visible), each with a reference seastate shown shaded. The values input and the

blocking scheme are largely arbitrary.



Figure 2-2: Example of a Seastate Scatter Diagram Window

How LifeFrequency uses this data is described shortly. First the specification of

directionality data is summarised.

Directionality

Long-term directionality effects are accounted for in LifeFrequency by considering storm

directions from eight compass headings. For each direction, a percentage occurrence value is

input via a window of the LifeFrequency GUI. Obviously, the sum of all occurrences must

total 100%. You also have the option of specifying the name of an individual file containing

vessel RAOs for each direction, or all of the RAOs may be in a single RAO file.

FATIGUE DATA

Before describing how LifeFrequency uses all of this data to produce fatigue life estimates,

the input data in the last of the three categories of the ‘Introduction’ above, namely the

fatigue specific data, is now summarised. Firstly, you are required to identify the fatigue

analysis hot spots, these being simply the points on the structure for which fatigue life

estimates are required.

Hot spots are defined as belonging to hot spot sets. For each set you input i) a stress

concentration factor (SCF), ii) an S-N curve, and iii) (optionally) a threshold thickness. You

also specify the required stress type, whether bending, axial or combined bending and axial.



SCF specification is standard, and the specified SCF values multiply the stresses calculated by

Flexcom/LifeFrequency to account for various stress raisers. For S-N curve specification,

a range of options is provided to allow a wide degree of generality. A particular curve may be

defined by two parameters m and K such that the curve is given by NSm = K, where S

represents stress range and N number of cycles to failure. Such a curve plots as a straight line

on log-log scales. An endurance limit (a stress range below which no fatigue damage results

regardless of the number of cycles) may be optionally specified.

Alternatively, a series of m and K values may define the curve over particular regions,

representing a piecewise-linear log-log plot. In the most general case, a particular curve may

be specified as a series of (S, N) data pairs.

The specification of a threshold thickness allows you to take account of the fact that the

fatigue strength of some structural members can be dependent on material thickness, with

fatigue strength decreasing with increasing thickness. If you specify a threshold thickness for

a particular hot spot set, the stresses calculated by Flexcom/LifeFrequency are further

multiplied by a factor f given by:

41

⎟⎟⎠

⎞⎜⎜⎝

⎛=

btt

f (2.1)

Here bt is the threshold thickness you specify; and t is the greater of bt and the actual

thickness of the particular location under consideration (this ensures that f is always greater

than or equal to 1). Note that although bt is specified for a hot spot set, f is computed

individually for each location in the set, since the structure thickness may vary within a hot

spot set. The specification of bt is optional for each set; by default thickness effects are

omitted.

Finally, a particular hot spot can belong to a number of hot spot sets, each with a different

SCF and/or S-N curve and/or threshold thickness. In this way the effect of variations in

these parameters can be evaluated in a single LifeFrequency run.



LIFEFREQUENCY ANALYSIS PROCEDURE

The rest of this chapter describes how LifeFrequency uses the data described above to

produce fatigue life estimates. A schematic of the procedure is presented in Figure 2-3.

Figure 2-3: LifeFrequency Analysis Procedure

The procedure is as follows. For every combination of i) reference seastate and ii) wave

direction with non-zero % occurrence, the program combines these seastate parameters with

the Category (i) data in the file you specified, to produce a Flexcom input file for each

combination. LifeFrequency then, without user intervention, runs each of these Flexcom

analyses, and post-processes the results to obtain stress RAOs (transfer functions). The stress

RAOs for a particular reference seastate and wave direction are then used to produce stress

spectra for all of the remaining seastates within that block for that direction. In this way stress

spectra are produced for every combination of seastate and wave direction in the long-term

Control Module

Category (i) Data

Category (ii) Data

Flexcom Input Files Analysis

ModulePost- processing

Flexcom RAO Files

Storage file (.sto)

Output file (.lif)

LifeFrequency

Category (iii) Data

Verification file (.ver)



environmental data. Note that the assumption implicit in this procedure is that stress RAOs

are invariant with respect to seastate over short “distances” within the scatter diagram.

After the Flexcom analyses (including postprocessing) for each reference seastate/direction

combination have been completed, LifeFrequency proceeds to the fatigue life prediction

process proper. The fatigue life at a particular location is found by looping over all of the

seastates in the scatter diagram and all of the storm approach directions, and computing and

accumulating the fatigue damage due to each combination.

For each combination, the first step is to extract the required hot spot RAO or RAOs from

the Flexcom RAO files and to transform and/or combine these as required. The appropriate

RAO file will depend on what seastate is being analysed and what block this corresponds to

in the scatter diagram.

If you specify that combined stresses are to be considered at a particular location, then

LifeFrequency scans the Flexcom RAO output for axial force RAOs and RAOs of bending

about both local axes. The axial force RAOs are transformed to axial stress and the two

bending RAOs are transformed to bending stress. The three RAOs are then combined to

produce combined stress RAOs. The combining of the RAOs uses complex arithmetic to

include the effect of relative phasing between the stress components. Note that

LifeFrequency produces fatigue life estimates for eight points (denoted ‘stress points’)

around the section circumference as shown in Figure 2-4, and so bending stress RAOs are

factored as appropriate depending on the actual ‘stress point’ under consideration.



Figure 2-4: Hot Spot Stress Point Locations

Once LifeFrequency has read and evaluated the RAO data it requires, the next step in the

fatigue analysis is to use this data to produce a hot spot stress spectrum according to the

formula:

)(|)(|)( 2 fSfHfS ησ = (2.2)

where )(fSσ is the output stress spectrum, )(fH is the stress RAO or transfer function,

)(fSη is the particular seastate spectrum, f denotes frequency, and x denotes the

magnitude of the complex quantity x . Note that the seastate spectrum )(fSη may be either

Pierson-Moskowitz or Jonswap; you specify which when inputting the seastate scatter data.

The availability of this option requires that LifeFrequency incorporates an algorithm to

select values for the three parameters usually used to define a Jonswap spectrum (peak

frequency, γ and α ) for each seastate, since these are defined only in terms of Hs and Tz or

Tp. The form of this algorithm is detailed later.

The various quantities required to complete the fatigue analysis can now be evaluated from

the calculated hot spot stress spectrum, or more correctly from the moments of the stress

spectrum about the origin, which are defined as:



dffSfm nn )(

0σ∫

∞

= (2.3)

where mn denotes the nth spectral moment and the remaining symbols are as described

previously.

In order to complete the analysis using these moments, certain assumptions are made

regarding the distribution of stress peaks and ranges. The first assumption concerns the

probability distribution function (pdf) that can be used to determine the probability of

occurrence of various stress peaks. You can choose between either the Rayleigh distribution

or Dirlik’s rainflow range distribution. The Rayleigh distribution is completely defined by m0,

the zeroth moment or the area under the stress spectrum curve. This distribution is suitable

for stress spectra that are narrow banded. The Dirlik distribution is defined by m0, m1, m2,

and m4, the zeroth, first, second, and fourth moments of the stress spectrum. This

distribution is more appropriate when stress spectra are broad banded. Since either

distribution refers to stress peaks and in fatigue analysis stress ranges are of interest, the

further assumption must also be made that each peak magnitude is half the magnitude of the

corresponding stress range. The probability of occurrence of various stress ranges in the

response to a particular seastate can therefore be calculated by dividing the area under the

corresponding probability distribution curve into a finite number of areas.

The total number of all stress peaks (and hence stress ranges) in one year for a particular

seastate i, for a particular direction j, denoted Mij, can be calculated from m0, m2 and m4, the

zeroth, second and fourth moments of the stress response spectrum respectively, as follows:

)sin(

)direction ofoccurrence(%*)seastateofoccurrence(%*)sin(year1

σzT

jiijM = (2.4)

where Tzσ, the mean stress up-crossing period, is given by:

2

0

mm

Tz =σ (2.5)



The probability of occurrence of a particular stress range Sk in the response to seastate i and

direction j, denoted pij(Sk), is evaluated by integrating the area under the distribution curve

between appropriate ordinates, thus:

∫Δ+

Δ−

=SS

SSkij dxxpSp )()( (2.6)

where p(x) is the probability distribution, and SΔ is chosen on the basis of a suitable

subdivision of the area under the curve into a finite number of areas. The Rayleigh

distribution is given by:

)2/exp()( 02

0

mxmx

xp −= (2.7)

The Dirlik distribution is given by:

21

0

23

22

2Z-1

)(2)(

222

m

ZeDeR

ZDe

QD

xp

ZRZQ −− ++= (2.8)

where:

2

2

1 1)(2

ββ

+−

= mxD (2.9)

21

4

2

0

1⎟⎟⎠

⎞⎜⎜⎝

⎛==

mm

mm

TT

xm

cm (2.10)

21

40

22

⎟⎟⎠

⎞⎜⎜⎝

⎛==

mmm

TT

z

c

σ

β (2.11) 02 m

xZ = (2.12)

1

23 ))((25.1D

RDDQ

−−=

β (2.13)

RDD

D−

+−−=

1)1( 2

112

β (2.14)

213 1 DDD −−= (2.15) 211

21

1 DD

DxR m

+−−−−

=β

β (2.16)

4

2

mm

Tc = (2.17) 1

0

mm

Tm = (2.18)



The actual number of occurrences in one year of stress range Sk in response to seastate i,

direction j, denoted nij (Sk), or simply nijk, is given by:

ijkijijk MSpn )(= (2.19)

The damage due to stress range k in seastate i, direction j, as defined by the Palmgren-Miner

Rule, is found by dividing the actual number of occurrences of stress range Sk, that is nijk, by

the number of cycles of this stress range required to cause failure. This latter quantity is

denoted N(Sk) or Nk, and is found from the appropriate S-N curve. Denoting the damage

due to stress range k in seastate i, direction j, as dijk we write:

k

ijkijk N

nd = (2.20)

and the accumulated damage in the response to seastate i due to all stress ranges and

directions, denoted di, is given by:

∑∑∑∑ ==j k k

ijk

j kijki N

ndd (2.21)

The accumulated damage in one year due to all seastates, which is denoted d1, is given by:

∑=i

idd1 (2.22)

According to the Palmgren-Miner Rule the fatigue life at a particular hot spot is 1/d1 years.

