16th INTERNATIONAL SHIP AND OFFSHORE STRUCTURES CONGRESS
20-25 AUGUST 2006
SOUTHAMPTON, UK
VOLUME 1
COMMITTEE I.2
LOADS
COMMITTEE MANDATE
Concern for environmental and operational loads from waves, wind, current, ice, slamming, sloshing,
weight distribution and operational factors. Consideration shall be given to deterministic and statistical
load prediction based on model experiments, full-scale measurements and theoretical methods.
Uncertainties in load estimations shall be highlighted.
COMMITTEE MEMBERS
Chairman:
Prof.
Dr.
Mr.
Mr.
Dr.
Mr.
Prof.
Prof.
Mr.
Prof.
Dr.
Dr.
Prof.
Dr.
Dr.
P. Temarel
X.B. Chen
A. Engle
G. Hermanski
J. Jankowski
G. Kapsenberg
H. Kawabe
S.Kruger
T. Kukkanen
S. Mavrakos
W. Pastoor
B. Pedersen
H.L. Ren
L. Sebastiani
J. Xia
KEYWORDS
Cables/risers, fatigue, green water, ice loads, multi-bodies, parametric roll, rogue waves, slamming,
sloshing, uncertainty analysis, VIV, wave loads.
2
ISSC committee I.2: Loads
CONTENTS
1.
INTRODUCTION ............................................................................................................................... 4
2.
ENVIRONMENTAL LOADS ON SHIPS ......................................................................................... 4
2.1 Computational Methods for Wave-induced Loads .................................................................. 4
2.1.1 2D Nonlinear Methods ................................................................................................ 4
2.1.2 3D Linear Methods ...................................................................................................... 6
2.1.3 3D Nonlinear Methods ................................................................................................ 9
2.2 Analytical Methods in Hydroelasticity ................................................................................... 12
2.3 Measurements ......................................................................................................................... 13
2.3.1 Model Experiments.................................................................................................... 13
2.3.2 Full-scale Measurements ........................................................................................... 15
2.4 High Speed Craft..................................................................................................................... 17
2.5 Large Amplitude Roll ............................................................................................................. 18
2.6 Ice Loads ................................................................................................................................. 20
2.7 Wind Loads ............................................................................................................................. 22
3.
ENVIRONMENTAL LOADS ON OFFSHORE STRUCTURES .................................................. 23
3.1 Computational Methods for Fixed and Floating Structures ................................................... 23
3.1.1 First and Second Order Wave Loads and Induced Responses.................................. 23
3.1.2 Wave-current Interactions ......................................................................................... 24
3.1.3 Multi-body Interactions ............................................................................................. 24
3.2 Cables, Risers and Column Systems ...................................................................................... 27
3.2.1 Column Systems ........................................................................................................ 27
3.2.2 Mooring and Cable Systems ...................................................................................... 28
3.3 Vortex Induced Vibrations...................................................................................................... 29
3.3.1 Semi-empirical Models ............................................................................................. 29
3.3.2 SHEAR7 .................................................................................................................... 30
3.3.3 Application of CFD and Other Theoretical Methods to VIV Prediction ................. 30
3.3.4 Experimental and Field Measurements ..................................................................... 30
4.
LOADS DUE TO IMPACTS AND EXTREME EVENTS ............................................................. 31
4.1 Slamming ................................................................................................................................ 31
4.1.1 Local Slamming ......................................................................................................... 31
4.1.2 Global Slamming ....................................................................................................... 34
4.2 Sloshing ................................................................................................................................... 36
4.3 Green Water ............................................................................................................................ 38
4.4 Impact Loads on Offshore Structures ..................................................................................... 40
4.5 Rogue Waves .......................................................................................................................... 41
5.
PROBABILISTIC METHODS ......................................................................................................... 42
5.1 Short-term Distribution ........................................................................................................... 42
5.2 Long-term Distribution ........................................................................................................... 44
6.
UNCERTAINTY ANALYSIS .......................................................................................................... 45
6.1 Uncertainty in Measurements - Model and Full-scale ........................................................... 46
6.2 Verification and Validation of Numerical Codes ................................................................... 47
7.
FATIGUE LOADING ....................................................................................................................... 48
8.
RULES DEVELOPMENT FOR SHIPS ........................................................................................... 50
9.
CONCLUSIONS................................................................................................................................ 52
9.1 Environmental Loads on Ships ............................................................................................... 52
9.2 Environmental Loads on Offshore Structures ........................................................................ 53
ISSC committee I.2: Loads
9.3
9.4
9.5
9.6
9.7
3
Loads due to Impacts and Extreme Events............................................................................. 54
Probabilistic Methods ............................................................................................................. 54
Uncertainty Analysis ............................................................................................................... 55
Fatigue Loading ...................................................................................................................... 55
Rules Development for Ships ................................................................................................. 55
REFERENCES
4
1.
ISSC committee I.2: Loads
INTRODUCTION
The content of this committee’s report is dictated by its mandate, as well as the expertise of its
membership. Its structure follows along similar lines to that adopted in ISSC 2003. Wave-induced loads
on ships are dealt within two different sections, namely 2 and 4. The former focuses on 2D and 3D
methods, examining current practice in linear and progress in nonlinear methods together with
applications of so called CFD (Computational Fluid Dynamics) methods. In addition full-scale and
flexible model test measurements are reviewed. The latter focusses on impact related loads, namely
slamming, sloshing and green water. The section on offshore structures focusses on multi-body
interactions and floating-mooring system interactions, with particular reference to instabilities and the
clashing event for the latter. In addition current status on vortex induced vibrations is reviewed.
Developments for VLFS are not included in this report, as these are within the remit of Specialist Task
Committee VI.2. As with previous reports, current state of progress in short- and long-term predictions
is examined and their interaction with the development of rules discussed. Uncertainties in experimental
and full-scale measurements and computational methods are discussed with reference to the verification
and validation process. This is an extremely important issue that is beginning to gain ground where
dynamic loads are concerned, but has yet to reach the level attained in steady state computations and
measurements.
A number of new subject for this committee areas have also been incorporated. There is a
comprehensive analysis of ice loads and a separate section devoted to large amplitude roll, due to the
significance of these issues. Loads induced by rogue or freak waves make for another area of concern for
designers of ships and offshore structures. Consequently the emerging small body of work on loads
induced by such waves has been reviewed. Comprehensive review of fatigue loading was presented in
the last ISSC by the Special Task Committee VI.1, which no longer exists. The latest developments in
this area are discussed in this report, as the committee’s expertise could stretch this far.
2.
ENVIRONMENTAL LOADS ON SHIPS
2.1
Computational Methods for Wave-induced Loads
Owing to the presence of forward speed and inherent hydrodynamic and geometrical nonlinearities,
computations of motions and loads are still far from a state of mature engineering science. Strip
methods, based on 2D linear potential flow computations in the frequency domain, have been used for
engineering purposes, because they are very efficient, robust, and relatively accurate in low to moderate
sea states. However, in recent years, attention tends to be focussed on refining 3D effects and improving
inclusion of nonlinearities in rough seas. Thus, as a natural trend, there are moves from the frequency
domain to the time domain, from strip theory to fully 3D schemes, from linear to nonlinear problems,
and also from potential flow to viscous flow computations.
2.1.1
2D Nonlinear Methods
Although in use for more than half a century, linear strip methods are still competitive despite their
relatively crude assumptions. Even though there is a clear tendency nowadays to switch over to 3D
methods, strip theories, both linear and nonlinear, are still widely in use. Nonlinear strip methods are
often used in cases where nonlinear effects play the dominant role, such as large amplitude motions. For
example Xia (2005) formulated the nonlinear hydrodynamics forces, including the momentum slamming
force in a unified seakeeping model. This formulation is within the framework of potential flow theory
and is particularly effective for heave, pitch and vertical bending moment prediction of large
displacement ships such as containerships. Two major fields of applications can be identified in the past
few years where the nonlinear methods have been successfully used. Firstly, most problems related to
capsizing of passenger vessels due to large scale flooding (e.g. vehicle deck damage) are treated with
specialized 2D methods, where one (typically the roll motion) or more degrees of freedom are treated
ISSC committee I.2: Loads
5
nonlinearly (e.g. Cramer et al 2004). The other field concerns problems related to excessive motions in
rough weather, such as parametric rolling or broaching to. These methods also treat selected
combinations of degrees of freedom, depending on the nature of the problem, nonlinearly in time
domain; whilst the remaining degrees of freedom are treated linearly. In this context there is still the
need to also improve 2D linear codes for situations relating to specific problems associated with new hull
forms and configurations (e.g. Grigoriopoulos et al 2003) or increased speeds. Nonlinear strip methods
are robust enough to avoid numerical problems which may occur in 3D codes, e.g. for non-zero forward
ship speed in quartering waves when ship’s forward speed is close to the speed of the wave packet,
resulting in an infinite sway RAO in linear theories or unstable results in nonlinear panel codes. In
addition an important advantage of 2D methods, say compared to RANS (Reynolds Averaged NavierStokes) methods, is their ability to cope with irregular short crested waves. As a result of several
incidents with container vessels, active operator guidance begins to play a major role and a large amount
of data needs to be generated for on board use; a fact which makes 2D methods still attractive due to
calculation time considerations.
Grigoriopoulos et al (2003) performed a sensitivity study for the application of linear strip methods to
vessels with large overhanging, semi-submersed transoms. They compare the results from ordinary strip
methods with 3D calculations and experiments. Although there were some discrepancies in the pitch
RAO due to the immersed transom problem also with the strip methods, the authors conclude that they
could handle this type of problem better than the 3D methods up to a Froude number of 0.3; the problem
with the 3D methods is most probably due to numerical problems related to the large semi-immersed
transom. Bruzzone (2003) compared the results from ordinary strip method with those from a 3D
Rankine source method and model test measurements for a high speed mono-hull and a catamaran
configuration. The author concluded that both methods could handle the problem approximately with
the same accuracy; nevertheless for the catamaran, where 3D effects play a more dominant role, the 3D
method was somewhat superior. Begovic (2004) used a 2½ D high speed theory to predict the motions
of fast and slender vessels in head seas. It was concluded that this theory significantly overestimates, by
comparison to measured values.
Nonlinear strip methods were used to predict the consequences of large scale flooding for passenger
ships. Vassalos et al (2003) and Turan (2003) applied their nonlinear code DAMSIM, developed to
predict large scale flooding consequences in beam seas, to demonstrate that the method is able to predict
the effect of several design alterations with sufficient accuracy. Comparisons with model tests results
appears to be satisfactory. van’t Weer and Serra (2003) applied their nonlinear code FREDYN to the
prediction of the sinking time of a damaged cruise liner. This method was originally developed to
simulate large amplitude motions in severe seas and consists of an approach that combines linear and
nonlinear potential flow forces with manoeuvring and viscous forces. The method was extended to solve
water on deck problems as well as internal flooding. A sensitivity analysis was carried out with respect
to damage extents and several damage cases, including raking, were studied. Valanto (2005) used a
nonlinear strip theory code named ROLLS to calculate sinking times of damaged passenger vessels. This
method treats the roll and surge motions in a nonlinear manner in time domain, whilst the other degrees
of freedom are handled by linear RAOs. The righting levers are determined according to Grim’s concept
of the equivalent wave and water on deck is modelled by Glimm’s method.
Cramer et al (2004) used the ROLLS code to predict the capsizing sequence of a Ro-Ro vessel in
following seas. The agreement between simulations and model test performed in the deterministic wave
scenario is good, as can be seen in Figure 1 for a 200m Ro-Ro vessel (Billerbek 2005). The authors also
presented limiting wave heights for the sliding of unlashed cars on a vehicle deck. They suggest that
information on dangerous situations obtained by their method should be used for on board active
operator guidance. Krüger and Ihms (2004) used the same approach to determine capsizing frequencies
of a range of multi-purpose vessels and bulk carriers. Their results are presented in the form of polar
diagrams identifying limiting wave heights, for a set of ship parameters and operational conditions, for
the ship to fulfil a limiting criterion, namely the capsizing criterion by Blume (1987). A typical example
is shown in Figure 2 for a Ro-Ro vessel.
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ISSC committee I.2: Loads
Figure 1: Capsizing sequence for a Ro-Ro vessel in stern quartering waves simulated by nonlinear strip
method ROLLS (left) and the corresponding time steps from a model test (right) in
deterministic wave sequences (Billerbek 2005).
2.1.2
3D Linear Methods
Linearisation of the problem considered is justified when the ship motion amplitude is small compared to
the ship reference length. This is applicable when the incident wave amplitude is small compared to its
length. The potential flow is represented by boundary distribution of sources and/or normal dipoles with
strength of singularities determined by the boundary condition. This forms the basis of numerous
boundary element methods for numerical determination of 3D flow. First and higher order panels,
ISSC committee I.2: Loads
7
widely discussed by Bertram (2002), are used. B-spline surfaces have become an industry standard for
geometry representation in CAD systems. The particular Green’s functions of the mathematical problem
determining the diffracted and radiated velocity potential correspond to the particular cases of free
surface condition: with forward speed or without forward speed. The sources and/or dipoles are,
depending on the singularity type, distributed over:
 the wetted surface of the hull and over the part of the free surface if the Rankine singularity,
which does not satisfy the free surface condition, is used, e.g. Jansen et al (2003), Kazemi and
Incecik (2004);
 the wetted surface of the hull and over waterline contour if Green’s function with forward speed,
which automatically satisfies the free surface condition, is used, e.g. Boin et al (2003), Guilbaud
et al (2003), Inoue and Kamruzzamman (2004);
 the wetted surface of the hull if Green’s function without forward speed, which automatically
satisfies the free surface condition, is used, e.g. Ahmed et al (2004), Kim and Shin (2003a).
Figure 2: Polar Diagram computed for the prediction of large amplitude roll in irregular seas. The iso
lines represent limiting wave height satisfying Blume’s (1987) capsizing criterion. The
significant wave length is equal to ship’s length (Krüger and Ihms, 2004).
The Rankine singularity was used by Kazemi and Incecik (2004) to analyse the interaction between a
floating offshore structure and waves. The numerical model is based on the weighted residual technique
and the so called direct element method was developed to compute the semi-submersible motion in six
degrees of freedom as a response to encountered waves. Jansen et al (2003) used a combined
Rankine/Kelvin source method to solve the wash waves problem. The domain was divided into an inner
and outer one. Kelvin sources are distributed on a vertical matching wall, positioned at the outer edge of
the inner domain, to satisfy a boundary condition used in the Rankine source solution in the inner
domain. Such an approach means avoiding reflections at the outer edge of the inner domain. The farfield waves can be computed using the solution on the matching wall together with the Kelvin source
distribution. The body panels were assumed to be parabolic having a linearly varying source strength.
The free surface panels were flat having a constant source strength. Comparison of computed and
measured longitudinal wave cuts showed good consistency. Kim and Shin (2003a) used Non-uniform
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ISSC committee I.2: Loads
Rationale B-Spline (NURBS), which represents 3D geometric surfaces precisely in the boundary integral
representation, to solve the diffraction and radiation problem for a hemisphere floating without forward
speed.
Practical application of the Green’s function without forward speed to wave diffraction-radiation
problems is relatively simple and was presented in previous reports of this Committee. Therefore, in this
report the focus is on the Green’s function with forward speed. Development of a practical numerical
scheme requires an efficient form of this function. Two main types, based on alternative representations,
are used (Noblesse and Yang 2004b):
 definition by simple Fourier integrals that involve relatively complicated special functions
applied, for example, by Guilbaud et al (2003), Inoue and Kamruzzamman (2004), and
 expression by single Fourier integrals along the steepest descent integration path in the complex
Fourier plane (namely Bessho’s method) applied, for example, by Maury et al (2003).
Nevertheless, these Green’s function forms are relatively complicated and numerical quadrature cannot
give correct results for a panel and a collocation point close to the free surface, for which the integrand of
the Green’s function, given in integral form, oscillates with an indefinitely increasing amplitude and
frequency, as discussed by Guilbaud et al (2003).
