Analyses |
 
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Analyses |
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The base node is fixed in the 3 translational degrees of freedom. Vessel boundary conditions are specified in the first three DOFs at the uppermost node. The initial position of the vessel reference point, at approximately 9m above the MWL, and the RAOs are also input.
The only change here is that an 18.5° hang-off angle is requested via the Solution Criteria Automation feature. All of the boundary conditions are unchanged and carry through automatically from the initial static analysis.
Additional rotational vessel boundary conditions are used to fix the upper end of the riser at the desired 18.5° hang-off angle.
A piecewise-linear current, varying between 0.15 m/s at the mudline to 0.3 m/s at the MWL, is applied to the riser. The boundary conditions again remain unchanged and are carried through automatically from the hang-off analysis.
Three random sea analyses are performed. In each case the seastate is characterised by a Pierson-Moskowitz wave spectrum with a Tz of 9s. Three different Hs values are specified, namely 1m, 2m and 3m. The boundary conditions remain unchanged and are carried through automatically from preceding analyses. Since vessel boundary conditions and RAO data have previously been input, dynamic motions are automatically applied with the application of wave loading. Purely for efficiency reasons, the time domain simulation is analysed for ½ hour only, whereas a 3 hour simulation would generally be considered recommended practice.
Again, three Pierson-Moskowitz spectra, with a Tz of 9s and Hs values of 1m, 2m and 3m, are specified, for comparison with the time domain. Like the time domain, no specification of boundary conditions is required in the frequency domain: all of the boundary condition data carries through from the current analysis.
A modal analysis is carried out to calculate the natural frequencies and mode shapes of the steel catenary riser. The riser is naturally designated as an SCR for the purposes of Shear 7 output. The output is based on the first 50 modes and 500 equally spaced segments. The first 100 eigenpairs are requested, as recommended practice is to specify twice the number of natural frequencies as you are actually interested in. Note that output is requested for the set entitled SCR only, as this comprises riser elements only, and excludes the upper flex joint and rigid I-tube element. The composition of this set is actually defined in the Flexcom static analysis, and as the definition automatically carries through, there is no need to redefine it again in the modal analysis.
A frequency domain fatigue analysis is performed using LifeFrequency to estimate fatigue damage and predict fatigue life. This example illustrates the operation of LifeFrequency in the Postprocessor with Stress Spectra mode. An initial static analysis precedes a series of near and far static offsets, each of which is then followed by a Flexcom random sea analysis, to determine the dynamic riser response to a fatigue load case matrix. LifeFrequency is then run in the program Postprocessor with Stress Spectra mode of operation, to accumulate the fatigue damage from the individual seastates.
The model used is very similar to that of the time domain dynamic analysis examined in the preceding section of this example. In this case however, the vessel has an initial yaw orientation of zero, so that offsets in the local vessel surge axis correspond to near and far offsets of the SCR. Also the specified RAO data is heading independent, and corresponds to head seas only.
A relatively simplistic fatigue matrix of 12 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 table below presents the fatigue load case matrix.
Fatigue Load Case Matrix
Load Case |
Offset Case |
Seastate Data |
Offset (m) |
Drift Data |
Percentage Occurrence |
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Hs (m) |
Tz (s) |
Amp. (m) |
Period (s) |
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1 |
Near |
0.75 |
5.24 |
4.84 |
0.16 |
138.50 |
4.4 |
2 |
Near |
1.25 |
5.27 |
5.01 |
0.24 |
174.22 |
10.4 |
3 |
Near |
1.75 |
5.77 |
5.28 |
0.51 |
196.46 |
9.6 |
4 |
Near |
2.25 |
6.26 |
5.63 |
0.83 |
193.05 |
8.4 |
5 |
Near |
2.75 |
6.89 |
6.00 |
1.15 |
193.05 |
5.8 |
6 |
Near |
3.25 |
7.72 |
6.31 |
1.36 |
180.18 |
3.4 |
7 |
Far |
0.75 |
5.24 |
4.39 |
0.16 |
136.80 |
7.8 |
8 |
Far |
1.25 |
5.27 |
4.20 |
0.24 |
183.15 |
14.4 |
9 |
Far |
1.75 |
5.77 |
4.01 |
0.51 |
193.05 |
13.2 |
10 |
Far |
2.25 |
6.26 |
3.79 |
0.85 |
196.46 |
12.0 |
11 |
Far |
2.75 |
6.89 |
3.62 |
1.17 |
196.46 |
7.4 |
12 |
Far |
3.25 |
7.72 |
3.52 |
1.31 |
200.00 |
3.2 |
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.
Fatigue data comprises the analysis SCF and S-N curve. For this example a stress concentration factor of 1.2 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.
A sample frequency domain cycle counting analysis is performed using Histogram to illustrate its operation. It is based on the same fatigue load case matrix as the preceding fatigue analysis, and the results are output in the form of response histograms. In this example, a response histogram of bending moment is requested for the location of minimum fatigue life as predicted in the preceding fatigue analysis. 20 “bins” or divisions are specified going from a minimum of 0 to a maximum of 100. the bending moment data is assigned a scale factor of 0.001, so the range of the corresponding response histogram is from 0 to 100kNm.