This is the procedure used to predict fatigue life in LifeFrequency.

Two Special Cases

There are two special cases of the above general procedure for dividing the scatter diagram

into blocks and nominating a reference seastate within each block. Flexcom allows you to

choose these cases with a simple keyclick. The first is where you want to have only a single

block (encompassing the full scatter diagram) with a single reference seastate. In this case,

LifeFrequency does one random sea analysis only for each wave direction with non-zero %



occurrence. The RAOs from these analyses are used for all of the seastates in the scatter

diagram, but otherwise the fatigue analysis proceeds exactly as per Eqs. (2.2) to (2.22).

The second special case is slightly different. In this case you want Flexcom to do a random

sea analysis for every seastate in the scatter diagram, for every wave direction with non-zero

% occurrence. This is equivalent to making every cell of the scatter diagram into both a

seastate block and the reference seastate for that block.

The fatigue life calculations are slightly different in this case to the general procedure outlined

above – but only slightly. The result of doing a Flexcom random sea analysis for every

seastate for every wave direction is that you have immediately the axial force and bending

moment spectra that are required to complete the fatigue analysis. There is no requirement in

this case to postprocess the random sea results to produce response RAOs. So in effect the

fatigue calculations begin at Eq. (2.3), the calculation of the moments of the combined stress

spectrum. Otherwise the procedure is exactly the same as in the general case.

It is important to be clear that this second special case is not LifeFrequency running in the

Postprocessor with Stress Spectra mode described in Chapter 3, although the effect is naturally

very similar. In the LifeFrequency postprocessor mode you have to run off all of the

Flexcom random sea analyses yourself before running LifeFrequency. In this second

special case of the Stand-alone mode, LifeFrequency automatically performs all of the

Flexcom runs before then proceeding directly to the fatigue life calculations.

JONSWAP SPECTRUM

The Jonswap spectrum is defined by three parameters, namely fp (peak frequency), γ

(peakedness parameter) and α (Phillips constant). When you describe a Jonswap spectrum in

terms of Hs and Tz or Hs and Tp, then LifeFrequency uses special algorithms to select

appropriate values for fp, γ and α . These are now summarised.

For the case of a scatter diagram defined as Hs/Tz combinations, the method adopted here is

one due to Isherwood [1] who publishes in his paper of 1987 a revised Jonswap spectrum

parameterisation based on empirical data published by Huomb and Overvik [2]. This

procedure will not be described in detail here; the interested reader is referred to the



publications referenced, or to Flexcom Technical Note 7, ‘Alternative Jonswap Spectrum

Formulations’.

For the case of a scatter diagram defined as Hs/Tp combinations, LifeFrequency first

categorises each seastate based on the value of the parameter (Tp /√ Hs). Values for γ and

α are then calculated according to Table 2.1 below; fp is simply 1/Tp.

Table 2-1: Calculation of Jonswap Parameters

Parameter Regime

Windsea Regime

(Tp /√ Hs) < 3.6

Jonswap Range

3.6 < (Tp /√ Hs) < 5

Swell Regime

(Tp /√ Hs) > 5

α 2.73 Hs2 / Tp

4 0.036 – 0.0056(Tp /√ Hs) 5.07 Hs2 / Tp

4

γ 5 exp{5.75 – 1.15(Tp /√ Hs)} 1

A NOTE ON UNITS

LifeFrequency is an integrated package that incorporates the following modules:

− The main Flexcom Analysis module

− The Frequency Domain Postprocessor module

− LifeFrequency itself, the frequency domain fatigue life prediction module

To ensure compatibility between these different modules, LifeFrequency must embody

some assumption concerning units. In LifeFrequency, you have the two choices concerning

units, as follows:

1. Input the data in one of two standard combinations of units and allow the program to

keep track of inputs to ensure correct subsequent usage.

2. Use a consistent set of units that is not one of the two standard combinations,

without any assistance from the program in ensuring correct usage.



The following are the two standard systems of units that you can use to prepare the various

LifeFrequency data files:

− SI units

Mass - kg; Length - m; Time - s

Force - N; Moment - Nm

Stress - N/mm2 (MPa) (S-N curve specification)

Value of g (gravitational constant) - 9.81m/s2

− Imperial units

Mass - slugs; Length - ft; Time - s

Force - lb (lbf); Moment - ft lb

Stress - ksi (kips/in2) (S-N curve specification)

Value of g (gravitational constant) - 32.2 ft/s2

If you specify to LifeFrequency that you are using one of these standard units sets, you do

not need to nominate which one. The program determines which set of units is being used

from the value you specify for g in inputting the Category (i) data in the Flexcom Analysis

module. This will obviously be equal to either of the above values (to within 5%), otherwise

the program will terminate with error.

REPEAT RUNS

Repeat analyses, where the structural and seastate input data remains the same, can in many

cases be carried out by LifeFrequency without the necessity of continuously performing all

of the Flexcom analyses. This is achieved through the use of a storage file generated in an

initial fatigue run. This storage file contains all the structural data and all of the RAO files

generated in postprocessing the individual Flexcom analyses. In the repeat analysis, the

required files are extracted from the storage file by LifeFrequency, and the analysis then



proceeds as before. This allows you to quickly examine the effect of varying fatigue specific

data, such as SCF or S-N curve.

Note though that only RAOs are preserved in the storage file. If your fatigue analysis

approach is based on performing Flexcom random sea analyses for all seastates in the scatter

diagram (the so-called second special case above), the results of the individual Flexcom runs

are not stored for subsequent reuse (the storage file would be enormous). In fact these files

are deleted at the end of the LifeFrequency run. So if you want to repeat a fatigue analysis

of this type, LifeFrequency must rerun all of the individual Flexcom analyses.

REFERENCES

1. Isherwood, R.M., “Technical Note: A Revised Parameterisation of the Jonswap

Spectrum”, Applied Ocean Research, Vol. 9, No. 1, 1987, pp. 47-50.

2. Houmb, O.G. and Overvik, T., “Parameterisation of Wave Spectra and Long Term Joint

Distribution of Wave Height and Period”, Proceedings of Conference on Behaviour

of Offshore Structures (BOSS), Trondheim, 1976, Vol. 1.

Chapter 3 - Postprocessor with Stress Spectra Operation


CHAPTER 3 - POSTPROCESSOR WITH STRESS

SPECTRA OPERATION

This chapter provides the background to the program Postprocessor with Stress Spectra mode of

operation in the following sections:

− ‘Introduction’ gives an overview of the program Postprocessor with Stress Spectra mode.

− ‘Operation’ details the LifeFrequency procedure in this mode.

− ‘Units’ discusses how units for forces, stresses etc. are handled in this mode.

INTRODUCTION

You run LifeFrequency in Postprocessor with Stress Spectra mode when you have yourself

performed Flexcom frequency domain random sea analyses for each combination of wave

height, wave period, and wave direction in the fatigue load case. The input to LifeFrequency

in this case is a list of Flexcom output file names, together with a % occurrence value for the

combination of conditions that each analysis considered. LifeFrequency in this case

operates as a simple postprocessor to Flexcom. This mode of operation is in contrast to the

Stand-alone mode described in Chapter 2, where LifeFrequency undertakes all stages of the

fatigue analysis directly.

A situation where you might need to run LifeFrequency as a Flexcom postprocessor is

where you want to vary environmental conditions other than just wave height, wave period

or wave direction. For example, you might want to specify different offsets for, say, near, far

and cross cases – LifeFrequency does not allow you to vary offset in this way. On the other

hand, you might want to nominate different drift conditions for different seastates. If you do,

you must run the individual Flexcom random sea analyses yourself before running

LifeFrequency in Postprocessor with Stress Spectra mode.



OPERATION

The actual LifeFrequency fatigue calculations in this mode are only slightly different from

the Stand-alone mode calculations of Eqs. (2.2) to (2.21) of the previous chapter. Obviously

the result of doing a Flexcom random sea analysis for every seastate for every wave direction

is that you have immediately the axial force and bending moment spectra that are required

for the fatigue analysis. So the fatigue calculations begin at Eq. (2.3), the calculation of the

moments of the combined stress spectrum. Otherwise the procedure is exactly the same

from this point. In this regard, this postprocessor mode is very similar to the second special

case of the stand-alone mode discussed previously. This special case is where LifeFrequency

does a Flexcom analysis for every combination of wave parameters. The similarities between

the two situations are obvious.

Because you (rather than LifeFrequency) run the individual Flexcom analyses, and because

LifeFrequency is dealing directly with the stress spectra produced by these runs, there is no

need for the fatigue program to know the actual combinations of environmental conditions

corresponding to each run. The only environmental data required is the % annual occurrence

of this combination. So the dialog for inputting the LifeFrequency Postprocessor with Stress

Spectra mode data is as shown below.

Figure 3-1: Pre-run Analyses Dialog

Further details about this dialog are provided in Chapter 5. The percentage value you input

here is used in a slightly amended form of Eq. (2.4), where it replaces the product “(%

occurrence of seastate i) * (% occurrence of direction j)”. The amended form of the equation is:



s)(inTn)combinatiothisofoccurrence(%*s)(inyear1

zσ

=ijM (3.1)

Other than this, the fatigue calculations are exactly as described in Chapter 2.