Boin et al (2003) and Guilbaud et al (2003) demonstrated that the difficulties reduce when the
computations are performed after interchanging the integrals over the panels and waterline segments with
the integrals representing the Green’s function. For a polygonal panel the surface integral can be
transformed into a contour integral using Stokes’ theorem. A good accuracy with moderate
computational time was obtained except when the source point is located close to the free surface. In this
case an extrapolation technique was used. Inoue and Kamruzzamman (2004) solved the diffraction –
radiation problem for a Wigley hull moving with forward speed in regular waves. First order panels and
Green’s function in the form proposed by Inglis and Price were used. Comparisons were made with
experimental measurements. The free surface wave patterns were calculated for steady and unsteady
motions around a Wigley hull. The effect of motions on the wave pattern is more prominent at the lower
range of frequencies.
Different methods of calculating Green’s function and their integrations over panels or segments have
been introduced into two seakeeping codes by Maury et al (2003). The comparison showed that the
derivatives of the Green’s function are more difficult to integrate than the function and that it is
impossible to use, with reasonable accuracy, a numerical method of integration – such as the Gauss
method for a field point close to the free surface. Results for Series 60 hulls showed the existence of
irregular frequencies, but these are less abrupt compared to those observed at zero forward speed.
Calculations performed by neglecting the waterline integral showed an increase in the amplitudes of
irregular frequency oscillations, denoting that this integral has a strong damping effect on the irregular
frequencies. The calculated wave elevation patterns overestimate the amplitude of the measured wave
field downstream of the hull. The reason of the difference has not yet been explained. Very high values
of the unsteady free surface elevation appear behind the hull if the waterline is neglected as reported by
Guilbaud et al (2003). The latter additionally concluded, on the basis of calculation of added masses and
damping coefficients, that forward speed affected these coefficients only in the low range of frequencies.
Noblesse and Yang (2004a) derived a boundary integral representation which is weakly singular in
comparison to the classical one. Classical representation defines the potential in terms of Green’s
function and its gradient, whilst the weakly singular representation only in terms of Green’s function.
Numerical application in the classical representation showed that the contribution of the surface integral
over the wetted surface can be, to some extent, cancelled by the line integral, resulting in loss of
accuracy. This loss of accuracy, can, in general, be reduced in the weakly singular representation
indicating that this may provide a useful alternative mathematical basis for numerical purposes.
A fully satisfactory, as well as reliable and practical, solution cannot be developed before removing in a
consistent and rational way the aforementioned difficulties. One way of overcoming them, proposed by
Noblesse and Yang (2004b), is the use of “Simple Green’s Function”, which satisfies the linear freesurface boundary condition in the far field and approximately satisfies the linear free-surface boundary
ISSC committee I.2: Loads
9
condition in the near field. A distribution of singularities over a near field portion of the free surface in
the vicinity of the waterline is then required. This Green’s function is expected to provide a more
efficient way of solving the forward speed seakeeping problem. Another way consists of analysing the
effect of small parameters neglected in the analysis procedure of perturbation. One of them is the surface
tension often ignored in describing water waves around large floating bodies, since its effect is
considered to be significant only for rather short waves commonly called ripples whose wavelength is of
the order of centimetres. However, the theory of gravity waves may yield waves of very short length
which cannot be ignored and cause substantial difficulties in modelling them. The analyses by Chen
(2002) in frequency domain and Chen and Duan (2003) in time domain showed that including the effect
of surface tension not only yields more realistic description of ship waves but also eliminates the
singularity of the Green’s function when both the source and field points are at the free surface. Another
effect is fluid viscosity which gives large dissipations to ship waves of small wavelength so that the
singularities associated with pure-gravity waves disappear as shown by Chen (2005a). These benefits are
likely to be influential in the development of practical computational methods.
Usually, Green’s function methods neglect the steady flow component, discussed by Bertram (2002),
who claims that the explicit consideration of the steady potential changes the results for computed heave
and pitch motions, for wave length of similar magnitude to the ship’s length, by as much as 20% - 30%.
The influence of the steady flow on the prediction of hydrodynamic coefficients, exciting forces and
motions, was investigated by Ahmed et al (2004), using Green’s function without forward speed. It was
concluded, based on the result of calculations for Series 60 and NPL hull forms, that the influence of the
steady flow is, in general, small. Pitch related actions appeared to be influenced the most.
Numerical solutions for the hydrodynamics of bodies with forward speed in time domain were studied by
Kara and Vassalos (2003). Numerical results obtained for a hemisphere and a Wigley hull showed that
the steady problem effects are quite small by comparison to the magnitude of radiation-diffraction related
values. Time domain simulation of ship motions in short crested irregular waves were carried out by
Inoue and Zakaria (2004, 2005). The radiation forces, for non-harmonic motion, were included in the
equations of motion in the form of convolution integrals. The relevant impulse response functions were
calculated using the cosine transform of the frequency dependent damping coefficients, which in turn
were obtained from the Green’s function with forward speed. Time domain simulations were carried out
to determine ship’s vertical displacement relative to irregular waves. The results obtained support the
Class NK requirements.
2.1.3
3D Nonlinear Methods
2.1.3.1 Time Domain Methods
The time-domain approach is advantageous to study nonlinear problems even in the framework of the
free-surface Green’s function method. There may be several levels of approximations in treating
nonlinear problems. The simplest one using the time domain Green’s function is that the Froude-Krylov
and restoring forces are computed exactly but the radiation and diffraction forces are retained as linear.
This approximation does not increase the computation time as compared to the linear formulation and
accounts for dominant nonlinearities in ship motions and wave loads in large amplitude waves. Along
with this approach, Sen (2002) performed computations of wave loads and large amplitude 3D ship
motions with forward speed. Attention was mainly focussed on the difference between linear and
nonlinear results, and computations were performed for a Wigley hull and a Series-60 model over a
variety of wave and speed parameters. It was shown that a considerable influence of nonlinearities exists
in predicting the instantaneous location of the hull in waves, which is crucial in determining the keel
emergence and deck wetness.
The so-called “body-exact” (body-nonlinear) formulation for the radiation and diffraction problems is the
next higher level of approximation for nonlinearities. In this formulation the transient free-surface
Green’s function is used and thus the free surface boundary condition is linear, but the body boundary
condition is satisfied on the instantaneous wetted surface under the undisturbed free surface. Therefore,
10
ISSC committee I.2: Loads
the computation time in the body-nonlinear formulation greatly increases by comparison to the linear
problem. Commercial codes based on this formulation are available at present, e.g. LAMP version-4
developed initially by Lin and Yue (1991). Kataoka et al (2002, 2003) also investigated the 3D bodynonlinear problem. Although the formulation is the same, they improved the numerical scheme to
reduce the computation time, particularly in the development of a fast calculation scheme for the
transient free-surface Green’s function. The geometrical nonlinear effects of the ship’s hull (such as bow
and stern flares) on the hydrodynamic pressure and wave-induced ship motions were studied.
Comparisons were made with experiments and other calculation methods for Wigley models with and
without flares above the still water level. They found that the amplitude of heave motion near resonance
and the peak value in the added resistance were markedly reduced by the flare effects and that the change
in pressure due to nonlinear effects originated largely from the hydrostatic restoring term.
The time domain analysis is a natural avenue to deal with extreme wave problems. The fully-nonlinear
approach may be ranked as the highest level, but this approach for 3D ship motions is still in an
elementary state of development. Shirakura et al (2002) focussed on establishing a 3D fully-nonlinear
numerical wave tank; but when the forward speed is present numerical solutions based on the Mixed
Eulerian-Lagrangian (MEL) method tend to be unstable in the time marching. The computational
requirements of this MEL method are still too heavy and its capability to deal with arbitrary geometries is
too limited to be routinely used in ship design. Linear and weakly-nonlinear approaches by means of
Rankine panel methods are more efficient. A hybrid calculation scheme, using a Rankine source method
for the near field and the time domain free surface Green’s function to satisfy the radiation condition at a
far field, was studied by Kataoka et al (2004). This hybrid scheme is essentially the same as a
commercial code LAMP version-4, but the analysis in the far field is carried out in a space fixed
coordinate system, which makes the scheme more stable at the expense of numerical efficiency.
Validation of the scheme was carefully performed through comparisons with other calculation methods
and experiments and through sensitivity studies of several parameters involved in the method.
Lin and Kuang (2004) tried to solve fully nonlinear seakeeping problems by a pseudo-spectral method,
combining a local flow analysis near the ship boundary with the global flow analysis by a spectral
method. The model can be used to study both strong and weakly nonlinear interactions between an
arbitrary high speed vessel and arbitrary environment because it combines the pseudo-spectral method in
global operation and the finite element ship boundary. Furthermore, unlike previous ship motion
models, which typically linearise the six degrees of freedom to calculate six velocity potentials (as well
as two more due to diffracted and incident waves), the model solves the six degrees of freedom ship
motion equations exactly by calculating the pressure on the wetted surface of the ship and body buoyancy
forces due to ship displacement, as well as their moments at each time step. The model calculated one
total velocity potential instead of eight. However, the ship motion model can still be significantly
improved for cases such as the prediction of the unsteady ship motion in irregular sea. For example, the
dissipation should be a function of each frequency of the irregular sea instead of the function of natural
frequency. Lin and Engle (2005) applied this method to study the pitch and roll motions of a high-speed
vessel in irregular head and beam seas.
2.1.3.2 CFD Applications in Evaluation of Motions and Loads
There exist strongly nonlinear phenomena that the potential flow theory cannot deal with, such as wave
breaking, green water, slamming with fragmentation of fluid and entrainment of air. Furthermore, for the
prediction of viscous resistance and damping force on a ship advancing and oscillating in waves, freesurface viscous flow computations are prerequisite. Here the term of CFD is used to mean numerical
calculation methods which can deal with viscous flows and/or highly nonlinear phenomena, in contrast
to the potential flow calculation methods. The finite difference, the finite volume, the finite element
method and the particle methods may be typical numerical calculation methods to be categorized within
the term of CFD.
ISSC committee I.2: Loads
11
(a) RANS codes for wave loads and ship motions
Recent developments in computer technology enabled us to implement viscous flow simulations without
explicit approximations. Most of the viscous codes for computing ship motions in waves solve the
RANS equations and the continuity equation. For example Weymouth et al (2003) computed heave and
pitch motions of ships in head waves using an extension of the RANS code developed at the University
of Iowa. After numerical verification, comparisons were made with experimental results for a modified
Wigley model. These confirmed good agreement over a wide range of Froude numbers, wavelengths
and wave amplitudes. Orihara and Miyata (2003) also developed a RANS code named WISDAM-X,
using the finite-volume method and a Marker and Cell-type (MAC) solution algorithm. An overlapping
grid system, a curvilinear body-fitted grid for the near field and a rectangular grid for the far field, was
employed to simulate the wave generation, the interactions of ships with incident waves and the resultant
ship motions. The free surface was captured by the density function method. Unlike other recent works
on unsteady CFD, main interest was placed on the added resistance in waves, and validation was
performed through a comparison with measured results of the S-175 container ship. A fairly good
agreement was shown not only for vertical plane wave loads and heave and pitch motions, but also for
the added resistance.
The current work on CFD simulations at Hamburg Ship Model Basin was reported by Hochbaum and
Vogt (2002), which aims at accurate simulations of seakeeping as well as manoeuvring problems. The
interface capturing was based on the level-set method and computational grids were generated with
commercial software to reduce time for grid generation. Although some results are shown, extensive
work on the validation of the code is still being performed. Similar efforts in solving for the wave loads
and ship motions based on the RANS formulation were reported by Xing-Kaeding and Jensen (2004)
and Wilson et al (2004). The results by Wilson et al (2004) showed the capability of the method for
resolving complex free surface topologies associated with high Froude number, bluff geometry, and
incident waves and the promise for application to large amplitude motions and manoeuvring.
Luquet et al (2004) presented a new method for studying wave-body interactions, in which all unknowns
of the problem were split into the sum of an incident term and a diffracted term; the former may be
provided by a nonlinear calculation method based on potential flow. Then a set of the RANS equations
was modified to compute only for the nonlinear diffracted flow. The boundary conditions were also
modified to define the diffracted problem only, which are satisfied by introducing boundary-fitted
curvilinear coordinates. The resultant formulation is named SWENSE (Spectral Wave Explicit NavierStokes Equations) approach. Numerical computations were performed for the DTMB Model 5512, and
predictions were compared with benchmark experiments. The results for unsteady components of the
force and wave pattern look promising, but the steady components need to be improved.
(b) CIP-based methods for violent flows
In the context of nonlinearities in seakeeping problems, of vital importance are not only global loads and
ship motions but also localized, strongly nonlinear phenomena, such as slamming, water on deck, green
water impact, and sloshing. In these strongly nonlinear phenomena, the free surface will be highly
distorted, and wave breaking and air trapping may occur. For these extreme cases, conventional
numerical approaches based on the potential flow theory will break down, and sharp pursuit of the
interface between water and air will be a key issue. Along these lines a CFD technique using the CIP
(Constrained Interpolation Profile) method was studied by Hu and Kashiwagi (2004). The CIP-based
method is relatively easy to extend to 3D simulations with acceptable resolution and computation time,
because rectangular Eulerian grids were used. Hu (2004) showed an example for a container ship moving
in large amplitude waves at Fn=0.23 (wave length=ship length, wave height/wave length=0.1). This
application included the occurrence of water on deck and wave breaking, which may be sufficient to
indicate that the CIP-based method is very robust even for strongly nonlinear wave-body interactions.
Further validation should be conducted through a quantitative comparison with experiments.
(c) Particle methods for violent flows
The CIP-based method is robust and can deal with strongly nonlinear free-surface flows. However, as
long as a fixed Eulerian mesh is used the numerical diffusion is unavoidable and the resolution will be
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ISSC committee I.2: Loads
worse in 3D problems. Sueyoshi and Naito (2003) applied the so-called MPS (Moving Particle Semiimplicit) method to seakeeping problems, such as motion of a damaged ship in waves, sloshing and wave
impact by green water. In this method 3D computations can be performed without major modification of
the computer code, but the computation time may become prohibitive if the number of particles is very
large for the sake of high resolution. Sueyoshi (2005) devised numerical techniques, such as a cell
portioning method and the parallel computing with optimum memory distribution, to enable calculations
with more than a million particles within practically acceptable computational time constraints.
In contrast to the MPS method, which is popular in Japan, the SPH (Smoothed Particle Hydrodynamics)
method seems to be more popular and applied to seakeeping problems mainly in Europe. This method is
based on a gridless Lagrangian method, same as the MPS method. However, unlike the MPS method,
the kernel function is used to discretise the Navier-Stokes equations and the continuity equation through
a convolution with the variables under consideration. In addition the equation of state for the pressure is
adopted without solving Poisson’s equation for the pressure. The SPH method may be seen as an
emerging technique for solving strongly nonlinear and transient 3D wave-body interaction problems
(Imas 2004). Other examples of the SPH method can be found in section 4.1.
2.2
Analytical Methods in Hydroelasticity
Theoretical models used to predict the hull girder response, e.g. whipping, are usually based on modal
decomposition. For instance, Malenica et al (2003) investigated the hydroelastic response of a very
flexible ship-like floating body. The structural response was modelled using non-uniform Timoshenko
beam theory, whilst the hydrodynamic part made use of the 3D boundary integral equation method. Both
dry and wet modes shapes were evaluated and vertical responses (motions/distortions and displacements
at various positions) obtained in regular waves using a frequency domain analysis. Special attention was
paid to correctly model the hydroelastic effects on the hydrostatic restoring actions. Predicted results
were compared with model test measurements for an elastic barge (two different stiffness configurations)
in regular waves, showing a good agreement in terms of the linear transfer functions (i.e. RAOs). By
applying convolution integral technique it was also possible to investigate the transient response of this
structure in time domain. Comparison between model tests and calculations for a few extinction tests
showed that the proposed methodology reproduces fairly well the time traces of the vertical
displacements at different positions along this barge model. A study comparing predictions from a range
of 2D and 3D methods for these barge models is taking place as part of a European Project
(MARSTRUCT 2003). Hirdaris et al (2003) applied the 3D hydroelasticity analysis to a bulk carrier,
allowing for both symmetric and antisymmetric distortions. The dry hull analysis, to obtain natural
frequencies and mode shapes, was carried out using both beam and 3D idealisations, the latter using shell
elements in FE (Finite Element) software. Consequently, for the latter, the modal internal actions are
represented in the form of element or nodal stress tensors. These are transformed to global wave-induced
loads, such as bending and torsional moments, shear forces etc, through the introduction of transverse
cuts along the hull. Comparisons were made between load predictions in regular waves for three fluidstructure interaction models, namely beam-strip (2D method), beam-3D panel and 3D structure-3D
panel.The agreement is good for the symmetric loads (e.g. vertical bending moment). There are,
however, differences between 2D and 3D methods for the antisymmetric loads (e.g. torsional and
horizontal bending moments). The authors concluded that these differences were due to the assumptions
involved in treating warping in beam idelaisations, especially in areas of structural discontinuities.
Miao et al (2003) extended the 3D frequency domain hydroelasticity analysis to formulate the dynamic
loads on a trimaran travelling in irregular seas, including the effects of slamming, namely bottom/flare
for main hull and outriggers and wet-deck slamming. A 3D structural idealisation is used (see Hirdaris et
al 2003), but longitudinal cuts are also required to obtain modal internal actions for loads such as prying
and splitting moments for this multi-hulled vessel. The steady state responses were obtained by solving
the equations of motion in the frequency domain. The unit impulse response functions matrix was also
determined using Fourier transformation. The transient hull response was then obtained through
convolution integral formulation. The time domain steady state response in irregular seas, defined by
wave spectra, was obtained through superposition. The impact pressure was evaluated using the Stavovy
ISSC committee I.2: Loads
13
and Chuang empirical theory based on the steady state relative motions between the wave surface and a
given panel in a prescribed slamming area. A case study for the trimaran travelling in head and oblique
irregular long-crested seas was presented. There were no comparisons with model or full-scale
measurements. The authors assessed the soundness of the approach used based on the quality of the
results obtained.
Takeda et al (2004) assessed the effect of fluid compressibility on the hydroelastic vibrations of ship
hulls. To this end a FE analysis method was derived to solve the Helmholtz equations for compressible
fluid flow. An experiment to validate the theoretical model was also set up using an exciter test on a box
shaped model and measuring vertical and lateral accelerations and hydrodynamic pressures. A FE model
of the test specimen was generated and coupled with the compressible fluid model. Comparison between
measurements and calculations showed that inclusion of fluid compressibility greatly improves the
predictions in some cases. It was also shown that accounting for fluid compressibility improves the
accuracy of vibrations predictions for the superstructure of a Post-Panamax container ship.
In relation to the prediction of the short-term extreme hydroelastic response, Wu and Moan (2005)
briefly reviewed the so-called hybrid method and POT (Peak-Over-Threshold) technique in relation to
the SL-7 container ship design study, to assess the sensitivity of the hydroelastic response to stiffness
level, stiffness distribution and modal damping. The hybrid method is based on the modal
decomposition of the measured hydroelastic response in time domain, which can be limited to the first
vertical mode in the case of the longitudinal global dynamic loads. The linear and nonlinear component
of each contribution was considered separately. The linear response can be statistically represented
based on standard spectral theory. The nonlinear response is not a Gaussian process so that its peak
distribution does not follow Rayleigh’s distribution; instead the 3-parameter Ochi generalised Gamma
distribution was used, suitably modified by the POT technique in order to account only for peaks that
exceed a certain threshold level. One advantage of the POT technique is that the asymptotic cumulative
distribution of the excesses can be analytically expressed. The use of hybrid method in conjunction with
the POT technique is, therefore, a very efficient tool for evaluating the effects of main design parameters
on the extreme short-term hydroelastic response. The authors concluded that stiffness distribution was
not important; lower stiffness level could reduce extreme responses, especially in hogging. With
reference to modal damping, a 50 % variation resulted only in reduction of 5% and 10%, respectively, for
the extreme sagging and hogging responses.
2.3
Measurements
2.3.1
Model Experiments
There are essentially two different experimental methodologies currently in use for measuring motions
and loads on elastic models :
 fully flexible models and
 flexible segmented models using either a flexible backbone or flexible joints.
Fully flexible models are, in principle, closer to the real-life hull; however, there are some drawbacks. In
particular it is difficult to build a model which accurately reproduces the full-scale ship flexibility and
still has sufficient transverse stiffness to resist the dynamic loads experienced during the tests. A good
review of the technological issues of manufacturing and using full flexible models at CSSRC (China
Ship Scientific Research Centre) is given by Wu et al (2003b) underlining the importance of these tests
in the validation of hydroelastic codes. They have constructed models for a barge, destroyer and for the
S-175 container ship from plastic (ABS) plates of 2 mm thickness. Although there were no longitudinal
stiffeners in the model, the model appeared to be too stiff, resulting in too high natural frequencies of the
deformation modes. No details of the measurement of the strains in the model are given; classical strain
gauges are known to give problems because of local heating of the plastic material. Good correlation
between measured stresses in the deck of the destroyer and predictions using 3D hydroelasticity analysis
were shown. The results with the free running S-175 model were used in the report of the ISSC Special
Task Committee on Extreme Hull Girder Loading (ISSC 2000). They showed a contribution of the 2-
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ISSC committee I.2: Loads
node deflection mode to the vertical bending moment of the same order as the first harmonic component
for larger waves. The main limits of this set-up are that it is only practically possible to scale the first
vertical mode and that it provides direct measurements of local stresses but not global dynamic loads,
which have to be derived from the measurements.
The model used by Okland et al (2003) comprised segments connected with adjustable stiffness joints.
Such an arrangement allows for the correct scaling of the first vertical mode with relative ease by
comparison to fully flexible models. By comparing FE calculations for the continuous and segmented
models, the authors showed that it is possible to assess the relative accuracy of the segmentation with
respect to a given slamming load time history. They also showed that a model with two segments
reproduces fairly well the vertical bending moment at amidships, but that the location of the cut was
quite important and should be decided based on ad hoc FE calculations. In addition it was shown that
vertical shear force at quarter lengths can be well reproduced by a model with two segments; however, in
the case of very short slam pulses models with 3 or 4 segments should be used as the influence of higher
modes may become significant. The effectiveness of a two-segment model in reproducing the whipping
bending moment at amidships was confirmed by Bacicchi et al (2004) for large cruise ships. The same
technique was successfully applied for the measurement of wet-deck slamming loads of a fast catamaran
by Ge et al (2005). Their model was converted from a rigid catamaran by cutting it into pieces,
connected by softer material. Each side hull was divided into three sections longitudinally, with an
aluminium frame mounted in each section. The hull sections were connected by steel springs and
aluminium transducers longitudinally and transversely. The wet-deck comprised four rigid sections. The
flexibility of the model was controlled through the connections; the transverse connecting springs and
beams were longer and, hence, softer than the longitudinal ones.
Another technique consists of connecting separately each segment to a flexible longitudinal beam via
instrumented struts. Its disadvantage is that the beam must be carefully designed and manufactured to
produce the desired modal deformations. The first vertical mode can be scaled using a uniform beam but
scaling the other modes requires a non-uniform beam. Experiments with a segmented fast deep-V ferry
(mono-hull) were reported by Ciappi et al (2003) and Dessi et al (2005). The model comprised six
segments, separately connected to a continuous non-uniform elastic beam (backspline) via joints
instrumented with strain gauges to measure the loads in the cuts. The backspline was rectangular, hollow
and made of aluminium alloy. It was shaped using 20 elements, each of different constant section in
order to model as accurately as possible the scaled bending stiffness distribution of the ship. The design
and verification of the set-up was based on 3D FE calculations. The segments were made watertight
with rubber strips, which appeared to have a large influence on the damping of the deformation modes
(in air). Dry vibration tests were performed to investigate the modal correspondence between the
physical and the FE models, whereas the frequency correspondence was verified with wet vibration tests.
The dry vibration tests confirmed the effectiveness of the model in reproducing the first three vertical
bending modes. Dessi et al (2005) used the same set-up to show the applicability of the Output-Only
technique in identifying the wet modal parameters of a vibrating structure in water. The basis of this
technique is the assumption that the output response is caused by a broadband excitation (i.e. white
noise) of the structure. Modal parameters can be found by several solution techniques such as FFT or
orthogonal decomposition. The objective of these experiments was measuring the whipping response in
waves; no detailed pressure measurements were carried out on the hull. Cusano et al (2003) carried out
segmented model tests, complementing full-scale measurements and calculations, for a deep-V fast
mono-hull ferry. A fibreglass 1:30 model was constructed using six segments rigidly connected to each
to an elastic backbone, representing the real distribution of the bending stiffness along the ship.
Numerical investigation of the structure by FE models produced the required dimensions for the
backbone girder. The hydroelastic tests were carried out in the towing tank where it was possible to
reproduce recursive slamming events followed by whipping phenomena in severe operational conditions.
Interesting experiments were carried out in the BGO-First towing tank in France (Malenica et al 2003).
The aim of the experiments was to validate a computer program for the ship girder’s elastic response.
The model was a barge consisting of 12 elements, connected with elastic plates. The motions were
measured using an optical system (Krypton) that can follow 6 targets, which were placed on every other
ISSC committee I.2: Loads
15
element of the barge, simultaneously. The experiments gave results for the first two deflection modes in
regular and irregular head waves and as a result of an impulsive load on the bow. The results showed a
good correlation with simulations using linear diffraction theory and modelling the girder of the barge as
a Timoshenko beam. The amplitudes of the deformation modes showed clearly the differences between
the wet and the dry eigenmodes.
Whipping loads due to aft body slamming on a large cruise ship were performed by Kapsenberg et al
(2002, 2003). The authors commented on the use of segmented models for evaluating the hydrodynamic
force during impact. They pointed out that what is directly measured is the dynamic response of the
vibrating segment in water and that in order to derive the exciting hydrodynamic force it is necessary first
to invert the response and then to subtract the inertia force. They proposed a two-step procedure. An
array of 33 pressure sensors was mounted on the stern of a very rigid model and the local impact loads
were measured. The model was then cut in half, scaling the frequency of the 2-node vertical mode of the
ship, allowing measurements of the global whipping loads while repeating the measurement of pressures
at the stern. They showed that it was possible to use the total measured integrated pressure on the
aftbody to accurately reproduce the whipping response of the ship. On the other hand Ciappi et al (2003)
derived the hydrodynamic contribution from the total measured force on the bow segment and filtered it
to separate the whipping component from the wave component. The experimental slamming force was
then compared with the theoretical one, evaluated on the basis of measured vertical motions of the ship
and Wagner’s theory, showing good agreement.
Hermundstad et al (2004) also made use of a segmented model with a flexible backbone to measure the
whipping loads on a Ro-Ro ship due to bow flare slamming; details of the experimental set-up are not
given. Additional experiments at BEC (Bassin d’Essais des Carenes) and MARIN are known, but results
are not available in the open literature. The experiments at BEC were carried out on a beamlike model
constructed from very dense foam. The objective of these experiments was to verify the dry and wet
deformation modes. Tests in regular waves were carried out measuring the springing response and also
the response due to an impulse (by hammer). The tests at MARIN were for a free running model of a
ferry. The model comprised 5 segments, connected through a flexible back bone. The objective was to
measure the whipping response due to impacts at the bow. The bow segment was instrumented with 23
pressure gauges for detailed impact pressure measurements.
Analysis of the measurements is quite important. Du et al (2004) illustrated the application of wavelet
techniques as an attractive alternative to standard Fourier analysis. Wavelets are a relatively new
mathematical tool, especially suited to analyse composite time series arising from the superposition of
stationary random processes and highly transient responses. This method was applied to the
measurements for nonlinear heave, pitch, vertical acceleration and vertical bending moment obtained
from the flexible model of the S-175 container ship in regular head waves. The measurements were also
processed using standard Fourier analysis. The results showed that the wavelet method is very efficient
in extracting the high-frequency whipping component of the vertical bending moment without
significantly affecting the data as, for instance, in the case of high-pass filtering which may distort the
signal introducing a phase lag. The accurate decomposition of the time history of the bending moment
into low frequency and high frequency components allowed detection of impact occurrence and
characteristics.
2.3.2
Full-scale Measurements
In an effort to better understand the limits and capabilities of design rules for novel hull forms, Thomas
et al (2003a, c) analysed results of full-scale load measurements for two large (length between 90 and
100m) high speed (design speed 40 knots) catamarans both in trial and regular service conditions. Each
vessel was fitted with a series of 16 strain gauges at various locations, a TSK wave meter, linear
accelerometers and rate gyros. In the first study, types of slamming and their design consequences as
well as the effects of operational conditions are discussed. A Froude number based on relative vertical
velocity at the bow is suggested with a threshold value of 0.15 being required for a slam event to occur.
In the second analysis, results were obtained from full-scale trials of the Incat Hull 050 to develop
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ISSC committee I.2: Loads
realistic load cases for extreme slam events. The load cases were then applied to an FE model of the ship
with the resulting sagging moment compared with DNV (Det Norske Veritas) rules. Results of the
analysis showed that the measured slam load was larger and further forward than that would have been
suggested by DNV rules. Thomas et al (2003b) carried out a spectral analysis of the strain gauges results
clearly showing two distinct frequencies for all gauges, corresponding respectively to the first torsion
mode ( 1.5 Hz) and the first longitudinal mode ( 3 Hz). The average decay coefficients of the
whipping response generally ranged between 0.1 and 0.2. In order to determine frequency, damping and
mode shape of the first longitudinal vibration mode exciter tests were performed on both vessels by
dropping the anchor and immediately restraining it with an electric winch. Four accelerometers,
positioned along the centreline of the vessel, measured the structural response confirming the frequency
of the first longitudinal mode. Normal mode analysis via 3D FE calculations was performed to
determine the primary dry and wet modes of the two vessels accounting for the effect of the added mass.
The comparison of these calculations with the full-scale exciter tests showed a good agreement when
changes in loading condition are accounted for.
Investigations of the structural loads on large fast ferries was presented by Cusano et al (2003) using fullscale measurements, segmented model tests and calculations for a deep-V fast mono-hull ferry. The
measurement system consisted of: three long-base strain gauges, 12 pressure gauges on the forward part
of the hull, strain gauges on the bottom shell plating near the pressure gauges, GPS, roll/pitch
inclinometer, four vertical accelerometers and a wave height meter mounted on the ship forecastle. Inservice data were collected for 1.5 years. The calculations were performed by dynamically loading a 3D
FE model of the ship with a slamming time series reproduced by a 2D boundary element method.
Comparisons between calculated and measured vertical bending moments showed good agreement.