UNITS

Chapter 2 describes how you have the option of using one of two standard systems of units

(SI or Imperial) in setting up a LifeFrequency analysis in the Stand-alone mode, and how, if

you invoke this option, the program automatically determines which system you are using

from your value for the gravitational constant g. This option is also available for the

Postprocessor with Stress Spectra mode. What happens if you invoke this facility (using Options –

Units:), is that LifeFrequency reads the value for g from the postprocessing output file

produced by the first Flexcom analysis listed in the Pre-run Analyses dialog shown above in

Figure 3-1. The assumption is that you used the same value of g in all your analyses; to do

otherwise would be unusual.

What this mainly affects in the Postprocessor with Stress Spectra mode input data is the

specification of S-N curves and SCFs. S-N curve data is usually input in units consistent with

stresses in MPa (SI units) or ksi (Imperial units). However, the axial forces and bending

moments in your Flexcom output files are typically in N and Nm (SI units) or lb and ft.lb

(Imperial units). In early versions of LifeFrequency, this meant that you typically used your

SCFs to transform stresses to units consistent with your S-N curve(s). So for example, if you

were using SI units and wanted to specify a SCF of 1.2 and stress ranges in MPa in your S-N

curve, you specified an SCF of 1.2*10-6 to ensure compatibility. Likewise for Imperial units, if

you wanted to use ksi in defining your S-N data, the SCF you specified was 1.2*6.9444*10-6

or 8.3333*10-6.

Now you can specify Automatic units, an SCF of 1.2, and your S-N curve in MPa or ksi, and

let LifeFrequency take care of ensuring consistency of units thereafter.

Chapter 4 - Postprocessor with RAOs Operation


CHAPTER 4 - POSTPROCESSOR WITH RAOS

OPERATION

This chapter provides the background to the program Postprocessor with RAOs mode of

operation in the following sections:

− ‘Introduction’ gives an overview of the program Postprocessor with RAOs mode.

− ‘Operation’ details the LifeFrequency procedure in this mode.

− ‘Units’ discusses how units for forces, stresses etc. are handled in this mode.

INTRODUCTION

The LifeFrequency Postprocessor with RAOs mode of operation combines elements from the

other two modes described in the last two chapters. It is similar to the Stand-alone mode in

that you input the wave scatter diagram and directionality data in full, and you divide the

scatter diagram into blocks and nominate a reference seastate in each block in the same way.

What is different from the Stand-alone mode is that you must run the Flexcom frequency

domain random sea analyses yourself, before running LifeFrequency, for each combination

of reference seastate and direction with non-zero % occurrence. In this regard the Postprocessor

with RAOs mode resembles the Postprocessor with Stress Spectra mode. Even here though there is

another difference. In addition to running the Flexcom analyses, you must also postprocess

them to generate RAOs of axial force and bending moment at the locations of interest (‘hot

spots’), since LifeFrequency requires these to complete the fatigue calculations as per the

Stand-alone mode.

OPERATION

The actual LifeFrequency fatigue calculations in this mode are identical to the Stand-alone

mode calculations of Eqs. (2.2) to (2.22) of Chapter 2.

The actual data inputs you specify are also very similar to the Stand-alone mode. You specify

the wave scatter diagram and the directionality data using exactly the same dialogs as for the



Stand-alone mode. There is however one additional category of data required, and that consists

of the names of the Flexcom analyses you ran for the scatter diagram reference seastates.

You input this data using the Pre-run Analyses with RAOs dialog, the format of which is shown

below.

Figure 4-1: Pre-run Analyses with RAOs Dialog

Further details on this window are provided in Chapter 5, however the important points to

note are as follows. You use the first two columns to identify a combination of Hs and Tz or

Tp, which must correspond to a reference seastate in your wave scatter diagram; the third

column identifies a direction, which must correspond to one of the directions with non-zero

% occurrence you specified using Seastate Directions. The last column is then used to specify

the name of the Flexcom analysis you ran for this combination of seastate and direction.

Note that you must fill in a row in this dialog for every reference seastate for every direction

with non-zero % occurrence. So, for example, if you have five reference seastates and four

directions, you must have 20 rows in your Pre-run Analyses with RAOs specification. When you

come to actually run your LifeFrequency analysis, the GUI does check this for you, and if

there is a combination in the environmental data without a Flexcom file name here, the

program prints an error message to that effect and the fatigue analysis does not run. Instead

you remain in the GUI so you can correct the error.

You will recall from the previous chapter that you also use a Pre-run Analyses dialog when you

run LifeFrequency in the Postprocessor with Stress Spectra mode. However, the format of the

dialog is different depending on which mode you have nominated, as you can confirm by

comparing Figure 4-1 with Figure 3-1.



UNITS

Chapter 2 describes how you have the option of using one of two standard systems of units

(SI or Imperial) in setting up a LifeFrequency analysis in the Stand-alone mode, and how if

you invoke this option the program automatically determines which system you are using

from your value for the gravitational constant g. This option is available for the Postprocessor

with RAOs mode as well. What happens if you invoke this option (using Options – Units:) is

that LifeFrequency reads the value for g from the data produced by the first Flexcom

analysis in your list in the Pre-run Analyses with RAOs dialog shown above in Figure 4-1. The

assumption is that you used the same value of g in all your analyses; to do otherwise would

be unusual.

What this mainly affects in the Postprocessor with RAOs mode is the postprocessing of your

Flexcom analyses. S-N curve data is usually input in units consistent with stresses in MPa (SI

units) or ksi (Imperial units). However, the axial force and bending moment RAOs in your

Flexcom RAO files are typically in N/m and Nm/m (SI units) or lb/ft and ft.lb/ft (Imperial

units). One option you could use would be to use a scale factor in your Flexcom

postprocessing to generate RAOs units consistent with your S-N curve(s). So, for example, if

you were using SI units and wanted to specify stress ranges in MPa in your S-N curve, you

could specify a postprocessing scale factor of 1*10-6 for both axial force and bending

moment RAOs. This would give RAOs in MN/m and MNm/m in your RAO file, leading to

stresses in MPa in LifeFrequency. For Imperial units, a similar procedure could apply.

However, this is not necessary. It is easier to specify a scale factor of 1 everywhere when

postprocessing; then nominate Automatic units in LifeFrequency, and let LifeFrequency

take care of ensuring consistency of units thereafter.

Chapter 5 - Reference


CHAPTER 5 - REFERENCE

This chapter provides a detailed reference for all of the data inputs required for

LifeFrequency. It contains only a single section, ‘LifeFrequency - Reference’.

LifeFrequency – Reference



Analysis Title

Location: LifeFrequency

Purpose: To specify a title for a LifeFrequency run.

Window:

Data Inputs:

Input: Description

Title: A title of up to 80 alphanumeric characters. This will

subsequently appear on all LifeFrequency output.



Name of Flexcom File


Purpose: To specify the name of the file containing the structure model data.

Window:

Data Inputs:

Input: Description

Flexcom File: The name of the file in which you input and saved the

LifeFrequency Category (i) input data, that is, the structure finite

element model and the general environmental data. See Notes (a)-

(e) below.

Notes:

(a) This dialog is available only when you are running LifeFrequency in Stand-alone mode.

(b) The data in this file is input via the Flexcom Analysis module - the file required by

LifeFrequency is the GUI input file (file type fl3). It should include all of the data you

would normally specify for a Flexcom dynamic analysis, with two exceptions as detailed

below.

(c) It is not necessary to specify wave data in this file, because wave data will be inserted

into the Flexcom input file for each reference seastate dynamic analysis by the

LifeFrequency control module, as described in Chapter 2. However the file can contain

wave data, and no error will result. One reason why you might include wave data is in

order to specify selected frequencies for the Flexcom wave spectrum discretisation. If



you do input random sea data with selected frequencies, the actual spectrum parameters

you specify (for example Hs and Tz for a Pierson-Moskowitz spectrum) will be ignored,

but the selected frequencies will be inserted into all the reference seastate input files by

the control module.

(d) The Flexcom file may contain data in the Vessel – RAO File dialog, but this will be

ignored by LifeFrequency. The name or names of files containing RAOs for individual

or all wave directions are required inputs in the LifeFrequency Seastate Directions dialog.

(e) The Flexcom GUI file type fl3 is not required when inputting the Flexcom file name.



Units


Purpose: To specify the units employed in inputting the LifeFrequency data.

Window:

Data Inputs: None

Notes:

(a) Chapters 2-4 describe how you can use either a pre-defined set of units or a user-defined

consistent set when inputting LifeFrequency data. You use this drop-down menu to tell

LifeFrequency the set you are using. The default is Automatic.

(b) Pre-defined units can be either SI or Imperial, as described in Chapter 2. You do not

need to specify which; LifeFrequency automatically determines this from the value you

use for g, the gravitational constant. This explains the significance of the Automatic

button.



PDF


Purpose: To specify the probability density function to be used in calculating fatigue

life estimates from stress spectra.

Window:

Data Inputs: None

Notes:

(a) This drop-down list allows the selection of the probability density function (pdf) for use

in the fatigue life calculations. Selecting Rayleigh (the default) selects the standard

Rayleigh pdf, while selecting Dirlik selects the rainflow range pdf proposed by Dirlik.

The Dirlik pdf is more appropriate when stress spectra are broad banded; the Rayleigh

pdf is narrow banded. Further details can be found in the section ‘LifeFrequency

Analysis Procedure’ in Chapter 2.



Hot Spot Sets – Define


Purpose: To define the fatigue analysis hot spots, that is the locations on the

structure for which fatigue life estimates are required.

Window:

Data Inputs:

Input: Description

Set Name: A unique set label or name.

Element(s): The numbers of the elements comprising the set. These are input

in the standard format used in the Flexcom Analysis module.

Local Node: The location on the elements of the set for which fatigue life

estimates are to be calculated. This can be one of four locations,

namely the element first or start node, the element midpoint, the

element second or last node, or all three nodes. You choose

between locations using the drop-down list shown below. The

default location is the First node of the elements of the set

Notes:

(a) Particular locations may belong to different hot spot sets. A fatigue life estimate will be

calculated for each occurrence of a particular location.



Properties – Stress


Purpose: To assign effective structural properties to hot spot sets for use in

calculating bending and axial stresses.

Window:

Data Inputs:

Input: Description

Set Name: The hot spot set to which the properties are to be assigned. This

defaults to all elements.

Do: The effective outer diameter for the elements of the set. The

specification of data in this column is optional, as indeed it is for all

columns. If you do not specify a value for Do, how

LifeFrequency chooses a default depends on whether you used

the Flexible Format or the Rigid Format in inputting geometric data in

Flexcom. If you used the flexible riser format, then the default is

the drag diameter for the elements of the set. If you used the rigid

riser format, then Do here defaults to Do in the Flexcom data.



Di: The effective internal diameter for the elements of the set. Again

this entry is optional. The default is the internal diameter specified

in your Flexcom data.

Recalculate: You use this drop-down list to indicate to LifeFrequency how

default values for A, Iyy and Izz are to be chosen if any of the

subsequent three columns are left blank.

The default value of Yes means that LifeFrequency recalculates

the parameter in question using the values you specified for Do

and/or Di. The alternative of No means LifeFrequency is to use

the same value as Flexcom did for the parameter in question,

regardless of whether you have already specified effective Do

and/or Di values for this set. See Notes (b)-(g) below.

A: The effective cross-sectional area for the elements of the set. This

entry is optional. If omitted, then how LifeFrequency chooses a

default is governed by your input in Column 4, Recalculate. See Note

(b) below.

Iyy: The second moment of area about the local y-axis for the elements

of the set. This entry is optional. If omitted, then how

LifeFrequency chooses a default is governed by your input in

Column 4, Recalculate. See Note (b) below.

Izz: The second moment of area about the local z-axis for the elements

of the set. This entry is optional. If omitted, then how

LifeFrequency chooses a default is governed by your input in

Column 4, Recalculate. See Note (b) below.

Notes:

(a) The purpose of this menu is to input values to be used in calculating stresses, both

bending and axial, during a LifeFrequency analysis.



(b) For the default of Yes in the Recalculate drop-down list, default values for A, Iyy and Izz

are calculated using the following:

( )4

22io DD

A−

=π

( )64

44io

yyDD

I−

=π

yyzz II =

Here Do and Di are the inputs described above, default or otherwise

(c) The main Analysis module has a menu for specifying stress properties which is similar to

this one, except for the Recalculate column (the rationale for this option is explained in

Note (h) below). The main Analysis module doesn’t actually use the data if you specify it

there, but it is echoed to analysis output files where it can be accessed by the Frequency

Domain Postprocessing module and by LifeFrequency. What this means depends on

whether you are running LifeFrequency in Stand-alone mode or in either of the

Postprocessor modes.

(d) If you are running in Stand-alone mode, and if you specify stress properties in inputting

the Flexcom data in the file you specify in the LifeFrequency Name of Flexcom File

dialog, then you do not need to specify these properties again in LifeFrequency; they

automatically carry through.

(e) If you are running in either Postprocessor mode, then LifeFrequency reads stress

properties from the output files produced by the first Flexcom analysis in your Pre-run

Analyses list. So if you specify stress properties in the Flexcom data for that analysis,

once again you do not need to repeat them here.

(f) The Properties – Stress dialog in the main Analysis module operates in exactly the same way

with regard to default values of A, Iyy and Izz as this window does, when Recalculate is

set to Yes here.



(g) The rationale for the two Recalculate options is as follows. This Properties – Stress facility

was introduced in a more recent version of the software. Prior to that, you only had an

option to specify an effective external diameter Do in a Diameter column on the Fatigue

Data – Properties dialog. If you did invoke the option to change Do, then LifeFrequency

did not recalculate A, Iyy and Izz; so you had in fact no facility to vary these values.

The No option on the Recalculate drop-down list is provided to allow users of a previous

version of LifeFrequency to repeat exactly the fatigue analyses run with that version.

For example, to repeat exactly a LifeFrequency Version 4.1 fatigue analysis in which

you specified a Do value for a hot spot set, you invoke this window, specify Do, and set

Recalculate to No. The hot spot stress properties should then be identical to previously.



Fatigue Data – Properties


Purpose: To assign properties specific to fatigue life calculations to each hot spot

set.

Window:

Data Inputs:

Input: Description

Set Name: The hot spot set to which properties are to be assigned. This

defaults to a set named All which comprises all elements of the

structural discretisation.

S-N Curve: The name or label of the S-N curve to be used for this set. You

assign a unique name to each S-N curve when inputting S-N curve

data using the facilities to be described later in the chapter.

SCF: The stress concentration factor (SCF) to be used in fatigue

calculations for this set.

Stress: The stress type to be used in the fatigue calculations for this set.

You can choose between bending, axial or combined bending and

axial using the drop-down list shown below. The default stress type

is bending only.



Tb: The threshold thickness for the inclusion of thickness effects. See

Notes (a), (b) and (c) below.

Output: An option to nominate how many fatigue life estimates are to

included in the LifeFrequency output file per hot spot.

LifeFrequency calculates fatigue life estimates at eight points

around the outer circumference (these points are known as “stress

points”). The drop down menu allows you to choose how many of

these are echoed to the program output file.

The default is Minimum, which means one value only, the minimum

value, is output. The alternative is All, which means all eight values

are output.

Notes:

(a) The specification of a threshold thickness allows you to take account of the fact that the

fatigue strength of some structural members may be dependent on material thickness. If

you specify Tb for a particular hot spot set, the stresses calculated by

Flexcom/LifeFrequency are multiplied by a factor f given by

41

⎟⎟⎠

⎞⎜⎜⎝

⎛=

bTT

f

(b) Here T is the greater of Tb and the structure thickness at the location under

consideration. Effectively, f functions as a further SCF. Note that f is always greater

than or equal to 1, and is calculated individually for each hot spot of a set, since T can

vary between hot spots in the same set.

(c) The specification of Tb is optional. By default, thickness effects are ignored unless you

explicitly specify a threshold thickness.

(d) If you are using one of the two standard systems of units as discussed in the section ‘A

Note on Units’ in Chapter 2, or in either of the sections headed ‘Units’ in Chapters 3

and 4, then there are specific units for inputting Tb. If you are employing SI units, then



Tb is input in mm. If you are using Imperial units, the Tb is input in inches. If on the

other hand you are using a consistent , “User Defined” set of units then you must input

Tb in the same unit of length you used, for example, in defining nodal coordinates in the

Flexcom input data.



Log-Linear S-N Curve – Define


Purpose: To specify parameters for S-N curves which plot as linear on log-log axes.

Window:

Data Inputs:

Input: Description

S-N Curve: A unique name or label for the S-N curve.

m: The first parameter defining the S-N curve. See Note (a) below.

K: The second parameter defining the S-N curve. See Note (a) below.

Endurance Limit: A stress value below which no fatigue damage occurs, regardless of

the number of cycles.

Notes:

(a) S-N curves are generally defined in the form KNS m = where S denotes stress range,

N the number of cycles to failure at this range, and m and K are constants. Taking

logarithms of both sides and rearranging gives:

Klogm1

Nlogm1

Slog +−=



which is the equation of a straight line when log S is plotted against log N. In this case

m is the inverse slope and K is a function of the line intercept. These are the parameters

input above.



Piecewise Log-Linear S-N Curve – Define


Purpose: To specify parameters for S-N curves which plot as piecewise linear

segments on log-log axes.

Window:

Data Inputs:

Input: Description


m: The first parameter defining the S-N curve segment. See Note (a)

below.

K: The second parameter defining the S-N curve segment. See Note

(a) below.

N1: The number of cycles value defining the lower end of the line

segment where these m and K values apply.

N2: The number of cycles value defining the upper end of the line

segment where these m and K values apply.



Notes:

(a) This window is used to input S-N curve data when the S-N curve plots as a series of line

segments on log-log axes. In this case, particular combinations of m and K define the

curve over regions defined in terms of the N values at either end.

(b) Use as many lines as you need to completely define the S-N curve. Simply leave Column

1 blank for second and subsequent lines. For subsequent curves, put the new S-N curve

name in Column 1 and specify the curve data in the same way.

(c) When you use this specification, LifeFrequency automatically checks to ensure that the

specified S-N curve is continuous from region to region, that is, that there are no gaps or

discontinuities at the changeover points between curve regions. The presence of such a

gap will cause LifeFrequency to terminate with error.

(d) You should be careful when using this option that the S-N curve is defined over the

complete range of values likely to be of importance in a particular analysis. Note

especially that at the high cycle end of the curve, no fatigue damage is assumed to occur

at stress ranges below the minimum value specified. In effect this represents a fatigue

endurance limit.



Data Pairs for S-N Curve – Define


Purpose: To specify S-N curves directly as (S, N) data pairs.

Window:

Data Inputs:

Input: Description


S: The stress range.

N: The number of cycles which causes fatigue failure at this range.

Notes:

(a) Use as many lines as you need to completely define the S-N curve. Simply leave Column

1 blank for second and subsequent lines. For subsequent curves, put the new S-N curve

name in Column 1 and specify the curve data in the same way.