Shin et al (2004a) presented the measurements of longitudinal hull girder stresses obtained through a hull
monitoring system installed on board of a bulk carrier of approximately 300 m long. The system
comprised two long-base strain gauges (placed amidships port and starboard), a vertical accelerometer at
the bow and a pitch/roll inclinometer. The monitoring was performed along the service line from Korea
to Brazil. A comparison of the data collected in one month (from Korea to Cape town) was carried out
with calculations based on 2D strip theory for the amidhsips vertical bending moment. The calculations
referred to the sea conditions recorded in the log-book. The comparison showed similar trends, but
differences in the magnitudes were attributed to uncertainties in logged sea conditions, especially wave
heading and period. The authors also discussed recent IMO (International Maritime Organisation)
recommendations on having hull monitoring systems installed on ocean going vessels. Storhaug et al
(2003) reported on the installation of a hull monitoring system on board of a large ocean going ship,
consisting of: wave radar for directional sea spectra measurement, GPS for ship speed and course,
Motion Reference Unit (MRU) for ship motions, strain gauges for global stresses in the hull girder,
accelerometers for vertical accelerations and pressure transducers for bottom pressures. The
measurements presented in this paper refer to 11 loaded and 11 ballast voyages, equivalent to a duration
of 6 months in the open sea. The measurements showed the presence of the 2-node vertical vibrations,
assumed to arise from springing excitation as bottom and bow-flare slamming events were very rare. A
possible cause of the observed hull springing could, however, be stern slamming. The accuracy of wave
radar was questionable. A comparison of full-scale measurements with calculations was also performed
using different numerical codes, namely nonlinear 3D Rankine source in time domain using modal
decomposition to model hull flexibility and various nonlinear strip theory formulations using beam
configurations to model hull flexibility. The wave frequency results were in fairly good agreement with
the measurements for all methods used. On the other hand predicted high frequency results deviated
significantly from measurements. The main reason for this failure was attributed to the inaccurate
prediction of the exciting force, and the possibility of overpredicting stern flare slamming effects. The
authors also showed that springing vibrations can be statistically modelled using a one degree of freedom
system driven by wave excitation.
Sato et al (2005) discussed full-scale measurements on a LNG ship and the differences between assumed
design operational conditions and actual wave encounters. Long-based strain meters were used to
measure hull girder stresses over a three year period. By locating the strain meters within the passenger
ISSC committee I.2: Loads
17
deck, thermal effects were assumed to be negated. Adjusting measured strains to the ship’s upper deck
were accomplished by considering the distance from the neutral axis.
Results of full-scale trials on planing craft were presented by Garme and Rosen (2003). The trials
indicate that, contrary to conventional wisdom, the largest impact loads do not necessarily occur in a
head seas condition. Maximum loads during this trial were found to be present at an oblique heading of
30o (0o denoting head seas). While operations in head seas result in larger motions and relative
velocities, bow sea conditions give rise to smaller deadrise angles that can more than offset the benefits
of bow sea operations.
2.4
High Speed Craft
As the need for high speed transport grows, the marine industry has responded by designing a variety of
novel hull forms. However, the use of novel hull forms leads to a pushing of the design envelope,
beyond which traditional means of hull form evaluation can be considered acceptable.
Moan (2003) presented a general review of recent developments of criteria and analysis methods of high
speed craft. The need for performing direct computations is highlighted as it is felt that the continuing
advances in hull form design and materials can not be properly addressed by previous knowledge and
rules. Although classification societies now allow designers to utilize a first principles approach, the
complex nature of high speed craft has limited the use of such methods in the overall design process.
Along those lines, the need to augment rule based design with a first principles approach is discussed by
Wang et al (2005). The overall procedure utilizes all levels of technology, ranging from frequency
domain predictions, time domain simulations and comparisons with historically based vessel rules. By
using such an approach, designers can take advantage of efficiency of frequency domain analysis to help
determine the general trends of a hull form’s dynamic response in a seaway. Time domain simulations
are then used to determine if there exists any nonlinear behaviour that may lead to unacceptable
performance. Overall results are then compared with existing vessel rules to ensure that any lessons
learned from previous designs are addressed.
Addressing the needs of the designer, Pastoor and Tveitnes (2003) discussed a method to account for
changes in ship speed and/or heading in developing an overall ship operational profile. The procedure
identified the need to ascertain critical responses, response criteria, operator actions and prioritisation of
operator actions. Given the uncertainty associated with limiting response criteria the authors suggest that
sensitivity studies be performed in order to determine the effect of changes to criteria. In theory the
proposed methodology is suitable for both conventional and multi-hull ships. However, in practice,
limitations in the numerical simulation methods for high speed ships precludes such an approach for
general use. Boote et al (2004), presented a process for designing structural scantlings of trimaran based
on a first principles approach. Although HSC (High Speed Craft) rules are considered, the authors note
that application of such rules for a trimaran are not appropriate due to differences in motions and load
concerns specific to a trimaran design. The proposed approach applied a recently developed 3D
frequency domain panel code to support short and long term load analyses. While the overall approach is
applicable to both mono- and multi-hulled vessels, nonlinear behaviour (i.e. whipping, asymmetric
hog/sag) was not directly accounted for.
With respect to the testing of catamarans, Okland et al (2003) discussed the general procedures
performing loads testing with a segmented model. While reasonable results can be obtained by using a
basic two-segment model, the authors stated that a minimum of 4 segments is required to get accurate
measurements of acceleration. The effect of slamming of the wet-deck on multi-hulls continues to be a
design issue. Zhao (2003) presented a generalized Wagner solution for predicting impact forces and
pressures for a catamaran with and without a centre bow. In addition, a series of computations were
made to examine the effect that roll angle has on the impact forces of a ship with a centre bow. It was
determined that impact pressures increased with increasing roll angle. As for the case of a catamaran
with a flat wet deck, it was determined that impacts will take place in the fore-body of the wet-deck in
long waves and that the location of impact will move further aft as wave length decreased.
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There are developments originating from Delft University related to high speed vessels with a very
slender bow and a downward sloping contour. These investigations were continued by Keuning et al
(2002) and Eefsen et al (2004). The idea behind this development is to reduce the peak vertical
acceleration at the bow by reducing the nonlinear effects at water entry. For high speed vessels with a
normal V-shaped bow there is a clear distinction between the distribution of the positive and negative
vertical acceleration at the bow that can amount to a difference by a factor 2. The newly developed AXE
bow, features very slender waterlines and forward sections that are almost vertical. This shape shows
distributions of the positive and negative accelerations that are much closer indicating a much more
linear behaviour. These conclusions are based on numerical results using a nonlinear strip theory and
experimental results (Keuning et al 2002). The reduced vertical accelerations will also reduce the
whipping of the ship and the fatigue life; this aspect is not covered in the quoted literature.
For high speed planing craft most of the effort involves use of 2D potential flow theory, with
nonlinearities accounted for by the treatment of the instantaneous underwater hull form. Applications
appear to be limited to vertical plane responses only. This is reflected in the lack of availability of
validation data relating to planing craft responses in oblique seas. Other methods were also applied. For
example, Sclavounos and Borgen (2004) developed a 3D Rankine panel method to predict the motions
of a high speed, foil assisted, mono-hulled vessel (Froude number 0.6). In this paper the SWAN-2
Rankine panel method is extended to include the effects of lifting appendages and in particular passive
hydrofoils. Bertram et al (2003) described three methods to simulate planing craft in waves. One is
based on Wagner’s theory of hydrodynamic impacts, the others used a RANS solver applying different
computational grids to the boat motions. Comparisons were made with experimental results for a Froude
number of 0.4.
2.5
Large Amplitude Roll
Large amplitude rolling has become a significant problem with relevance to new ship designs, such as
large container vessels or Ro-Ro ships. This may occur due to parametric excitation and pure loss of
stability on the crest or sometimes in a beam sea resonance condition.
Parametric excitation has its source in the change of righting lever between crest and trough in
longitudinal seas. It depends on the relationship between the frequency of these changes, i.e. the wave
encounter frequency, and the roll natural frequency. Theoretically it can occur at approximately 2:n
ratios between these two frequencies, where the integer n=1, 2, 3, … . In practice the cases for n=1,
when the wave encounter frequency is approximately twice the roll natural frequency, and n=2, when the
wave encounter and roll natural frequencies are nearly equal, are of importance. Typically the former
case (n1) occurs in head and bow quartering seas (e.g. France et al 2003, Belenky et al 2003, Kreuzer
and Sicherman 2004), but can also occur in following seas (e.g. Umeda et al 2004). The latter case (n2)
is typically associated with following and stern quartering seas (Krüger et al 2004). Following the
incident associated with a Post-Panamax C11 class containership effort focussed on parametric roll in
head and bow quartering regular waves and seas. For example France et al (2003) reported on
experimental and numerical investigation on a C11 containership. They used the FREDYN and LAMP
codes, which include nonlinear effects, in their numerical analyses and showed that such tools are
suitable for simulating these phenomena. In regular waves the authors confirmed a set of conditions for
the occurrence of parametric roll, namely : wave encounter frequency nearly twice the roll natural
frequency, ship length of the same order as wave length, roll damping (which is speed dependent) below
a certain threshold and wave height above a certain threshold. They also confirmed occurrence of
parametric roll in irregular seas, where it occurs suddenly causing large roll amplitudes within two or
three cycles. If the resultant roll amplitudes are severe enough, they may lead to cargo loss, due to failure
of cargo securing equipment, or even capsizing. Sometimes in head seas large rolling angles occur if the
vessel reduces speed close to zero, after having hit a large wave or wave group. In this situation the
vessel may suffer from heavy rolling if the induced roll moment is large enough, e.g. for vessels with
large bow flare. This phenomenon is sometimes related to parametric rolling, but large roll amplitudes
mostly occur as a result of insufficient damping due to low speed and excessive roll moment generation
due to the large bow flare. Levadou and Gaillarde (2003) continued with numerical simulations for the
ISSC committee I.2: Loads
19
C11 containership, using FREDYN, by investigating a range of speeds, headings (head and bow
quartering seas), significant wave heights and load conditions. Their investigations showed that high
sustained speeds reduce the risk of parametric roll. Following seas were not investigated, but the authors
noted the possibility of parametric roll occurrence for such cases at low or zero speed. From full-scale
observations at high values of metacentric height, parametric rolling problems are typically associated
with head sea scenarios (Lövstadt and Bloch Helmers 2004). However, systematic model tests have
demonstrated clearly that the problem also occurs in stern quartering seas and low values of initial
stability, especially when the vessel has sufficient time to stay on the crest (Krüger et al 2004). Due to
the alteration of the initial metacentric height between crest and trough, as well as due to the
acceleration/deceleration of the vessel, critical resonances may differ significantly from linear
estimations of resonance scenarios and cover typically a range of courses, speeds and wave lengths. In
this respect, the behaviour of the vessel in regular and irregular waves differs significantly.
Recent full-scale observations (DNV 2005) have shown that especially container vessels are very often
operated in bow or stern quartering seas which lead to large rolling motions. Consequently, a necessity
to update wave induced hull pressures based on the consideration of large rolling is necessary. The cargo
loss for container vessels has been the subject of several investigations. Shin et al (2004c) applied
several codes (i.e. FREDYN and 3D LAMP) to a range of large container vessels to evaluate criteria for
parametric roll, showing both codes capable of predicting the relevant phenomena in head seas with
sufficient accuracy. Ribeiro e Silva et al (2005) applied a partly-nonlinear time domain model with five
degrees of freedom (all rigid body motions except surge) to analyse parametric roll in head seas. The
nonlinearities included correspond to the evaluation of restoring coefficients using the instantaneous
wetted surface. Other hydrodynamic effects were obtained from a strip theory, although viscous effects
were included in roll damping by comparison with decay tests. Comparisons were made with
experiments in regular waves on a containership and the authors conclude that the method is capable of
predicting parametric roll in regular and irregular head seas. Umeda et al (2004) on the other hand made
use of experimentally measured roll restoring moment in their analysis of a containership in head and
following seas, using a system with one degree of freedom. Clauss and Hennig (2003) developed a
nonlinear wave theory which allows the numerical formulation of harsh waves and also the
transformation of the wave surface upstream to generate wave maker signals in model tests. They
obtained a numerical wave model which includes the possibility to introduce freak wave sequences into
any irregular sea state. Using this technique, they could generate tailored deterministic wave sequences
that could be used to generate wavemaker signals for model tests (Hennig et al 2003). Kühnlein and
Brink (2002) developed a new model testing technique using these tailor made irregular seas where the
model was allowed to travel freely and all six degrees of freedom were measured by video signals. The
combination of these two techniques allows generation of validation material from model tests, as not
only the motions of the model were measured, but also the time dependent wavy surface is known in
each time step. Using this testing technique, hull bending moments, shear forces and torsional moments
were measured for two Ro-Ro models in stern quartering seas. It was found that the influence of the
rolling motion, especially on the torsional moment, is significant. Hennig (2005) used nonlinear wave
theory to generate tailor made wave sequences for capsizing model tests of a Ro-Ro ferry. The capsizing
sequence was defined beforehand by numerical simulations and then verified during the corresponding
run in the towing tank. The results showed that it was possible to define and repeat deterministic
scenarios that lead to large amplitude roll motions in model testing and a database was created with the
purpose of validating numerical models. Krüger (2006) analysed the cargo loss of a Panamax container
vessel in stern quartering seas applying Cramer and Krüger’s (2001) nonlinear strip theory. This is a
time domain method where roll and surge are modelled and it was validated against a series of systematic
model tests using vessels characterised by large stern flare. An example of the simulation produced is
shown in Figure 3. Container vessels are vulnerable to large rolling amplitudes in quartering seas and the
method predicted this phenomenon with sufficient accuracy. Krüger (2006) concluded that the vessel
suffered from large amplitude motions caused by 1:1 resonance parametric roll problem in irregular stern
quartering seas.
Large amplitude rolling may also occur, though rarely, in beam sea scenarios when the wave length is
short enough and the encounter frequency is close to the natural frequency of the vessel. This is mainly
20
ISSC committee I.2: Loads
associated with the so called dead ship condition. Themelis and Spyrou (2003) investigated lashing
forces in a Ro-Ro vessel under intensive rolling in beam sea scenarios by directly solving the differential
equation of rolling motion. They obtained time series of the rolling angle and determined lashing forces,
including trailer dynamics.
Figure 3: Capsizing due to parametric rolling in stern quartering seas, calculated by the nonlinear strip
method ROLLS (Cramer and Krüger 2001).
2.6
Ice Loads
The Specialist Committee V.5, on Structural Design for Ice Loads, of the ISSC served two terms, namely
1997 and 2000. Therefore, it is incumbent upon this committee to address the subject of ice loads.
Exploration for petrol, natural gas and mineral resources in places such as, the Arctic, Newfoundland,
Alaska, the Okhotsk Sea etc resulted in a significant increase in demand for ice class ships, particularly
tankers. The development of ice-strengthened ships for year-round navigation in Arctic regions
prompted interest in the subjects of hull-ice interaction and improvement to structural designs capable of
resisting extreme ice loads. Questions of equivalency of different ice-class rules have been raised again.
Verification of designs and constructions for relevant ice operations is a high priority item.
Measurements (model experiments and full-scale trials) and analytical/numerical methods are used to
investigate the strength of the hull structure
Gagnon (2004) and Crocker et al (2004) discussed population and environmental and physical aspects of
ice loads due to collision with Small Ice Mass to Parent Iceberg (SIMPI). This term describes small
ISSC committee I.2: Loads
21
icebergs, bergy bits or growlers. Free-floating parallelepiped-shaped growlers were impacted with a
plate designed to simulate a ship bow by Gagnon (2004). The tests were conducted at speeds ranging
from 0.2 to 3.0 m/s, at three growler orientations, and at three plate impact angles. The results indicated
that the peak loads were increasing linearly with impact speed and also with impact angle. The highest
peaks were observed when the long axis of the growlers was normal to the impact plate surface.
Johnston and Gagnon (2005) presented MOTAN, an inertia measuring system, to evaluate impact loads
between the mass of ice and a ship, and its validation using data from model and full-scale experiments.
The model and full-scale tests were carried out on the CCG icebreaker Terry Fox during a collision with
iceberg ice. The model and full-scale vessels were used to create controlled impacts, and the global force
was measured on the impact plate. Experimental results were compared to those obtained from MOTAN
installed in the model and on the ship in two locations. The best correlation between MOTAN derived
and measured loads was for sway, pitch and surge force. Ralph et al (2003) described a strain gauge
array system used to measure the ice impact loads on the Terry Fox. These trials are quite unique, as
they are the only case of a deliberate test of ship-iceberg collision. Three independent systems capable of
determining the impact load were employed. Lensu and Hänninen (2003) presented a methodology for
short-term ice load prediction using a prototype ice load monitoring system installed on vessels operating
in ice-infested waters of the Baltic Sea. The system provided real time information on ice loads and on
ice damage risk to the ship. The estimate of damage risk is based on the probability of occurrence of
high ice loads against the hull. The load predictions were derived from statistics of monitored ice
induced loads (peaks) during short periods. The impact of environment (ice cover, ice thickness, ice
type) and vessel operational conditions (speed, manoeuvring) on predicted loads was also discussed.