(b) You should be careful when using this option that the S-N curve is defined over the

complete range of values likely to be of importance in a particular analysis. Note

especially that at the high cycle end of the curve, no fatigue damage is assumed to occur

at stress ranges below the minimum value specified. In effect this minimum stress

represents a fatigue endurance limit.



Mode


Purpose: To choose between the three LifeFrequency modes of operation.

Window:

Data Inputs: None

Notes:

(a) The various modes of program operation are described in Chapters 2-4. The default is

Stand-alone.

(b) You specify data for the option you selected in one or both of the sections below the

Mode of Operation section in the GUI, namely Environment and Postprocessor. Only some of

the dialogs in these sections will be accessible, depending on which mode you selected.

The dialogs for all options are described in the following pages.



Seastates


Purpose: To choose between formats for inputting the seastate scatter diagram in

Stand-alone and Postprocessor with Stress RAOs modes.

Window:

Data Inputs: None

Notes:

(a) The options for inputting the fatigue analysis scatter diagram are discussed in Chapter 2,

‘Stand-alone Operation’. The Selected Seastates format is the most general case, and the

other two options correspond to the ‘Two Special Cases’ discussed in Chapter 2. The

options are in fact more or less self-explanatory.

(b) To specify the actual scatter diagram data you use the Seastate Scatter Diagram dialog. The

format this dialog takes depends naturally on which of the options you choose here. The

various formats are described on the following pages. Because as it is the most general

case, the format for the Selected Seastates option is described first. The formats for the

others are variations on this general case, and are described after it.



Seastate Scatter Diagram – Selected Seastates


Purpose: To input the fatigue analysis wave scatter diagram, to group the seastates in

the diagram into blocks, and to nominate a reference seastate for each

block.

Window:

Notes:

(a) The Seastate Scatter Diagram dialog is more complex than the other input dialogs, so its

operation is described under a number of sub-headings. These are Data Input Modes, Edit

Values Mode, Mark Reference Seastates and Set Axes.

Data Input Modes:

Since you can use this window to perform three different tasks, there are three data input

modes displayed as radio buttons at the top right-hand corner of the window. These modes



are called Edit Values, Mark Seastate Blocks and Mark Reference Seastates. What happens when

you choose each of these modes is described below. There are also a number of facilities

specific to this window, which are available along the bottom of the window (in addition to

the usual ones of OK, Cancel and Help). These facilities are also described in the following

sections.

Note that by default the scatter diagram is defined in terms of significant wave height Hs and

mean zero up-crossing period Tz. How to change this to Hs and wave spectrum peak period

Tp is also described shortly.

Edit Values Mode:

The Edit Values mode is used to input and/or change (edit) the individual entries in the

scatter diagram “cells”. You simply input into each cell the number of occurrences in a given

period of the particular combination of Hs and Tz/Tp values which that cell represents. This

given period is typically one year, but the duration is in fact immaterial - LifeFrequency

transforms the data you specify into percentage occurrence values, so it is the relative

magnitudes only of the entries that are of importance. You do not have to input a value into

all cells. If there is no occurrence of a particular combination of Hs and Tz/Tp, simply leave

the corresponding cell blank.

The Delete All button at the bottom of the window can be used in Edit Values mode to clear

all cells in the scatter diagram of data. You are prompted to confirm your request to delete all

entries to prevent accidental loss of data.

Mark Seastate Blocks:

The Mark Seastate Blocks mode is used, as its name implies, to group seastates into blocks, as

described previously in Chapter 2. This task can be performed at any stage during the input

of the scatter diagram data, but would typically be performed after all of the Hs/Tz or Hs/Tp

data has been input in Edit Values mode.

When you click on the Mark Seastate Blocks button, a rectangular cursor with a diagonal line

( ) appears on the screen. You simply move this cursor to one corner of the block you

want to define, and press the left hand mouse button. Then you drag the cursor to the cell on



the corner of the block, which is diagonally opposite the first cell, and release the mouse

button. The block you have defined will be surrounded by a thin black border, as for example

here.

Here a block has been defined with 15 seastates, with Hs values between 3 and 7 and Tz

values between 4 and 6 seconds inclusive.

If you click anywhere in an already defined seastate block when you are in Mark Seastate Block

mode that block becomes highlighted (the border around the block changes colour), and the

Delete Block button at the bottom of the window becomes active. (This facility is grey in the

pictures above, indicating that it is inactive or presently unavailable.) If you click on Delete

Block, the block border disappears, but the individual entries in the scatter diagram are

unaffected. This facility allows you to change the way in which seastates are grouped in

blocks without inputting the scatter diagram again in full.

The Delete All button at the bottom of the window can be used in Mark Seastate Blocks mode

to remove all block definitions, again without affecting the individual entries in the scatter



diagram cells. You are prompted to confirm your request to delete all blocks to prevent

accidental loss of data.

Mark Reference Seastates:

The Mark Reference Seastates mode is used, as its name implies, to nominate reference seastates

within each block, as again described previously in Chapter 2. This task can only be

performed after one or more seastate blocks have been defined.

When you click on the Mark Reference Seastates button, a circular cursor appears on the

screen ( ). You simply move this cursor to the cell which you want to nominate as the

reference seastate and click the mouse button. The cell nominated becomes shaded, as shown

in the figure below. Here a seastate with a Hs of 2 and a Tz of 5 seconds has been nominated

as the reference seastate for a block centred on that combination.

If you click on a seastate in a block where a reference seastate is already nominated, the

previous nomination becomes deselected.

The Delete All button at the bottom of the window can be used in Mark Reference Seastates

mode to remove all reference seastate definitions, again without affecting the individual



entries in the scatter diagram cells or the grouping of seastates into blocks. You are prompted

to confirm your request to delete all reference seastates to prevent accidental loss of data.

Set Axes

The only remaining facility in the scatter diagram window which has not been described

above is the Set Axes facility. This is available i) to nominate whether your scatter diagram

variables are Hs and Tz or Hs and Tp, and also ii) to change the Hs/Tz or Hs/Tp ranges in the

scatter diagram. When you first click on Stand-alone or Postprocessing With Stress RAOs the

window appears as shown in the ‘Window’ section above. Specifically, the window contains

cells for Hs values between 1 and 20 inclusive in steps of 1, and for Tz values between 1 and

19 seconds inclusive in steps of 1 second. You can change this using the Scatter Diagram Axes

dialog.

When you click on Set Axes ... the Scatter Diagram Axes dialog appears:

The T is: dialog is actually a drop-down list as follows:

The entries are self-explanatory. You can change any or all of the seven entries in the Scatter

Diagram Axes dialog as required. When you click on OK, the dialog disappears and the scatter

diagram reappears with the axes altered as per your instructions. For example, if you input

the following values in the Scatter Diagram Axes dialog:



then the default scatter diagram changes to the following:

It is strongly recommended that you use this facility only before inputting any data into a

scatter diagram, otherwise loss of data may occur.



Seastate Scatter Diagram – One Seastate


Purpose: To input the fatigue analysis wave scatter diagram as a single block, and to

nominate a reference seastate for that block.

Window:

Notes:

(b) This dialog is clearly very similar to that for the Selected Seastates option, and in fact differs

from it in only one respect. As you can see, the Mark Seastate Blocks option is disabled

and unavailable. This is because the entire scatter diagram constitutes a single block in

this case. Except for this one difference, this dialog is otherwise identical to the Seastate

Scatter Diagram – Selected Seastates dialog.



Seastate Scatter Diagram – All Seastates


Purpose: To input the fatigue analysis wave scatter diagram, without any definition

of blocks or reference seastates.

Window:

Notes:

(a) This dialog is clearly very similar to that for the Selected Seastates option, and in fact differs

from it in only two respects. As you can see, the Mark Seastate Blocks and the Mark

Reference Seastates options are disabled and unavailable. Because in this case you want

LifeFrequency to run a Flexcom analysis or analyses for every seastate in the scatter

diagram, there is no requirement to identify blocks or reference seastates. Except for the

unavailability of these facilities, this dialog is otherwise identical to the Seastate Scatter

Diagram – Selected Seastates dialog.



Spectrum


Purpose: To specify which wave spectrum type to use in the Stand-alone and

Postprocessor with Stress RAOs modes of operation.

Window:

Data Inputs: None

Notes:

(a) The data you specify here is used slightly differently depending on whether you’ve

nominated Stand-alone or Postprocessor with Stress RAOs mode.

(b) In Stand-alone mode, the data is used in two ways. Firstly, you use this option to tell

LifeFrequency which spectrum type, whether Pierson-Moskowitz or Jonswap, should

be used in all of the Flexcom analyses that LifeFrequency runs automatically.

Secondly, the spectrum type is also a necessary input when LifeFrequency is

subsequently using stress RAOs to generate stress spectra from wave spectra for the

various individual scatter diagram cells.

(c) In Postprocessor with Stress RAOs mode, the data is used in only the second of these ways,

since obviously you’ve already run the various Flexcom analyses when you run

LifeFrequency in this mode.

(d) When you specify Jonswap spectra, LifeFrequency uses the algorithm described in

Chapter 2 to calculate the Jonswap parameters fp, γ and α from the Hs and Tz/Tp

values in the scatter diagram.



Seastate Directions – Stand-alone Mode


Purpose: To specify long-term directionality data for the Stand-alone mode.

Window:

Data Inputs:

Input: Description

Direction: One of eight compass directions. The data in this column cannot

actually be altered. See Notes (a) and (b) below.

% Annual Occurrence: The percentage of 1 year during which storms occur from this

direction. See Notes (b) and (c) below.

RAO File Name: The name of the file containing the vessel RAOs for this direction.

See Notes (d) and (e) below.

Notes:

(a) “North” is defined as being the direction of the positive sense of the global Y axis.

“West” is then in the direction of the positive sense of the global Z axis, “South” in the

negative sense of global Y, and “East” in the negative sense of global Z. The other

directions are naturally intermediate to these.



(b) Waves in the “North” direction are defined as travelling in the positive global Y

direction, that is towards rather than from the compass point, and likewise for the other

directions.

(c) Data must be input on at least one row of this dialog, but it can be any row. You are not

required to input values on every row.

(d) The total of all of the % occurrence values must equal 100%.

(e) If your vessel RAOs for all wave headings are in a single file, then you can input the

name of that file on the first row with a non-zero % occurrence value, and leave Column

3 blank in subsequent rows. The following is an example of this specification – this

actually comes from the example drilling riser fatigue analysis from the next chapter.

As you can see, the RAO file name in the second and subsequent rows defaults to the

name specified in the first. The following would also be a valid, if highly unusual,

specification.

Here the RAOs are in two files, which are each used for 5 and 3 of the 8 compass

points, respectively.



(f) The way in which LifeFrequency uses this data is described in Chapter 2 in the section

‘Analysis Procedure’, but is summarised here for convenience. In the other dialogs of the

Stand-alone section of the GUI, you will have identified one or more reference seastates

(and each individual seastate in the scatter diagram may be a reference seastate).

LifeFrequency creates a Flexcom input file for each combination of i) reference

seastate and ii) direction in this dialog with non-zero % occurrence. The data in the

input file comes from three sources. The structure and general environment data comes

from the Flexcom file you specify in the Name of Flexcom File dialog. The RAO data

comes from the file in Column 3 of this dialog, in the row appropriate to the direction in

question. Finally the wave data comes from both the scatter diagram (Hs and Tz/Tp) and

from this dialog (wave direction).

(g) For example, in one of the fatigue load cases in the example drilling riser analysis of the

next chapter, the scatter diagram contains 12 blocks, and there are non-zero %

occurrence values for each of the eight compass directions in this Seastate Directions

dialog. So LifeFrequency automatically generates 12*8 = 96 individual Flexcom

random sea analysis input files, runs these in turn, postprocesses each one to extract the

required response RAOs, and finally computes the actual fatigue damage for all of the

seastates in the scatter diagram as described in Chapter 2.



Seastate Directions – Postprocessor with Stress RAOs Mode


Purpose: To specify long-term directionality data for the Postprocessor with Stress RAOs

mode.

Window:

Data Inputs:

Input: Description

Direction: One of eight compass directions. The data in this column cannot

actually be altered. See Note (a) below.

% Annual Occurrence: The percentage of 1 year during which storms occur from this

direction. See Notes (b) and (c) below.

Notes:

(a) For a discussion of the significance of the inputs here, refer to Notes (a) and (b) for the

preceding dialog, and also to Chapter 4, ‘Postprocessor with RAOs Operation’.

(b) Data must be input on at least one row of this dialog, but it can be any row. You are not

required to input values on every row.

(c) The total of all of the % occurrence values must equal 100%.



Pre-run Analyses – Postprocessor with Stress Spectra Mode


Purpose: To specify LifeFrequency data for the Postprocessor with Stress Spectra mode

of operation.

Window:

Data Inputs:

Input: Description

Flexcom Analysis: The name of the file containing Flexcom random sea analysis

results for a particular combination of environmental conditions.

% Annual Occurrence: The percentage of 1 year during which this combination of

conditions occurs.

Notes:

(a) You do not need to specify a file type, just the analysis root or generic name.



Pre-run Analyses with RAOs – Postprocessor with Stress RAOs Mode


Purpose: To specify LifeFrequency data for the Postprocessor with Stress RAOs mode

of operation.

Window:

Data Inputs:

Input: Description

Hs: The reference seastate significant wave height Hs.

Tz/Tp: The reference seastate mean zero up-crossing period Tz or peak

period Tp. You use Set Axes … on the Seastate Scatter Diagram dialog

to indicate which of these variables your time values actually

represent.

Direction: One of eight compass directions. You choose which one using the

drop-down list.

Flexcom Analysis: The name of the file containing axial force and bending moment

RAOs for this particular combination of environmental conditions.

Notes:



(a) You must specify an RAO file name here for each reference seastate for each direction

with non-zero % occurrence.

(b) You do not need to specify a file type in the Flexcom Analysis input, just the analysis root

or generic name.

Chapter 6 - Example Drilling Riser Fatigue Analysis


CHAPTER 6 - EXAMPLE DRILLING RISER FATIGUE

ANALYSIS

This chapter describes an example LifeFrequency fatigue analysis of a drilling riser, and is

divided into the following sections:

− ‘Introduction’ gives an overview of the example and describes the structure under

consideration.

− ‘Environment’ summarises the environmental conditions and tabulates the load cases

used.

− ‘Fatigue Data’ presents the fatigue-specific data used in the example.

− ‘Results’ summarises the results obtained.

− ‘Example Files’ lists the names of the files containing the input data for this example, all

of which are provided with the software.

INTRODUCTION

In this chapter the operation of LifeFrequency in the so-called Stand-alone mode of Chapter

2 is illustrated by means of an example fatigue analysis of a drilling riser. The riser analysed is

that used in Chapter 2, ‘Example 1 – Deepwater Drilling Riser’, of the Flexcom Examples

Manual. For a schematic of the riser stack-up and a summary of the riser input data you are

referred to Chapter 2 of the Flexcom Examples Manual.

In the LifeFrequency Category i) data specification for this example fatigue analysis, no

current or offset is specified. Imperial units are used throughout. Thickness effects are

ignored, and the fatigue analysis is based on bending stresses only.

ENVIRONMENT

The wave scatter diagram describing long-term environmental conditions for this fatigue

analysis is shown in Table 6.1. Hs values vary between 0.5 ft and 20 ft, and Tz values vary



between 4 and 13 seconds. The data in Table 6.1 is not intended to represent any particular

location, merely to demonstrate the operation of the software.

Table 6-1: Drilling Riser Fatigue Analysis – Wave Scatter Diagram

Tz (s)

4 5 6 7 8 9 10 11 12 13 0.5 136076 252100 255434 235832

2 321287 334477 298020 74558

3.5 272100 362849 383204 143217 167188

5 174127 296125 308157 275432 110168

6.5 175352 264871 260697 126533

8 117157 233065 231621 110175

Hs 9.5 111420 143196 102307 93240

(ft) 11 83161 90355 80073

12.5 67966 52943

14 32669 36253

15.5 11986 20976

17 13739

18.5 10200

20 1520 279

Three blocking schemes are used in this example to group the seastates of Table 6.1 into

blocks. The first scheme is shown in Table 6.2, which shows the scatter diagram divided into

12 blocks. A reference seastate is nominated for each block; the most frequently occurring

seastate is used. This scheme might be considered a reasonably standard application of the

blocking facility for this environmental specification.

The second blocking scheme is a variation on the first. 12 blocks are again specified, but in

this case there is only one seastate per block (which is by definition then the reference

seastate for that block). This scheme is illustrated in Table 6.3; note that the number of

occurrences per block is the same as in Table 6.2, except that in Table 6.3 all occurrences are

assigned to a single seastate. Running LifeFrequency in this way is similar to the so-called

Postprocessor with Stress Spectra mode of Chapter 3, except that LifeFrequency performs the

actual Flexcom runs in this case.



Table 6-2: Scatter Diagram Blocking Scheme – Multiple Blocks

Tz (s)

4 5 6 7 8 9 10 11 12 13 0.5 136076 252100 255434 235832

2 321287 334477 298020 74558

3.5 272100 362849 383204 143217 167188

5 174127 296125 308157 275432 110168

6.5 175352 264871 260697 126533

8 117157 233065 231621 110175

Hs 9.5 111420 143196 102307 93240

(ft) 11 83161 90355 80073

12.5 67966 52943

14 32669 36253

15.5 11986 20976

17 13739

18.5 10200

20 1520 279

Table 6-3: Scatter Diagram Blocking Scheme – Single-Sea Blocks

Tz (s)

4 5 6 7 8 9 10 11 12 13 0.5

2 709463 1198321

3.5 809076 1136043

5 552788

6.5 790445 619026

8

Hs 9.5 337777 365975

(ft) 11

12.5 189831

14

15.5 46701

17

18.5 2799

20



In the third blocking scheme one block only comprising the total scatter diagram is specified.

In this case the sole reference seastate is that with a Hs of 3.5 ft and Tz of 7 seconds (this is

the most commonly occurring seastate in the scatter diagram). The purpose of using these

three blocking schemes is obviously to compare the effect on fatigue life estimates of using

one and multiple blocks.

Likewise two directionality specifications are used in the example. These are shown in Table

6.4. In the first specification, waves approach from all eight compass directions, with %

occurrence values as shown in the table. In the second specification, waves approach from

one direction only, this being nominally the North.

Table 6-4: Directionality Specifications

Direction Case #1 Case #2

N 10% 100%

NW 15% 0%

W 5% 0%

SW 13% 0%

S 7% 0%

SE 8% 0%

E 21% 0%

NE 21% 0%

The three wave scatter diagram blocking schemes and the two directionality specifications are

combined into four overall environmental specifications or fatigue load cases as shown in

Table 6.5.



Table 6-5: Load Case Matrix

Load Case No. of Blocks No. of Seastates No. of Directions

1 1 43 1

2 12 43 1

3 12 12 1

4 12 43 8

As a check on the LifeFrequency computations, a time domain analysis with the Flexcom

fatigue postprocessor LifeTime is also undertaken for Load Case #3, corresponding to the

scatter diagram of Table 6.3 and one direction only. Results from this run are compared with

the LifeFrequency output in the ‘Results’ section later.