This system is envisaged to be also applicable for strategic route planning, and the determination of longterm statistics for development of design criteria and classification rules. Uto et al (2005) conducted
full-scale trials to measure the response of an icebreaker hull structure. The measurements were carried
out during operations in selected large ice floes in continuous and ramming icebreaking modes. In all
test cases the ice was less than 50 cm thick and covered by snow. For the tests the forward part of the
ship was instrumented. During trials the maximum ice load experienced was 750 kN/m in 50 cm ice,
which is higher than the design load specified by IA-Super class in the Finish-Swedish Ice Class Rules.
The authors also concluded that during continuous breaking, the peak loads depended strongly on the
operational speed of the vessel.
Frederking (2003) presented data collected during full-scale trials conducted on the icebreaker CCGS
Louis S. St. Laurent. The ship was instrumented to measure hull responses to ice loads in three
locations: bow, shoulder and bottom. This paper discussed the analysis of data from the bow location.
Six main frames were instrumented with strain gauges to measure the shear strain difference between
two stringers spaced 3 m apart. A FE model and analysis of the instrumented area were conducted to
transform the measured strains into loads. Environmental data, ice classification by type, ice thickness,
ridging and ice concentration, were based on hourly observations from the bridge and confirmed by
video record. As a result an average pressure on 30 sub-panels, and the total ice load on the instrumented
portion of the hull, were determined. The author indicated that local pressure can be related to design
area through a power relationship. Jordan et al (2005) discussed aspects of load exerted by an ice mass
on a structure. They presented two relationships, one for global loads and one for local loads. The
global loads represented the total force/pressure applied to a structure and the impact area was defined as
the projection of the ice mass onto the structure. The local loads presented were maximum pressure(s)
exerted on a particular contact area of the structure, and was represented by smaller area(s) of the
projected area. The local areas are subjected to pressures significantly higher than the global, averaged
out, pressures. The authors indicated that both local and global pressures decrease with increasing area
and noted the importance of load duration on average pressure. The presented analyses were based on a
full-scale fixed structure, and ramming data from icebreakers.
There has been a move towards plastic based limit state design analysis, to mitigate the consequences of
overload conditions. At the design load level the structure is intended to exhibit some plastic behaviour,
yet maintain substantial reserve against actual collapse or rupture. With this philosophy as a basis,
plastic limit states are needed in the design process, particularly for icebreakers and ice going vessels. A
22
ISSC committee I.2: Loads
new IACS (2003) standard for Polar Ship design, in the form of a Unified Requirement (UR) is in the
final stages of development. The UR is a construction standard that prescribes minimum scantlings
through a set of structural formulae. The UR formulae for shear area and section modulus are derived
from an analysis of plastic frame collapse. Daley et al (2005), Daley and Hermanski (2005), and Pavic et
al (2004) conducted numerical and experimental investigations of plastic based limit states to physically
validate the proposed rules. This is important given the novel formulation of the interaction effects. A
specific need to validate the proposed limit states with controlled physical tests relates to the possibility
of local buckling and similar instabilities. The plastic collapse limit states assume the frame stable, even
when fully plastic. The FE models were unable to show such instability, as the mesh size would have to
have been very fine, and the analysis would have had to be in ‘displacement-control’ mode. The physical
experiments will show if there are any conditions in which the stability issues negate the validity of the
limit states. The experimental specimens include full-scale size single frames, small grillages (three
frames together) and large grillages (three small grillages together) to investigate the full impact of
boundary conditions on the reserve plastic capacity of tested frames. Belenky et al (2005) conducted
plastic limit analysis to derive limit loads defined as a maximum static load sustained by a structure until
it fails. In this study the failure was defined as either disintegration, or plastic deformation to a nonusable form. The limit load was treated as a general criterion rather than a specifically defined
allowance. This allowed all elements of the structure to be designed to the same safety margin. The
study considered simple grillages with identical frames and a single stringer, as well as more complicated
sections with web frames and multiple stringers. The resultant formulae can be applied to the design of
side grillages for different type of ships subject to lateral loads, including ice and wave loads.
2.7
Wind Loads
For ships with large lateral windage areas, such as cruise liners or Ro-Ro passenger vessels, wind loads
have become a governing criterion in the so called dead ship condition, namely when the vessel is
exposed to beam seas and beam wind at zero speed due to loss of propulsion power (Iskandar and
Umeda, 2001). In this situation wind induced cross forces and heeling moments are dominant.
Furthermore, drifting forces at the underwater hull are generated which contribute to the heeling moment.
A detailed analysis of the related phenomena, both experimentally and theoretically, was requested by the
IMO/SLF 48 with respect to a revision of the weather criterion (Iskandar and Umeda 2005). The
revision was initiated by the suggestion that the wind loads assumed in the actual weather criterion are
too conservative for certain types of ship, especially large cruise liners. As a consequence, these loads
were studied by several groups of authors.
Bertaglia et al (2003a, b) analysed two large cruise vessels in the wind tunnel at different heeling angles.
They obtained cross forces and heeling moments for different angles of attack and heeling angles. Their
conclusion was that the measured loads were smaller than the prescribed ones by the IMO weather
criterion which would then lead to a smaller static heeling angle or required GM, respectively. Aage et
al (2004) collected and analysed many recent wind tunnel measurements for different types of ship when
suggesting a new approach for a wind criterion. They summarized the resulting wind heeling levers for
different ship types and gave recommendations for wind tunnel experiments. They found that for some
types of superstructure the resulting heeling moments could be larger than the prescribed IMO values,
especially when vortex separation at sharp corners plays a role. Bulian and Franchescutto (2004, 2005)
suggested a procedure to determine the effect of combined action of wind and waves on the rolling
motion. They also included in their model wind speed fluctuations using a horizontal gustiness
spectrum. Results were presented for the short term prediction of the capsizing probability of a cruise
liner and a fishing vessel. They concluded that for capsizing problems the wind gustiness plays a minor
role. Furthermore, they suggested a probabilistic model for the wind induced roll moment. Umeda
(2005) presented experimental results for wind heeling levers of a Ro-Pax ferry, suggesting alternative
procedures to fulfil the prescribed weather criterion. He concluded that the experimentally determined
heeling lever is significantly smaller than the value determined by the IMO procedure. He further gave a
summary on resulting wind velocities determined for some 50 vessels and compared them to the
prescribed design wind velocity by IMO.
ISSC committee I.2: Loads
3.
ENVIRONMENTAL LOADS ON OFFSHORE STRUCTURES
3.1
Computational Methods for Fixed and Floating Structures
23
As reported in the 15th ISSC (2003), the linear solution of wave diffraction and radiation around an
offshore structure has reached a mature level. Recent developments are essentially enhancements as
reported by Newman (2004) for WAMIT and by Chen (2004) for HYDROSTAR software. The
enhancements include the linear seakeeping coupling with the dynamic effects of liquid motion in tanks,
the effect of moonpools and the treatments of gap resonance between hulls.
3.1.1
First and Second Order Wave Loads and Induced Responses
There are still several important issues in the second order solution. The first is the development of new
formulations for the computation of second order loads and the degree of accuracy in the approximation
of low frequency wave loads reported by Naciri et al (2004) in which the results using different
approximation (and software) are compared. The second concerns the consistent solution of wavecurrent interaction (section 3.1.2). Another resides in the application to multi-body cases (section 3.1.3).
Furthermore, Molin et al (2005) investigated the third order interaction between incoming waves and
reflected wave fields from a vertical plate. The application to access the run-up along the side hull of a
barge in beam sea showed that the wave elevations are in good agreement between the third order results
and model test measurements which are significantly higher than those predicted by the linear or second
order theory.
Ren et al (2003) presented a 3D computational method of wave loads on turret moored FPSO tankers.
The linearised restoring forces acting on the floating body by the mooring system are calculated
according to the catenary theory, which are expressed as the function of linear stiffness coefficients and
the displacements of the upper ends of mooring chains. The hydrodynamics coefficients of the ship are
calculated by 3D potential flow theory (low forward speed). The equations of motion are solved in
frequency domain, and the responses of wave-induced motions and loads on the ship can be obtained.
Zheng et al (2004) presented an analytical method for the radiation and diffraction of water waves of a
rectangular buoy in infinite water depth. Analytical expressions for the radiated potentials and the
diffracted potentials were obtained using the method of separation of variables. The unknown
coefficients in the expressions were determined through the eigenfunction expansion matching method.
Wave excitation forces were calculated by two different approaches, namely using the radiated potentials
through Haskind’s theorem and using the diffracted potential. It can be seen that the latter approach for
wave forces on a rectangular buoy is much simpler than the former. Regarding multiple bodies, Wu et al
(2004b) presented a method for calculating the hydrodynamic force of a SWATH in waves. This is
carried out using 3D floating fluctuation source Green’s functions and the method of straight boundary
elements.
Bai et al (2003) investigated the nonlinear wave radiation of a surface-piercing body of arbitrary shape in
three dimensions using time domain second order method. In this approach, Taylor series expansions are
applied to the body surface boundary condition and the free surface boundary conditions; Stokes’
perturbation procedure was then used to establish corresponding boundary value problems at the first and
the second order of wave steepness with time independent boundaries. A boundary element method
based on B-splines was used to calculate the wave field at each time step, and the free surface boundary
condition is satisfied to the second order by a numerical integration in time. An artificial damping layer
was adopted on the free surface to avoid wave reflection. Additionally, a mathematical manipulation
was adopted to remove the second order spatial derivatives in the body surface boundary condition.
Wang (2004) presented a series of computational models for the statistical characteristics of random
wave motion. The parameters for fluid field induced by waves and the motions and encountered loads
for floating structures in waves were simulated. This paper deals with the parameters of the design wave
in Chinese coastal areas, the calculation of the fluid field induced by nonlinear waves, modifications to
the strip method and 3D source and sink distribution method in determining motions and loads
encountered in waves. These were validated and applied to the marine engineering practice.
24
3.1.2
ISSC committee I.2: Loads
Wave-current Interactions
Since the original work by Wichers (1988), the problem of wave-current interaction has received much
attention as its solution provides the so called wave drift damping, an important component in the motion
simulation of moored systems. Although the classical work in this subject area has been discussed in the
ISSC Loads Committee reports for 1997 and 2000, it is worth providing the important references in use,
e.g. Zhao and Faltinsen (1988), Wu and Eatock Taylor (1990), Nossen et al (1991), Clark et al (1993)
and Chen and Malenica (1996). The theoretical breakthrough is that the fundamental solution (Green’s
function) of wave-current interaction can be obtained by the derivatives of the zero forward speed
Green’s function. This results in an easier solution than that associated with forward speed. The
formulation of the Green’s function developed by Noblesse and Chen (1995) is more physically
consistent. Based on the use of this non-secular Green’s function, the consistent solution reported by
Chen and Malenica (1996) provides not only the global wave loads but also the correct wave kinematics
around the body. Furthermore, its extension to the multi-body case was carried out by Chen et al (2005),
which would not have been possible using the secular solution. Finally Lin and Li (2003) developed a
3D numerical model to investigate the problem of wave–current–body interaction. This model solves the
spatially averaged Navier–Stokes equations. Turbulence effects were modelled by a sub-grid scale
model using the concept of large eddy simulation.
3.1.3
Multi-body Interactions
The classical problem of multi-body interaction has recently received increasing attention due to
developments in offshore Floating Production Storage Offloading (FPSO) units. In addition more large
floating LNG terminals are being developed in remote offshore locations where marine environment can
be hostile. As the important part of the LNG system, the terminal can be of a barge type LNG/FPSO
including accommodation, gas preconditioning and liquefaction plant, a number of storage tanks and
offloading facilities. It also serves as a support for mooring LNG carriers during offloading operations,
as reported by Naciri and Poldervaart (2004). The mooring of LNG carrier side-by-side with the terminal
is considered as the preferred option. In the design of such mooring systems for LNG/FPSO terminals
and LNG carriers in deep water or shallow water zones, one key issue is the accurate simulation of low
frequency motions of the system, where the second order wave loading is well known as the main source
of excitation. In addition, the multi-body interaction and the dynamic effects of liquid motion in tanks
have to be taken into account in a consistent and efficient way.
Two important issues arise in the evaluation of second order wave loads. The first concerns the accurate
computation of drift loads. For a single body, the choice is between the near-field formulation of
pressure integration and far-field formulation based on the momentum theorem (Maruo-Newman). The
far-field formulation is preferred since it is very robust, but not applicable to multiple bodies, unless the
momentum theorem is applied in properly defined fluid regions surrounding each body of the multi-body
configuration. One approximation given by Fang and Chen (2002), applying directly the classical far
field formulation to evaluate drift load on each body, was commented on as inconsistent by Kashiwagi et
al (2005). Use of the near-field formulation appears to be the only way; but this is well known for its
poor convergence even when higher order boundary elements are implemented, as reported by ISSC
(2003). The so called middle-field formulation, recently developed by Chen (2005b), provides results as
accurate as the far field formulation and as general as the near-field formulation. Unlike the formulation
by Ferreira and Lee (1994) and Mavrakos (1995), which applies local momentum theorem, this new
formulation is derived from the pressure integration and can then be extended to compute the second
order low frequency loads. An example application of this method is shown in Figure 4, with the mesh
of the LNG terminal (right half) and control surfaces (left half) presented in Figure 4(i) and the resultant
non-dimensional transverse drift force in oblique waves of 195 o heading shown in Figure 4(ii). Three
meshes composed of 1490, 3816 and 7824 panels on the hull surface were used. The drift force was
calculated using the near-field, middle-field and far-field formulations for all 3 meshes and nondimensionalised by ( g L/2),  denoting water density, g gravitational acceleration and L the terminal’s
length. Although different symbols are used to denote the different meshes for the middle- and far-field
formulations, the predictions in Figure 4(ii) indicate that both formulations converged and the differences
ISSC committee I.2: Loads
25
due to various meshes are very small for the entire wave frequency range. On the other hand the results
for the near-field formulation are not convergent for the largest part of the wave frequency range.
(i)
(ii)
Figure 4: (i) Mesh of LNG terminal (right half) and control surfaces (left half); (ii) Resultant nondimensional transverse drift force against wave frequency (rad/s) using far-field, middle field
and near-field formulations – (a) 1490, (b) 3616 and (c) 7824 panels (Chen 2005b).
Another issue concerns the large wave kinematics in the confined area between bodies. Unlike the
resonant response of the body's motion associated with the balance of inertia and stiffness loads, this
resonant kinematics of fluid is due to the hydrodynamic interaction, namely wave kinematics annulled or
amplified by the complex scattering between bodies described by Huijsmans et al (2001). Within the
framework of the classical potential flow theory, there is not any limit in predicting wave elevations at
the free surface while the resonant motion in reality must be largely damped by different mechanisms of
dissipation. This unrealistic fluid motion magnifies the wave loads on the bodies. To hold the wave
motion back to a realistic level, Buchner et al (2001) developed a method consisting of placing a lid on
the gap in between the two bodies. The unrealistic wave kinematics is then suppressed. In fact, no wavy
elevation is possible under the rigid lid and notable perturbation around the ends of the lid due to the
diffraction effect can be observed. To allow for wavy motion on the lid Newman (2004) renders the lid
flexible using a set of basis functions in the form of Chebychev polynomials. The deformation of the
flexible mat (equal to the free-surface elevation) is then reduced by introducing a damping coefficient. A
26
ISSC committee I.2: Loads
new method presented by Chen (2004) is based on the introduction of a linear dissipation force in socalled fairly perfect fluid. The dissipation term appears in the boundary condition on the free surface. It
is shown that the method is efficient and in good agreement with measurements of model tests, although
the dissipation parameter remains to be determined by results of model tests or CFD computations. An
example of using this concept of dissipation area in the gap, applied to two side-by-side barges is shown
in Figure 5(i). The resultant free surface elevation at the centre of the gap, non-dimensionalised by the
incoming wave amplitude, against wave frequency (model scale) is shown in Figure 5(ii). In this figure
the predictions without (=0, broken line) and with (=0.016, solid line) dissipation are compared with
model test measurements (denoted by squares), where  is the dissipation factor. Further applications are
presented by Malenica et al (2005).