The dynamic analyses of this riser in the Flexcom Examples Manual consider a 2D

environment only (collinear waves, current and vessel motions). So RAOs at a single wave

heading only are included in the analysis specification. For this fatigue analysis, the simplified

RAO specification of the Examples Manual is replaced by RAOs defined as functions of

both frequency and wave direction. Specifically, the RAOs, which are typical of those for a

semi-sub, are defined at 17 wave headings and at 40 frequencies at each heading.

FATIGUE DATA

Fatigue data comprises the analysis SCF and S-N curve. For this example a stress

concentration factor of 1.5 is used throughout. The analysis S-N curve is an approximation

to the British Welding Institute Curve F, which is a log-linear curve with m and K values of

2.8 and 1.14815E9 respectively.

RESULTS

In the four fatigue analyses or Load Cases of this example, fatigue life estimates are requested

at 16 locations, these being from Elements 142 to 282 inclusive in steps of 10 elements, and

at Element 291. There is no particular significance to these locations and in reality very many

more hot spots would probably be specified. Figure 6-1 below compares the predicted



fatigue lives at these 16 locations for each of the four Load Cases. (Note the log scale on the

vertical axis.) In addition, Table 6.6 compares results at the two locations where the lowest

fatigue lives occur, near both the lower and upper flex joints.

0 1000 2000 3000 4000 5000 6000 7000 8000Distance Along Hot Spot Set (ft)

100

1000

1000

010

0000

Min

. Fat

igue

Life

(Yea

rs)

Load Case 1Load Case 2Load Case 3

Load Case 4

Figure 6-1: Comparison of LifeFrequency Results

Table 6-6: Summary of LifeFrequency Results

Minimum Fatigue Life (years) Load Case

Near Lower Flex Joint Near Telescopic Joint

1 273 261

2 695 256

3 844 343

4 2305 913

The results from Load Case 1 appear unreliable, certainly in the lower sections of the riser. It

is possible that another choice of reference seastate might produce fatigue life estimates in



better agreement with the other Load Cases – one possibility might be a seastate nearer the

‘middle’ of the scatter diagram, such as the combination of Hs = 9.5 ft and Tz = 8 seconds.

However the difficulty with this type of specification (one reference seastate only) is that in

the absence of the results from the other Load Cases it is difficult to benchmark the choice

of the one reference seastate. The results from Load Cases 2 and 3 show reasonable

agreement, with the analysis using RAOs predicting slightly higher fatigue lives.

A check on the Load Case 3 results is provided in Fig. 6.2, where the LifeFrequency results

for this case are compared with corresponding results from the Flexcom postprocessor

LifeTime. Note that the time domain results are based on only 30 minutes of simulation for

each of the 12 individual random seastates. Tables 6.7 compares the minimum fatigue lives

from the two programs in a similar format to Table 6.6. ‘Lower’ in Table 6.7 refers to the

region near the lower flex joint, while ‘Upper’ refers to the corresponding area near the

telescopic joint.

100

1000

10000

0 1000 2000 3000 4000 5000 6000 7000 8000

Fatigue Life (years)

Distance along Hot Spot Set (ft)

LifeFrequency

LifeTime: Statistics

LifeTime: Spectra

LifeTime: Rainflow

Figure 6-2: Comparison of LifeFrequency and LifeTime for Load Case 3



Table 6-7: Comparison of LifeFrequency and LifeTime

Minimum Fatigue Life (years)

LifeTime

Location

LifeFrequency

Statistics Spectra Rainflow

Lower 844 687 589 758

Upper 343 476 469 489

The significance of the three fatigue life values from LifeTime is that that program uses

three methods to calculate fatigue damage and fatigue life. These are:

− Calculating the standard deviation (σ) and mean zero up-crossing period (Tz) of bending

stress directly from Flexcom output and then calculating fatigue damage from these

(these values are labelled Statistics in Fig. 6.2).

− Calculating the stress spectrum from the Flexcom time histories, and then evaluating σ

and Tz from the moments of this spectrum. These are then used to complete the fatigue

analysis as before (these values are labelled Spectra).

− Calculating damage directly from the Flexcom stress histories using the rainflow cycle

counting technique (these values are labelled Rainflow).

The LifeFrequency and LifeTime results show reasonable agreement overall, particularly in

view of the differences between the estimates produced by the different methods used within

LifeTime itself. It is worth pointing out that the time domain simulations on which the

LifeTime results are based are relatively short (3 hours would be more usual than the 30

minutes used here); and the computational effort required by the two fatigue analyses differ

dramatically (5 minutes for the LifeFrequency run as opposed to about 190 minutes for the

combined Flexcom/LifeTime analyses).

Finally, the effect of including long-term directionality can be gauged by comparing Load

Case 2 with Load Case 4 in Figure 6.1. Over most of the riser the inclusion of directionality

causes a doubling (at least) of the predicted fatigue life. This is very much in line with general

experience as reported in the literature.



EXAMPLE FILES

The input files for this example may be found in the ‘Examples\LifeFrequency

Examples\Example 1 - Drilling Riser’ subdirectory of the Flexcom installation directory and

are as follows:

− Static.fl3 Flexcom file with basic riser model data.

− Semi-sub.ves Vessel RAO file.

− Load Case 1.fl3 LifeFrequency file for Load Case 1.




Chapter 7 - Example SCR Fatigue Analysis with Stress Spectra


CHAPTER 7 - EXAMPLE SCR FATIGUE ANALYSIS WITH

STRESS SPECTRA

This chapter describes an example LifeFrequency fatigue analysis of an SCR using stress

spectra, and is divided into the following sections:

− ‘Introduction’ gives an overview of the example.

− ‘Model’ describes the structure under consideration.

− ‘Environment’ summarises the environmental conditions and tabulates the fatigue load

case matrix.





INTRODUCTION

In this chapter the operation of LifeFrequency in the so-called Postprocessor with Stress Spectra

mode of Chapter 3 is illustrated by means of an example fatigue analysis of an SCR. The

method used to carry out the fatigue analysis involves first using Flexcom to find the initial

static configuration of the SCR. This is then followed by a series of Flexcom random sea

analyses to determine the dynamic riser response to the fatigue load case matrix.

LifeFrequency is finally run in the program Postprocessor with Stress Spectra mode of operation,

to accumulate the fatigue damage from the individual seastates.

MODEL

The SCR is 2000m in length, situated in a water depth of 820m, which is filled with export

gas at an internal pressure of 15 MPa. The SCR is fixed to the seabed at a PLEM, and is

attached to a semi-submersible platform via a flex joint with a rotational stiffness of 40

kNm/°, at a distance of 10 m below the MWL. The horizontal distance between the PLEM



and the top of the riser is 1618m. The seabed is modelled as an elastic surface with a stiffness

of 70kN/m/m. Figure 7.1 diagrammatically depicts the SCR configuration.

Length of SCR = 2000 m

Semi-Submersible

Seabed

MWL

820 m

Hang-off angle, = 22 degreesθ

θ

Figure 7.1. Schematic of SCR Configuration

A total of 242 elements are used in the model, of which 240 are SCR elements. The

maximum element length is 10m, the length of the adjoining elements are progressively

reduced in length to a minimum length of 1m situated about 30m in the touchdown zone and

in the region of the vessel connection. The structural properties and environmental data used

in this analysis are summarised in the ‘Input Data’ section below.



ENVIRONMENT

In this analysis a simplified fatigue matrix of twelve load cases defines the long-term seastate

environment. In practical applications many more would typically be used. Six of the cases

represent ‘Far’ loading conditions and six are ‘Near’ cases. For each individual case, an

individual wave spectrum, mean offset, drift amplitude and drift frequency are defined; the

drift in all cases is in the vessel surge direction. Table 7.1 below presents the fatigue load case

matrix.

Table 7-1: Summary of Environmental Conditions

Load Near/ Seastate Data Mean Drift Data

Case Far Hs (m) Tz (s) Offset (m)

Amplitude (m)

Period (s)

1 Near 0.75 5.24 4.84 0.16 138.50

2 Near 1.25 5.27 5.01 0.24 174.22

3 Near 1.75 5.77 5.28 0.51 196.46

4 Near 2.25 6.26 5.63 0.83 193.05

5 Near 2.75 6.89 6.00 1.15 193.05

6 Near 3.25 7.72 6.31 1.36 180.18

7 Far 0.75 5.24 4.39 0.16 136.80

8 Far 1.25 5.27 4.20 0.24 183.15

9 Far 1.75 5.77 4.01 0.51 193.05

10 Far 2.25 6.26 3.79 0.85 196.46

11 Far 2.75 6.89 3.62 1.17 196.46

12 Far 3.25 7.72 3.52 1.31 200.00

For the nominal location in question, the current distribution is assumed to be very nearly

constant throughout the year, so the same current definition is used in all the Flexcom

random sea analyses. The current speed and direction both vary through the depth. Table 7.2

below summarises the current specification. Note that in this data ‘Elevation’ represents

distance above the mudline, and ‘Direction’ is in degrees anti-clockwise from the global Y-

axis.



Table 7-2: Analysis Current Specification

Elevation Velocity (m/s) Direction (°)

0. 0.24 -39.7

10. 0.24 -39.7

160. 0.18 -45.7

260. 0.18 -40.7

360. 0.13 -76.7

460. 0.10 -135.7

560. 0.14 -170.7

660. 0.28 177.3

760. 0.49 164.3

820. 0.50 165.3

FATIGUE DATA


concentration factor of 1.4 is used. The analysis S-N curve is log-linear, with m and K values

of 4 and 1.15*1015 respectively. No endurance limit is specified. Thickness effects are ignored

in this analysis.