(i)
(ii)
Figure 5: Prediction of free surface elevation in gap area between bodies. (i) Mesh for side-by-side
barges; (ii) Non-dimensional free surface elevation at centre of gap against wave frequency
(rad/s) – broken line denotes case without dissipation, solid line case with dissipation factor
of 0.016 and squares denote model test measurements (Chen 2004).
Zhang et al (2004) presented a wave load computation approach for direct strength analysis of semisubmersible platform structures. Considering the differences in shape between pontoon, column and
beam, the combination of accumulative chord length cubic parameter spline theory and analytic method
were adopted for generating the wet surface mesh of the platform. Hydrodynamics coefficients of the
ship were calculated using 3D potential flow analysis (low forward speed). The equations of motions
were solved in the frequency domain, and the responses of wave-induced motions and loads on the ship
were obtained.
ISSC committee I.2: Loads
27
Wang and Zou (2004) developed a 2D time domain coupled numerical model for efficient evaluation of
nonlinear wave forces acting on a moored ship in harbour. The fluid domain is divided into an inner
domain and an outer domain. The inner domain is the area under the ship section, governed by Euler
equations. The outer domain is the area outside the two sides of ship’s hull, governed by Boussinesq
equations. Matching conditions on interface boundaries between the inner and outer domains are the
continuation of volume flux and the equality of pressures. In addition, the boundary element method was
adopted to verify the coupled model.
Wu et al (2003a) calculated the hydrodynamic coefficients of a floating multi-body system using 3D
Green’s function method. Hydrodynamic coefficients as a function of the distance between floating
bodies were given. Wu et al (2005) used an eigenfunction expansion method to tackle the diffraction
and radiation for a floating vertical circular cylinder over a coaxial cylindrical caisson in water of finite
depth and in the presence of incident linear waves. The radii of the caisson and the floating vertical
circular cylinder are the same. The analytical solution is presented for the radiation potentials due to
heave, surge, and pitch and for the diffraction potential due to the diffraction of an incident wave acting
on the fixed cylinder. A set of theoretical added masses, damping coefficients and exciting forces is
proposed. The results from these expressions are the same as that of a cylinder in water of finite depth.
Two methods were presented for calculating exciting forces, producing the same results. Finally
analytical results of added masses, damping coefficients and exciting forces were obtained for different
depths of the caisson. It is concluded that the effect of the caisson on the heave and pitch motions of the
cylinder is notable, but not so notable on the surge motion．
Gou et al (2004) used the boundary integral equation method to study the hydrodynamic interaction
effects between wave and two connected floating structures. The hydrodynamic interactions between the
two bodies was considered. The amplitudes of the body motions were determined from the equations of
motion for the two bodies and the continuity conditions at the connection between the bodies. In order to
verify this method, the heave amplitude at the hinged joint and the relative angular deflection of the two
floating barges, which are connected by a hinge, were calculated and compared with the results from
Newman (2004).
3.2
Cables, Risers and Column Systems
3.2.1
Column Systems
Yilmaz (2004) studied the diffraction of water waves by an array of vertical cylinders of circular cross
section. In order to account for first order interactions amongst the cylinders, the body boundary
condition is satisfied for each cylinder considering the scattered wave field from other cylinders in an
iterative way. After each iteration, coefficients in the partial wave decomposition of the wave potential
are modified. Bhatta and Rahman (2003) studied wave loads due to scattering and radiation for a
floating vertical circular cylinder in water of finite depth. Wave loads were derived from the total
velocity potential which can be decomposed to four velocity potentials; one due to scattering in the
presence of an incident wave on fixed structure and the other three due to radiation, respectively, by
surge, heave and pitch motions in calm water. For each case, the velocity potential was derived by
considering two regions, namely interior and exterior. The complex matrix equations can be solved
numerically to determine the unknown coefficients for the computation of the wave loads. Numerical
results were obtained for different depth to radius and draft to radius ratios.
He (2004) examined the second order diffraction velocity potential of a vertical column in Stokes’ waves
according to perturbation theory and derived the total second order wave pressure and wave force. Two
methods were investigated. One applies the exterior region analytical solution directly and the other
applies analytical solution in the exterior region and simple Green’s function formulation is used in the
interior region.
28
3.2.2
ISSC committee I.2: Loads
Mooring and Cable Systems
The publications concerning the mooring and cable systems during the reporting period deal primarily
with the coupled floater-mooring global response. In this context, substantial aid is provided by the
enhanced capacity of modern computational systems. At the same time, it is evident that there is still a
great deal of interest for issues that influence the nonlinear dynamic behaviour of mooring lines and the
slow drift motion of the moored floaters. Specific examples are the touchdown of the cable with the
ocean floor, the drag damping induced by the mooring system on the floating structure and the snap- and
slack-loading impacts. Finally, it is interesting that the research community is occupied more and more
with mooring related aspects that lead to instability of the floaters. Some types of destabilization are
already identified as Mathieu type instabilities whilst others still require further investigation.
The prediction of the mooring-floater global response attracted special attention during the reporting
period. Tahar and Kim (2003) developed a computer program for hull/mooring/riser coupled dynamic
analysis of a tanker-based turret-moored FPSO in waves, winds and currents. Schellin (2003) published
the results of a comparative study for the mooring load acting on Single Point Moored tankers as well as
the corresponding horizontal motion response. This study was initiated by the Technical Committee I.2
of the 14th International Ship and Offshore Structures Congress 2000. Garrett (2005) performed a fully
coupled global analysis of Floating Production Systems, including the vessel, the mooring and the riser
system. Hong et al (2005) investigated both numerically and experimentally the basic interaction
characteristics of side-by-side moored vessels using a higher-order boundary element method combined
with generalized mode approach. Rebello de Souza and Fernandes (2005) developed a simplified model
that included wind and current effects and the elastic interactions between vessels. Their task was to
simulate the dynamic response of vessels in tandem for floating production applications. Finally Kim et
al (2005) developed a vessel/mooring/riser coupled dynamic analysis program for simulating the global
motion of a turret-moored, tanker-based FPSO designed for 6000 ft water depth. The vessel and line
dynamics are solved simultaneously in a combined matrix for the given environmental and boundary
conditions. The vessel global motions and mooring tension were tested at the OTRC wave basin for the
non-parallel wind–wave–current 100-year hurricane condition in the Gulf of Mexico.
As far as the individual impacts that influence the nonlinear dynamics of the lines that contribute to the
mooring system, there are several reported works that relate to different aspects. The bottom-line
interaction effect was studied by Ong and Pellegrino (2003) who proposed an alternative approach for
investigating the grounding with the ocean floor. A frequency domain analysis was used and the seabed
interaction comprised two primary actions: an axial stretching of the grounded cable and a catenary
action at the touchdown. It is shown that the seabed interaction is important even under small excitation.
With reference to the damping induced by the mooring system, Hamilton and Kitney (2004) presented
the development of a new approximate mooring line damping prediction tool for use a pre-process to
time domain modelling. According to the authors the tool developed is very efficient and robust
although it operates only in time domain and possesses only one degree of freedom per line.
Chatjigeorgiou and Mavrakos (2001) investigated the snap- and slack-loading. They studied the
nonlinear behaviour of the lower portion of a cable in hanged body deployment applications. Their
numerical model was based on a combination of two different finite difference schemes in order to
properly account for slack-loading and tension cancellation in the vicinity of the cable-body connecting
point. Vassalos et al (2004) performed model tests using a horizontally suspended submerged cable to
examine snap-loading. The results were obtained from monitoring the dynamic tension variation. They
showed that the dynamic tension increases with the amplitude and the frequency of excitation, while in
the non-slack condition the tension variation is primarily at the excitation frequency. Shah et al (2005)
presented a study for the reliability assessment of slack and taut mooring systems against instability. For
this purpose, first, stability analysis of slack and taut mooring systems was carried out and the unstable
regions were identified. Subsequently, knowing the unstable region(s), a methodology for reliability
assessment was proposed, which was based on Monte Carlo simulation technique.
ISSC committee I.2: Loads
29
In this respect it is important to note that the Mathieu type or Mathieu-Duffing type instabilities and
destabilizing effects in general receive special attention by the research community, especially in
connection with the risers’ lateral motions caused by the large heaving motions of the floater. In this
context, Koo et al (2004) studied the Mathieu type instability impacts on a spar platform dynamic
behaviour due to harmonic variation in the pitch restoring coefficients caused by large heaving motions.
In the developed simulation scheme, the heave/pitch coupling of the spar platform was investigated using
the modified Mathieu equation. Kuiper and Metrikine (2005) showed theoretically that the negative
pressurization influences the stability of riser only slightly and could not explain the contradiction
between theoretical predictions and experiments. The explanation can be found in the hydrodynamic
drag caused by surrounding water, which is shown to be an essential stabilizing factor.
Niedzwecki and Liagre (2003) presented a reverse system identification approach that utilizes
generalized coordinate and force functions to recover the value of the key system parameters for each
mode of vibration. To illustrate the analysis procedures, a single marine riser with general dampingrestoring type of nonlinearities was considered subjected to random wave excitation. Analytical
expressions as functions of the modes for bending stiffness and tension were derived and used for
comparison with the results obtained using system identification. Numerical simulations including bandlimited white noise and random wave excitation were used to explore the adequacy of the methodology
and the benefits of using modal analysis in the system identification procedure. Finally, comparisons
with experimental data were presented and the frequency variation of parameters obtained from system
identification procedures discussed.
Clashing between slender structures in marine environment is primarily considered in connection with
riser operations. Interaction between mooring lines is unlikely to occur unless there are floaters in close
proximity moving relatively to each other. Such a case was recently studied by Ji and Halkyard (2005)
who investigated the mooring line interference between a cell spar and a semi-submersible operating in
close proximity. Their results led the authors to suggest the use of intermediate buoys for avoiding
mooring line clashing. On the other hand, riser clashing is more likely to occur in deep water
installations because of the relatively small distance between the risers in high productivity FPSOs and
their elastic material which allows extreme lateral motions. In this context Sagatun et al (2002)
presented a time domain simulator for the dynamic interaction of two adjacent cylindrical risers moving
relative to each other in an ambient steady flow. Recently, Baarholm et al (2005) studied experimentally
the hydrodynamic interaction and clashing of two long cylinders in uniform steady current, while
Herfjord and Holmas (2005) presented a method for predicting the interaction between risers. Their
method was based on pre-established data for forces on risers in close proximity.
3.3
Vortex Induced Vibrations
Experimentation, semi-empirical models and CFD based models continue to be used within the context
of Vortex Induced Vibrations (VIV). Monitoring projects are in operation, providing much needed fullscale measurements.
3.3.1
Semi-empirical Models
VIV of free spanning pipelines was studied by Larsen et al (2004) by a combination of a semi-empirical
time domain VIV model and a nonlinear FE programme. They showed that nonlinear structural effects
are significant for the stresses at the shoulders.
VIV in waves was studied by Moe and Hagatun (2004). They used a semi-empirical time domain model,
including both the inline and cross flow motions, to analyse the vortex shedding induced vibrations of
riser guard tubes near the free surface. The model intended for current application was modified to
include the wave kinematics. They observed good qualitative match between their analytical model and
model test experiments.
30
ISSC committee I.2: Loads
Steel Catenary Risers (SCR) present new challenges to VIV analysis tools, as they are asymmetrical and
curved. SCR moreover fall in between rigid systems, such as conductors and shallow water risers, and
compliant systems, such as cables. Moe et al (2004) modified Moe and Hagatun’s (2004) semiempirical time domain model to handle SCRs with current impinging at an oblique angle. The numerical
results are compared with towing tank tests obtained as part of the STRIDE JIP (Willis 2001). Good
match was obtained between the predicted and measured motion envelopes. However, for some cases, it
was noted that response frequency and mode shape predictions deviated from the measurements.
3.3.2
SHEAR7
A number of experimental results regarding calibration of SHEAR7 input parameters have been
published. For example Vandiver et al (2005) reported on their lake model tests with high mode VIV.
The main focus of their paper is on drag coefficient at high mode response. The measured coefficients
were found to be 10-15% lower compared to that predicted by SHEAR7. Bridge et al (2005) reported on
model tests for single and bundled risers. Lift and added mass curves, as a function of forced vibration
amplitude are provided for a single pipe. They observed that their measured lift curves resulted in higher
predicted fatigue life compared with SHEAR7 default curve.
3.3.3
Application of CFD and Other Theoretical Methods to VIV Prediction
Solving VIV problems using CFD remains to be costly and cumbersome. A number of research groups
are working on finding feasible 2D and 3D schemes and hybrid 2½D scheme to solve VIV cases.
Martins et al 2004 demonstrated the possibilities of parallel processing using MPI (Message Passing
Interface) on a 6-PC cluster for their random vortex strip method. Runtime in the scale of days per load
case is required.
Willden and Graham (2004) studied the transverse VIV of a long (length to diameter ratio, L/D=1544),
flexible pipe, subjected to a uniform current profile (Reynolds number 3×105) using a strip theory model.
The pipe’s mass ratio (ratio of the pipe's mass to the mass of fluid it displaces) was varied between 1.0
and 3.0 in order to study its effect upon its vibration behaviour. Despite the inflow current being uniform
the pipe was observed to vibrate multi-modally. Furthermore, all of the excited modes vibrated at the
excitation (Strouhal) frequency. It was noted that the fluid, via its added mass, could excite modes
whose natural frequencies differed from the excitation frequency. It was observed that this occurrence
decreased with increasing mass ratio. Wanderley and Levi (2005) investigated VIV on a circular
cylinder, as basis for applications to the dynamics of risers. The numerical solution of the 2D RANS
equations was obtained for a circular cylinder supported laterally by a spring and a damper and free to
oscillate in the transverse direction. The Beam and Warming implicit factorisation scheme was used to
solve the governing equations and the Baldwin-Lomax model was used to simulate the turbulent flow in
the wake of the cylinder. The proposed numerical solution can provide a good description of the physics
of the phenomenon, including the Karman vortex street effects on lift and drag coefficients. The
numerical results for the transverse oscillation amplitude were compared with experimental data,
showing a fairly precise agreement even at the lock-in regime – which is difficult to simulate.
3.3.4
Experimental and Field Measurements
Sanchis et al (2005) presented results from PIV (Particle Image Velocimetry) measurements for the study
of the velocity field near a cylinder undergoing vortex shedding induced vibrations. The technique looks
promising for providing detailed comparison between numerical and experimental results. Experiments
carried out by de Wilde (2005) relate to a very long (12.60 m) riser section that showed higher
deformation modes. Strain measurements inside the riser were carried out using optical fibres.
Fibreoptics, as demonstrated in the laboratory by de Wilde and Huijsmans (2004), is a promising
technique for VIV measurement and monitoring as it allows for many measuring points for each optic
fibre; thus providing a compact system which is also immune to electrical noise. A new phenomenon
was reported by de Wilde et al (2003). They carried out forced oscillation tests in which the riser did not
move purely in the vertical direction, but moved in an arc. Although the in-line motions were just 1% of
ISSC committee I.2: Loads
31
the lateral motions, there appeared to be a large difference with pure vertical motions as can be seen in
Figure 6.
VIV is also an issue for SPAR platforms, although with different dimensions compared to risers. Irani
and Finn (2004) presented a model test procedure for the optimisation of the strake configuration. The
procedure was illustrated by case study model test programme and field measurements.
VIV LIft Force
1.5
EXCITATION
Unexpected
Positive Lift
0.5
Clv
old fwd
old bwd
0
0.5
1
1.5
new fwd
new bwd
-0.5
DAMPING
exp
-1.5
A/D
Figure 6: Results of oscillation tests carried out by de Wilde et al (2003), showing lift coefficient Clv
against oscillation amplitude/cylinder diameter (A/D). ‘New’ are purely vertical oscillations
with the carriage moving forward (‘fwd’) and backward (‘bwd’), whilst in the ‘old’ case the
cylinder moves in an arc; ‘exp’ denotes test measurements.
VIV measurements obtained in a dynamic umbilical is presented by Lyons et al (2003). The
measurements are from the FPSO Foinaven in 450 m of water, west of Shetland. The measurement
system comprised recordings of vessel motions, sea state, current and umbilical curvature. The
recordings include multimode VIV due to current, waves and combinations of these two. VIV excited by
the vessel’s heave motions is also presented, although the authors found that, in general, the vessel’s
motions tend to reduce the current-induced VIV. Results for non-dimensional motion amplitude,
frequency and drag amplification were provided. SHEAR7 benchmark runs were also given for
comparison with and synthesis of the measurements.
4.
LOADS DUE TO IMPACTS AND EXTREME EVENTS
4.1
Slamming
4.1.1
Local Slamming
Local slamming is defined here as a local impact pressure that can induce local structural deformations
and stresses, for example in the plates and stiffeners of a ship. Slamming may occur if part of the ship
emerges out of the water following immersion. The severity of the slamming depends on the magnitude
32
ISSC committee I.2: Loads
of relative velocity with respect to waves, body geometry and structural scantlings. Bow, bow flare and
flat bottom areas of the ships are typical areas where slamming can occur. At the first stage of slamming
fluid starts to accelerate violently and pressure increases rapidly. Air trapping can exist, especially for
flat bottom slamming. The slamming peak pressure can be very high but the duration is short and the
influence area is very small and local. During the impact, slamming pressure induces free surface
deformation and jet flow is formed in the vicinity of the body. The fluid structure interaction in local
structural areas might be important, indicating that the elasticity of the structure has influence on the
impact loads. Flexibility and deformation of the structure can affect impact velocity and, hence,
slamming pressure, indicating that hydroelasticity is important. Important parameters in hydroelastic
slamming are the wet natural period of the structure as well as the impact velocity and the impact angle
of the body relative to water surface. Short time scale, hydroelasticity and nonlinearities involved in the
free surface deformation and jet flow are demanding aspects in local slamming predictions. A review of
slamming in marine applications with future challenges was presented by Faltinsen et al (2004). One of
their main conclusions is that slamming should be considered together with the dynamic response of the
structure and very high pressures concentrated in time and space may not matter.
Hydroelasticity in the slamming of an elastic cone and wedge was investigated by Scolan (2003). The
importance of the deformation of the plate and the velocity of expansion of the wetted surface was
demonstrated. Scolan and Korobkin (2003a, b) developed a linear elastic model for a thin conical shell
coupled to a linearised Wagner model for impact pressures. The conical shell was modelled as a circular
plate and its dynamics were described by a single 4th order differential equation, which facilitates
hydroelastic coupling. The boundary value problem was formulated in terms of the displacement
potential for the flow and in the normal deflections for the plate. Both problems were solved
simultaneously using a modal approach. They showed that flow during impact can be described by
matching 3D Wagner solution in the main flow region to the 2D nonlinear solution in the jet region. The
important role played by elasticity was shown by comparing results of the simulation with free drop tests
for either a rigid or flexible cone. It is interesting to note that the first mode dominates during the initial
stages, whereas at the later stages higher modes also contribute. Khabakhpasheva and Korobkin (2003)
came up with simplified models to estimate slamming induced stresses in the thick plates of the wedge
that can be treated as almost rigid body. Reasonable estimates were obtained for maximum bending
stresses for thick wedge plating. Peseux et al (2005) presented a 3D FE approach to solve the Wagner
problem. Numerical solutions were validated using 2D wedge-shaped bodies with small deadrise angles
and a cone for the axisymmetric 3D case. In addition to the rigid body solutions the method was also
applied to analyse deformable bodies. Furthermore, drop test results were given for rigid and elastic
cones. Comparison between experiments and calculations showed good correlation for the rigid cone
when the deadrise angle is large. Some discrepancies were observed in the peak pressures for the elastic
cone, especially when the deadrise angle is small. These were partially attributed to not accounting for
the jet flow.
Wu et al (2004a) applied 2D method to calculate impact pressures when the vertical velocity is not
constant. Similarity solution was used for the flow at the initial stage of impact and analytical solution
for the jet flow. The time derivative of the potential in Bernoulli's equation was solved as another
unknown function in the same way as the velocity potential itself. Applying this type of direct
formulation to obtain the time derivative, numerical differentiation based on the velocity potential from
the prevous time step can be avoided. The direct formulation for the derivative of the velocity potential
was also used to express the impact force including the acceleration of the body. The boundary value
problem was solved numerically using the boundary element method (BEM) and updating the free
surface with a mixed Euler-Lagrangian approach (MEL). Experimental results for a wedge in free fall
were given. Measuring accelerations during impact. Calculated accelerations correlate quite well with
measured ones. Battistin and Iafrati (2003) presented a numerical method to predict impact pressures for
2D and axisymmetric bodies. Impact velocity was constant and the jet flow was approximated by cutting
the jet in the numerical simulations. The numerical solution was the same as that presented by Wu et al
(2004a). Extension to axisymmetric bodies is one step towards 3D methods. The difference, compared
to 2D methods, is the Green’s function used in the solution. Comparisons were made with other
theoretical and experimental results and satisfactory correlation was obtained. A simplified 2D method
ISSC committee I.2: Loads
33
based on Wagner's theory was presented by Kim and Shin (2003b). The nonlinear dynamic free surface
condition was approximated by an equipotential free surface condition. The numerical solution was
obtained using BEM and the free surface was updated with MEL approach. Calculated results correlated
well with experimental results for a ship’s bow section.
Kryzhevich (2003) developed an analytical model for the wet-deck slamming of fast twin-hulled vessels.
An initial value problem for the hydroelastic coupling between the impact-excited flow potential and the
vertical vibrations of the wet-deck was formulated using Green’s function approach for the flow and
modal decomposition for the elastic deformations of the cross-deck structure. Qualitative considerations
allowed the inclusion of a hydrodynamic damping force in the equations for the first vertical mode. This
force originated from dissipation mechanisms due to: energy discharge via spray jet, wetted area
expansion and associated increase of kinetic energy and momentum variation of the fluid involved in the
impact. It is claimed that this damping force is much higher than that due to internal structural damping,
implying that the vibrations excited by wet-deck slamming may have half the amplitude expected when
accounting only for structural damping. Nevertheless, it was also noted that these hydrodynamic
damping forces are very sensitive to the wave shape and the way it impacts the wet-deck, namely even
small variations in the initial conditions will significantly influence the results.
Ge et al (2005) developed a theoretical formulation suitable for the segmented flexible model of a highspeed catamaran. In their approach the hull comprised 3 rigid bodies each having two degrees of
freedom, i.e. translation and rotation in the vertical plane. The hydrodynamic forces on each body were
determined by the modified strip theory neglecting the effects of hydrodynamic interaction. On the
assumption that the water simultaneously hits the deck in transverse direction (that is by neglecting the
variation of the relative vertical motion in the transverse direction) a 2D boundary value problem was set
up at each time step to determine the flow potential associated with wet-deck slamming. Comparison of
predicted time traces against measured ones in regular head waves showed fair agreement. The
reliability of slamming predictions, in particular, was checked by comparing the vertical force on the
foremost part of the deck. The authors concluded that the agreement with the experiments did not
improve by the inclusion of the three-node bending mode in the calculations.
Air trapping effects in local slamming were investigated by Takagi and Dobashi (2003) and Takagi
(2004) using 3D BEM. The solution was based on displacement potentials rather than velocity
potentials. The body shape was a disk with circular hollow in order to describe irregularities on the sea
surface instead of modelling the water surface shape due to short crested waves. A mass-spring system,
without structural damping, was used to model global and local elasticity of the structure. Calculations
for an axisymmetric body showed that, due to trapped air larger, values for local spring forces were
obtained in model-scale than in full-scale. Froude's similarity law was used to scale the characteristic
dimensions from model-scale to full-scale and, hence, the pressure in the air pocket was not correctly
scaled. The results showed the importance of scaling effects in slamming.
Sakashita et al (2004) presented a numerical technique based on the so-called Moving Particle Semiimplicit (MPS) method. This method is capable of modelling fragmentation of incompressible fluids, is
robust and does not require grid generation. The authors used this technique for water impact problems
where the effect of fluid-structure interaction can be neglected, so that the calculated pressures can be
directly applied to a FE model to obtain transient structural response. Numerical predictions were
compared with drop tests for a 2D wedge, showing good agreement for strains, but not for pressures.
Another interesting approach for solving strongly nonlinear free surface deformations is Smoothed
Particle Hydrodynamics (SPH). This method was applied Colagrossi and Landrini (2003) to predict freesurface flow and impact pressures against vertical wall, including air entrapment effects. The dam
breaking problem was analysed and good results were obtained for the free surface flow compared to
other solution techniques. The calculated impact pressure against vertical wall showed discrepancies
compared to experiments. However, the authors also pointed out the difficulties in experiments with
reference to measuring violent pressure peaks and, hence, the possible high scatter in measured results.
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ISSC committee I.2: Loads
Engle and Lewis (2003) presented experimental results from drop tests of wedge shaped bodies. The
deadrise angles of the wedges were 10° and 20o. In addition, several different numerical approaches
were compared with experimental results. Rather good agreement between predictions from various
methods and measurements was obtained for the wedge with 20° deadrise angle. Gielen et al (2004)
compared results of flat panel drop tests with 2D numerical simulations using the fully-hydroelastic code
DYNA3D. The test box was purposely fitted with “skirts” in order to avoid 3D effects resulting in
asymmetry. It was noted that 2D calculations with symmetric models resulted in large added mass
values, compared to experiments. The reason for this discrepancy was explained by the fact that in
reality the skirts were not effective in implementing the symmetry condition, thus resulting in the
formation of a small “back” wave, whereas only a “front” wave was expected. In addition they adopted a
mass-spring-damper system to simulate their measurements. They concluded that this approach was
capable of describing the behaviour of their experiments, subject to calibrating the damping coefficient.
A study comparing predictions from a range of 2D and 3D methods with experimental measurements –
both pressures and stresses – for wedge impacts is taking place as part of a European Project
(MARSTRUCT 2003).
4.1.2
Global Slamming
4.1.2.1 Wave Impact and Slamming
Jensen and Mansour (2003) proposed an approach to estimate the effect of impulsive loads, like
slamming and green water on deck, on the wave-induced bending moment by a semi-analytical method.
The impulsive loads leading to transient vibrations were described in terms of magnitude, phase lag
relative to the wave-induced peak and decay rate. These loads can be due to flare slamming, bottom
slamming or green water loads as they all can be characterized by a short duration relative to the wave
cycle. The magnitude of these loads was estimated by published theoretical or experimental results. The
results are given in closed form expressions and the required information for the procedure is restricted
to the main ship dimensions: length, breadth, draft, block coefficient and bow flare coefficient together
with speed and heading. The formulae make it simple to obtain quick estimates in the conceptual design
phase and to perform a sensitivity study of the variation of the ship’s main dimensions and operational
profile. Chezhian and Faltinsen (2004) generalized Wagner’s theory to arbitrary 3D bodies and
calculated slamming forces on a 3D body. They also conducted model tests to measure both slamming
pressure and force. An idealized shape, comprising a cylindrical mid-body and hemispherical ends, was
studied. The wetted body surface was considered to be more important and, thus, calculated in greater
detail than the free surface elevation away from the body. Drop tests were carried out to verify and
validate the numerical simulation. The agreement between theory and experiment is good and 3D effect
was accounted. Xia (2005) provided a strip-theory formulation that deduces the momentum slamming
force from a unified seakeeping modelling. The formulation is within the framework of potential flow
theory. By satisfying the exact boundary condition on the time-varying body surface (but assuming
linearised free surface boundary condition), a 2D time-domain solution is presented which extends
Faltinsen’s (1990) momentum approach for water entry analysis. The method is particularly effective for
large displacement ships such as containerships. Moctar et al (2004) presented a procedure where a
seakeeping code is used to predict ship motions. Based on the motion prediction, slamming pressure and
force are modelled using a RANS code. In addition model test results are given for slamming pressures
and forces at the bow. Predictions compare reasonably well with model measurements.
Bow impact loading on floating offshore structures is related to steep waves occurring in random seas.
Voogt and Buchner (2004) proposed a design evaluation method to predict the bow slam loading
problem from the input (scatter diagram) to the output (predicted load and response levels) based on a
clear description of the bow slam physics. The method is based on second order wave theory to describe
the wave steepness and an empirical relationship between wave steepness and local impact. The position
of this impact follows from a coupled time domain analysis of the ship motions. The method assumes
long-crested waves, which are considered to be the worst case scenario.
ISSC committee I.2: Loads
35
(i)
(ii)
Figure 7: Rainflow count of the Vertical Bending Moment (VBM) in (i) head seas with 9m significant
wave height and 9 knots forward speed and (ii) following seas with 4m significant wave
height and zero forward speed (Kapsenberg et al 2003).
4.1.2.2 Whipping
Kapsenberg et al (2003), in their already mentioned segmented model experiments (see section 2.3.1),
showed the importance of the ratio of impulse period over resonance period for a flexible model and a
rigid model. By using a large number of pressure gauges, it could be deduced that the high pressure
ridge was relatively narrow. This meant that this ridge could be ‘lost’ in between two pressure gauges.
However, from the difference in time of the high pressure ridge passing the different gauges, the velocity
along the hull could be obtained. From this velocity and the assumption that the value of the pressure
changed linearly between neighbouring pressure gauges, a continuous model of pressure as a function of
space and time was obtained. These results are attractive in particular when using them as input for a
numerical analysis of the structure. A sample of vertical bending moment statistics is shown in Figure 7
for head and following sea states, illustrating the importance of aft body slamming.
Zhao et al (2004b) studied, both numerically and experimentally, the whipping in large ships (such as
cruise ships) induced by both bow flare and stern slamming. New experimental methods were developed
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ISSC committee I.2: Loads
to measure slamming forces at bow and stern and whipping responses at amidships. The results show
that whipping responses could be significantly larger than the wave contribution. Furthermore the
authors noted that both bow slamming and stern slamming were important for whipping responses.
Couty and Besnier (2004) performed a systematic sensitivity analysis of the hydroelastic response of a
hull girder subject to impulsive loads with respect to various structural parameters. An objective of this
study was to show that there are other transient phenomena, such as propagating flexural and shear
waves, which can play a significant role. To this end the hull was idealised as a Timoshenko beam,
allowing theoretical study of the propagation of flexural waves in response to a sharp pulse. Calculations
were performed using LS-DYNA, applying an ideal triangular load signal to simulate slamming force.
The influence of parameters defining the impact, such as rise time, duration and impulse magnitude, on
the amidships bending moment were investigated. Furthermore the effects of decreasing the shear area
and discontinuities in the cross-section moment of inertia on the amidships bending moment were
investigated. It was noted that the shear area may have an important influence. Comparison of beam and
3D FE models showed good agreement in terms of global loads. The authors also showed that good
agreement was obtained between direct integration and modal superposition methods.
As pointed out by Jensen and Mansour (2003), the effect of green water and bow flare slamming on
global dynamic loads can be accurately predicted only by nonlinear hydroelastic methodologies. These
are still not well suited for use in the routine design process due to their high computational demands,
especially for systematic use. In this respect it is very important to provide the designer with relatively
simple tools, applicable at early stages of the design process. A number of papers have addressed this
issue showing that a simple analytical model, with only one degree of freedom for the first vertical mode
of vibration, is capable of predicting reasonably well the whipping contribution to the global longitudinal
loads, provided that calibration with measurements (either model- or full-scale) is performed. Naturally,
the accuracy of such simplified methods depends on the accuracy of predicting the whipping related
excitation. For example Kapsenberg et al (2003) used such a simple analytical model, calibrated by
hitting the segmented flexible model at the aft end and comparing predicted and measured responses.