RESULTS

Fatigue results are requested for all nodes of the SCR finite element model, but over most of

the structure LifeFrequency reports that fatigue lives are ‘Infinite’. In the program

terminology this represents a predicted fatigue life of over 99,999 years. Table 7.3 below lists

the program output at the eight locations with the lowest fatigue lives. ‘Distance along SCR’

in this context is measured from the PLEM or seabed fixed point.




Node Number Distance along SCR (m) Fatigue Life (years)

74 708.5 1576

84 733 1996

85 734 1722

86 735 1767

238 1997 1487

239 1998 567

240 1999 209

241 2000 75

The fatigue “hot spots” occur in three locations. The first is about 708.5m from the PLEM,

and corresponds to the touchdown zone for the ‘Far’ case analyses. The second important

area for fatigue occurs at about 734m from the PLEM, and corresponds to the touchdown

zone for the ‘Near’ case runs. Finally, the third critical area is at the vessel connection, as

would be expected, where the overall minimum fatigue life of 75 years is predicted.

EXAMPLE FILES


Examples\Example 2 - SCR Using Spectra’ subdirectory of the Flexcom installation

directory and are as follows:

− SCR_Static.fl3 Flexcom static analysis file.

− SCR.ves Vessel RAO file.

− Near1_OffCur.fl3 Flexcom static offset and current analysis file (Near Case 1).

− Near1_Dynamic.fl3 Flexcom dynamic analysis file (Near Case 1).













− Far1_OffCur.fl3 Flexcom static offset and current analysis file (Far Case 1).

− Far1_Dynamic.fl3 Flexcom dynamic analysis file (Far Case 1).











− SCR.fl3 LifeFrequency fatigue analysis file.

INPUT DATA

Riser Properties

Table 7.4 below summarises the structural properties used in the model.



Table 7.4. Structural Properties

Component EIyy

(Nm2)

EIzz

(Nm2)

GJ

(Nm2

/rad)

EA

(N)

m

(kg/m)

p

(kg.m)

Di

(m)

Dd

(m)

Db

(m)

SCR 24.0E6 24.0E6 18.5E6 2935E6

110.17 1.81 0.2379

0.2731

0.2731

Rigid 1.0E11 1.0E11 1.0E12 1.0E12 0.1 0.1 0.0 0.01 0.01

where:

− EIyy Bending Stiffness about Local Y-Axis

− EIzz Bending Stiffness about Local Z-Axis

− GJ Torsional Stiffness

− EA Axial Stiffness

− m Mass/Unit Length

− p Polar Inertia of Cross-Section/Unit Length

− Di Internal Diameter

− Dd Drag Diameter

− Db Buoyancy Diameter

Vessel

The vessel reference point is located at {820, 1640, 0}, and has an undisplaced yaw

orientation of 0°. The vessel RAO data is presented in Figures 7.2 and 7.3.



0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5

Frequency (Hz)

RA

O (m

/m o

r deg

/m)

Heave Surge Pitch

Figure 7.2. Heave, Surge and Pitch RAOs

0

50

100

150

200

250

300

350

400

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5

Frequency (Hz)

Phas

e A

ngle

(deg

)

Heave Surge Pitch

Figure 7.3. Heave, Surge and Pitch Phase Angles



Internal Fluid

The riser is gas filled a

s follows:

Table 7.5. Internal Fluid Properties

Height (m) Density (kg/m3) Pressure (MPa)

290.0 880.0 18.008

−

Chapter 8 - Example SCR Fatigue Analysis with RAOs


CHAPTER 8 - EXAMPLE SCR FATIGUE ANALYSIS WITH

RAOS

This chapter describes an example LifeFrequency fatigue analysis of an SCR using stress

RAOs, and is divided into the following sections:

− ‘Introduction’ gives an overview of the example and describes the structure under

consideration.

− ‘Environment’ summarises the environmental conditions and tabulates the fatigue load

case matrix.





INTRODUCTION

In this chapter the operation of LifeFrequency in the so-called Postprocessor with RAOs mode

of Chapter 4 is illustrated by means of an example fatigue analysis of an SCR. The riser

analysed is the same as that used in the example in the previous chapter. Specifically, an SCR

of length 2000m in 820m of water is considered. The seabed is modelled as an elastic surface

with a stiffness of 70kN/m/m. For a schematic of the SCR configuration and a summary of

the riser input data you are referred to the previous chapter.

The method used to carry out the fatigue analysis involves first using Flexcom to find the

initial static configuration of the SCR. This is followed by a series of Flexcom random sea

analyses to determine the dynamic riser response to specified reference seastates. These

analyses are then postprocessed using Flexcom to generate stress RAOs for specified points

along the riser. LifeFrequency is finally run in the program Postprocessor with RAOs mode of

operation, to accumulate the fatigue damage from the scatter diagram seastates.



ENVIRONMENT

The wave scatter diagram describing long-term environmental conditions for this fatigue

analysis is shown in Table 8.1. Hs values vary between 0.3 m and 4.2 m, and Tz values vary

between 1 and 10 seconds. The data in Table 8.1 is effectively the scatter diagram from the

drilling riser analysis of Chapter 6 converted to Metric, and is not intended to represent any

particular location.

Table 8-1: Scatter Diagram Blocking Scheme

Tz (s)

1 2 3 4 5 6 7 8 9 10 0.3 136076 252100 255434 235832 0.6 270372 354477 298020 74558

0.9 272100 562849 323204 148217 167188 1.2 174127 296125 308157 275432 110168

1.5 175352 244871 240697 126533 1.8 117157 233065 231621 110175

Hs 2.1 111420 143196 96346 93240

(m) 2.4 83161 90355 65073

2.7 55672 32943 3.0 32669 26253

3.3 8101 15346 3.6 10232

3.9 10200 4.2 1520 279

The scatter diagram is divided into 12 blocks. A reference seastate is nominated for each

block; the most frequently occurring seastate is used. For this example the directionality data

has a non-zero occurrence for one direction only, nominally North.

For each reference seastate, the current distribution is assumed to be very nearly constant

throughout the year, so the same current definition is used in all the Flexcom random sea

analyses. The current speed varies through the depth. Table 8.2 below summarises the

current specification. Note that in this data ‘Elevation’ represents distance above the

mudline, and ‘Direction’ is in degrees anti-clockwise from the global Y-axis.



Table 8-2: Analysis Current Specification

Elevation Velocity (m/s) Direction (º)

0. 0.24 10.0

10. 0.24 10.0

160. 0.18 10.0

260. 0.18 10.0

360. 0.13 10.0

460. 0.10 10.0

560. 0.14 10.0

660. 0.28 10.0

760. 0.49 10.0

820. 0.50 10.0

FATIGUE DATA


concentration factor of 1.2 is used. The analysis S-N curve is log-linear, with m and K values

of 3 and 4.27*1011 respectively. No endurance limit is specified. Thickness effects are ignored

in this analysis.

RESULTS

Fatigue results are requested for 25 locations along the SCR finite element model, these being

from Elements 1 to 231 inclusive in steps of 10 elements, and Element 240. There is no

particular significance to these locations and in a real-world analysis very many more hot

spots would probably be specified. Table 8.3 below lists the program output at the four

locations with the lowest fatigue lives. ‘Distance along SCR’ in this context is measured from

the PLEM or seabed fixed point.




Node Number Distance along SCR (m)

Fatigue Life (years)

82 731.0 423

92 741.0 537

102 783.4 9267

241 2000.0 28

The critical areas along the riser with regard to fatigue occur in two locations. The first is

between 730m and 740m from the PLEM, and corresponds to the touchdown zone for the

riser. The second critical area is at the vessel connection, as would be expected, where an

overall minimum fatigue life of 28 years is predicted.

A check on these values can be obtained by running LifeFrequency in the Postprocessor with

Stress Spectra mode using the output from the 12 reference seastate analyses. To calculate a %

occurrence value for the 12 combinations of Hs and Tz, the numbers of occurrences in each

block are summed, and then expressed as a % of the total number of occurrences. This gives

the data shown in Table 8.4.

When this analysis is run, the fatigue lives in Table 8.5 are obtained; these show reasonable

agreement with the Table 8.3 values given the quite different analysis procedures. Fatigue

lives over the whole riser are compared in Figure 8-1 below, where again reasonable overall

agreement is reported.



Table 8-4: Seastate % Occurrences for Check Analysis

Hs Tz % Occurrence

3.9 9 0.2

3.3 9 0.5

2.7 7 2.2

2.1 7 5

2.1 6 4.9

1.5 6 10.3

1.5 5 11.2

1.2 6 8

0.9 4 15.7

0.9 3 14.7

0.6 3 17.7

0.6 2 9.6

Table 8-5: LifeFrequency Results, Postprocessor with Stress Spectra Mode

Node Number Distance along SCR (m) Fatigue Life (years)

82 731.0 535

92 741.0 677

102 783.4 11510

241 2000.0 36



0 500 1000 1500 2000Distance Along Hot Spot Set (m)

1010

010

0010

000

1000

00M

in. F

atig

ue L

ife (Y

ears

)

Postprocessor with RAOs ModePostprocessor with Stres Spectra Mode

Figure 8-1: Fatigue Life of the Riser

EXAMPLE FILES


Examples\Example 3 - SCR Using RAOs’ subdirectory of the Flexcom installation directory

and are as follows:

− SCR_Static.fl3 Flexcom static analysis file.

− SCR.ves Vessel RAO file.

− Fat01_Dynamic.fl3 Flexcom dynamic analysis file (Reference Seastate 1).

− Fat01_Dynamic.pr3 Corresponding postprocessing file.

























− SCR.fl3 LifeFrequency fatigue analysis file

LifeFrequency Manual

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