Once calibrated this model allowed the evaluation of the whipping loads, based on the measured local
pressures, with good accuracy. Furthermore the authors showed that the hydroelastic effects on local
loads can be neglected, at least in the case of aftbody slamming. The practical consequence of this
finding is the possibility of calculating the whipping response using local pressures, either measured or
calculated, from rigid body approximation. Bacicchi et al (2004) compared the results of different
hydroelastic models, namely 3D FE method, 1D FE method, 2D hydroelastic model and 1 degree of
freedom analytical model, with measurements from flexible segmented model tests for a cruise ship. It
was concluded that the simpler numerical methods, and in particular the analytical model, were all well
suited for use during the first stages of structural design as they require far less detailed information on
structural characteristics by comparison to 3D FE models. All methods used predicted the whipping
bending moment at amidships to similar levels of accuracy. Jensen and Mansour (2003) also modelled
the ship as a 1 degree of freedom system, identified by the natural frequency of the first vertical mode.
They applied this method to three different tankers in full load condition. The results were compared
with standard Rule requirements, showing a good agreement but there are no comparisons with
measurements.
4.2
Sloshing
The assessment of sloshing in ship tanks is important in order to design safe tank support and
containment structures, which are able to resist both quasi-static and impact loads considering both
fatigue and ultimate loads. In particular impact loads, caused by violent ship and fluid motions, are
difficult to assess as easy-to-use and accurate prediction methods are scarce or not fully developed or
verified yet. The LNG (Liquefied Nitrogen Gas) shipping industry is developing in a rapid pace with the
introduction of larger LNG carriers, offshore discharging operations and floating receiving terminals.
The main focus of investigations is sloshing of LNG in prismatic membrane tanks. The main advances,
for the sloshing impact inside the tanks, are on the following issues :
 Sloshing test facilities
ISSC committee I.2: Loads




37
Sloshing impact identification and characterisation
Scaling of model experimental results
CFD applications
Sloshing assessment methodology
Gavory (2005) presented a new 6 degrees-of-freedom (dof) hexapod sloshing test rig and discussed the
characteristics of both parallel and serial motion simulators. Most sloshing experimental work in the past
was limited to 2 to 4 dof. This work presented the first comparisons between results of tests with and
without heave and yaw of a 1/50th scaled no.2 tank from a 138000m3 LNG carrier. The comparison was
carried out for impact pressures for a high and a low filling case in head and beam seas respectively. For
the high filling case nearly all sensors showed a reduction in pressures when simulating with 6 dof
instead of 4. For the low filling case, however, an average increase of 42% was measured for the tests
with 6 dof instead of 4 dof. The same author also presented the application of PIV to measure liquid
sloshing velocities inside model tanks. He concluded that PIV appears to be a valuable tool for this
application and the preliminary results are encouraging, in particular for studying fluid velocities around
the tripod mast for a more accurate estimate of the hydrodynamic loads on this tower structure.
A sloshing impact is a localised phenomenon and accurate measurement of these local impact pressures
is a key factor to subsequent assessment of structural integrity. Different failure modes are to be
considered when analysing impact loads for different footprint areas. In this respect the measurement of
impact pressures by clusters of pressure sensors mounted very close together is an important aspect of
modern sloshing experimental testing. Gavory (2005), Pastoor et al (2005) and Rognebakke et al (2005)
discussed this issue and showed some example results of measured impact pressures as a function of
footprint area. A further important aspect of measuring impact pressures is the sampling rate as some
local impacts can have a very short rise time. Sampling rates up to 50 kHz are used for model testing at a
1 to 50 scale, as reported by Richardson et al (2005). They showed an example of an impact pressure
pulse when sampled with different sampling frequencies. A significant under-prediction of the peak
value and an over-prediction of the rise time might occur when a too low sampling rate is used.
In the past most sloshing model testing was done using regular motions tuned to get resonant sloshing
behaviour inside the tank. Most recent investigations applied irregular motion tests for storm conditions.
In this respect it is important to be able to characterise the sloshing impact loads statistically. Richardson
et al (2005) discussed this issue briefly by demonstrating the difficulty to estimate expected extremes for
a three-hour storm with sufficient confidence. Test durations over 30 hours were necessary for specific
cases. Pastoor et al (2005) discussed this issue further by showing exceedance probability curves for
measured impact pressure peak values for a high filling and a low filling case in head and beam seas
respectively. A large difference was shown for the tails of the statistical curves. The authors, therefore,
state that bluntly comparing short-term expected extreme values without accounting for any significant
difference in the statistical curves is to be avoided.
Zhao et al (2004a) discussed the characterisation of local impact pressures and proposed a novel postprocessing approach. They stated that large individual peaks of impacts do not necessarily give large
stress responses in the structure. The total impulse of an impact is an important parameter as well.
Hence they proposed to “filter” the measurements by calculating average pressures over different time
intervals chosen as fractions of the natural periods of the containment system.
Richardson et al (2005) and Pastoor et al (2005) presented sloshing tests with a variation of ullage gas
densities. Richardson et al (2005) showed a figure with impact peak values for tests with three different
gas-liquid density ratios: (a) a fluid-gas density ratio equal to the full-scale density ratio of LNG, (b)
air/water at 1 atmosphere and (c) vacuum. Because lower impacts were measured for case (a) they stated
that it is adequate to use air/water based model tests at 1 atmosphere. Pastoor et al (2005) conducted
similar tests, but both with a small and a large tank at a 1 to 70 and 1 to 20 scale, respectively. They
found trends similar to those presented by Richardson et al (2005), but when Froude scaling the
pressures it was noted that identical gas-liquid density ratios did not give identical pressures, which does
not support the conclusions by Richardson et al (2005). In fact the study by Pastoor et al (2005)
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ISSC committee I.2: Loads
recommends to change the gas-liquid density ratio, which in fact turned out to be quite similar to the
Froude scaling of the ullage pressure as recommended and applied in the past, e.g. Berg (1987).
The scaling of measured local impact pressures to full-scale is further discussed by Lee et al (2004).
These authors described the Froude (=incompressible) and compressible scaling laws and state that
compressible and incompressible impacts occur randomly during a sloshing simulation. Applying only
the incompressible scaling law might be overly conservative whereas applying only the compressible
scaling law might be non-conservative. Model experiments were compared with CFD predictions by
Lee et al (2004)
Several authors presented impact pressures measured in sloshing tests for different conditions, e.g.
Pastoor et al (2005), Lee et al (2004), Zhao et al (2004a) and Zalar et al (2005). In general all authors
measured large pressures for high filling conditions (~95% filling of tank height) in head waves and for
low filling (~30% filling of tank height) in beam seas. A limited amount of data is presented on crosssea testing as well, which can result in high pressure loadings as well. This supports the use of 6 dof
sloshing rigs rather than 2 dof rigs. Pastoor et al (2005), furthermore, described the effect of forward
speed and sea state severity. The authors showed that for high filling conditions in head waves a
significant reduction of the impact pressures was measured when conducting tests for lower forward
speeds. Changing the sea state severity however did not give a likewise change in impact pressures.
Especially for low filling conditions in beam seas a 50% reduction in significant wave height gave only a
20-30% reduction in impact pressures.
Both sloshing experimental and numerical simulations apply mostly linear ship motion transfer functions
as a basis to generate the irregular motions of the tank. Considerable effort has been conducted in the
past years to increase the prediction capabilities to couple the ship motion and sloshing simulation since
it is of course a coupled dynamic problem. Gaillarde et al (2004) showed experimental results of the
ship motions of a ship model tested in a model basin with variations of the filling level inside two tanks.
Especially for beam sea conditions large changes of the roll motion transfer function was obtained. Not
only a shift of the period of the roll transfer function peak was observed, but also changes in the peak
value. They also presented a numerical model, with a coupling between sloshing and ship motions using
a potential flow model for the fluid inside the tank. Good predictions of the ship motion transfer
functions were shown in comparison with model experimental results. No sloshing impact pressures
were measured during this test programme. Zalar et al (2005) presented a nonlinear time domain
coupling between a linear time domain ship motion program (HydroSTAR) and the Navier-Stokes solver
FLOW-3D. The effect of the coupling on the ship motion transfer functions was shown but not on the
sloshing pressures.
Most effort focussed on experimental investigations rather than use of CFD. Furthermore there appear to
be different opinions as to the applicability range of CFD for sloshing. Some authors, such Kim et al
(2003), apply CFD to predict violent sloshing causing localised impacts. Others, such as Pastoor et al
(2005), state that CFD techniques are not yet mature enough to predict local impact pressures. Not only
the capability of CFD to predict accurately local phenomena is of importance, but also its applicability to
simulate sufficiently long tank motion histories.
4.3
Green Water
The term green water refers to a situation when significant amounts water wash over the deck of a ship.
The ability to predict such loads has taken on many forms ranging from simplified empirical approaches
up through the application of RANS solutions. For example, Shin et al (2003), describe an approach for
predicting the effects of green water on both local and global structure. The approaches described allow
the user to utilize several levels of calculation methods to investigate the green water problem. The
levels which are discussed include a basic hydrostatic method, semi-empirical method and a shallow
water flow calculation using a finite volume approach. The semi-empirical method can be used to
provide a quick estimate of green water and its effect on ship motions and global loads. The finite
volume approach, contained in the shallow water model, can be used to simulate green water on deck for
ISSC committee I.2: Loads
39
a wide range of deck geometries. However, given the assumption that water flow over the deck is
constant, 3D effects are not addressed. A sample of results obtained from these various approaches in
head regular waves is shown in Figure 8.
Figure 8: Non-dimensional vertical bending moment simulations in head regular waves illustrating the
effects of Green Water evaluated using different methods; X indicates distance from the stem
(Shin et al 2003).
Barcellona et al (2003) performed a series of experiments examining the water shipping problem at zero
ship speed. In addition to measuring pressure forces, video imaging of the flow field in way of the deck
was also collected. Analysis of the data indicates that there are two parts to the time evolution of the
loading on a deckhouse front. The first peak is associated with the initial impact of the water, whereas a
second peak is the result of a backward plunging impact force. In order to better understand the physics
of the green water on deck problem, Tanizawa et al (2004) applied PIV techniques. This process
involves the seeding of the water with neutrally buoyant particles and through the combination of lasers
and high speed camera a 3D visualization of the free surface, as it runs across the deck of a ship can be
captured and analysed. Pressure gages were used to determine associated impact pressures during the
flow visualizations.
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ISSC committee I.2: Loads
Fonseca and Guedes Soares (2004b) compared numerical simulations, based on a nonlinear strip theory
approach with experimental results for a modern containership design. Analyses were done for both
regular and irregular wave conditions. Their findings suggest that proper correlation requires a numerical
model that can properly account for nonlinear effects as they relate to relative motions in large amplitude
waves. Gomez-Gesteira et al (2005) applied a Smoothed Particle Hydrodynamics (SPH) method to
examine the water on deck problem. The approach uses a Lagrangian frame of reference to simulate
waves hitting a horizontal platform. Comparisons with experimental results are shown. The overall
approach showed good agreement with experiments.
To address the specific issue of green water and its effect on local structure, Huijsman and van Groesen
(2004) developed a volume of fluid method technique for predicting the hydrodynamic impact problem.
The method utilizes an incompressible Navier-Stokes solution to represent the nonlinear characteristics
of the waves up to and including rogue waves. The authors caution that special care must be given to
grid resolution in solving the green water problem.
With the intention of providing the designer with a more basic engineering assessment method,
Stansberg et al (2004) developed a computer program suitable for predicting green sea loads on an
FPSO. The proposed method can be used to predict impact force or to apply inflow data, such as
horizontal wave particle velocity and relative wave elevation, into a more rigorous volume of fluid
method. General trends compare well with experiments. The problem of green water on an FPSO can
be considered to be similar to that of the dam break problem. However, Pham and Varyani (2005) have
shown that the traditional dam break problem will underpredict peak loads for cases where forward
speed is present. To account for the additional dynamic disturbances which are present, an alternative
CFD solution to the dam break problem including an initial velocity is discussed. Significant
improvement is noted when such a velocity is included.
To mitigate the effects of green water, Pham and Varyani (2004) examined the effects of breakwater
design on high speed container ships using a RANS based code. Two types of breakwater geometries
were examined, namely a V-shaped and a vane-type configuration. It was found that the V-shaped
design was more efficient in deflecting waters while the vane-type, with its system of small vanes and
gaps in between, was less prone to water pile up. In addition to breakwater shape, Varyani et al (2005)
investigated the effect that a perforated breakwater would have on reducing impact loads on container
stacks. The approach utilized a RANS based code (Fluent) with a laminar flow model, to predict the
impact loads on a breakwater with a range of perforated hole sizes. The results indicated that such
perforations will, in fact, reduce peak loads. The overall process that is discussed in the paper can be
used by designers to optimise the breakwater and surrounding structure. It is noted that the use of a
turbulent flow model would provide a more realistic simulation but was not used due to the
computational costs associated with 3D CFD simulations.
4.4
Impact Loads on Offshore Structures
Impact loads on Offshore structures, also called “wave in deck” loads, are closely related to green water
on deck of ships and sloshing in tanks Faltinsen et al (2004). For fixed offshore structures impact loads
become relevant when the air gap is too small, i.e. due to subsidence. Compared to green water on deck
and sloshing, modification of the air gap may be very expensive for offshore structures. Boundary
Element, Smooth Particle Hydrodynamics and Volume of Fluid (VOF) methods are being validated on a
pilot basis. Applications of CFD methods include both commercial codes, e.g. Stansberg et al (2005),
and development codes, e.g. Nielsen (2003). Cost will need to be reduced and throughput increased for
the CFD methods to become attractive for practical engineering uses.
Further development and calibration of Kaplan style semi-empirical models, which are the preferred
methodology for practical applications, are still ongoing. The method by Stansberg et al (2005) takes
into account the wave amplification due to the structure itself. The semi-empirical models are suitable
for engineering applications, but should be used with due care. It is recommended that numerical models
are supported with physical model tests. The model tests, in scale 1:10, reported by Sterndorff (2002)
ISSC committee I.2: Loads
41
were compared with numerical results by Nielsen (2003). He used a Navier-Stokes solver and tested
several VOF free surface capturing schemes. The so called CICSAM and Hyper-C free surface capturing
schemes were found to produce the best results. The numerical VOF model was applied to wave impacts
on single and multiple beams. Detailed time histories, on a per beam basis, were compared with model
test results and good agreement was observed. Ryu and Chang (2005) reported on the model
experiments of breaking plunging waves impinging on a dock-like structure. PIV and Bubble Image
Velocimetry (BIV) methodologies were applied to measure the flow velocities in the vicinity of the
structure. BIV is used as a supplementary technique in the aerated areas where PIV fails to provide
measurements.
4.5
Rogue Waves
Considerable attention has been paid over the past years to the subject of rogue waves. Both the physics
and the probabilistic analysis of such waves as well as the loads and responses induced by them on ocean
structures are of interest. Here the term rogue (or freak) wave is used to designate an exceptional wave,
which can be considered as an outlier in comparison with the rest of the waves in the train. Many
publications focus on the wave itself, e.g. Olagnon and Prevosto (2004). Only few papers study the
effect of rogue waves on ships and offshore structures. Whether rogue waves should be part of the
design load philosophy for ocean-going structures still remains a valid question. Buckley (2005)
classified extreme or rogue waves into two types : (a) long-crested, steep-fronted and of unusual height
and (b) short-crested and sharply breaking. He provided evidence for such wave types based on
interviews, incidents and collected wave data. He advocates a first principles design methodology, for
both ships and offshore structures, based on model testing, supporting development of suitable analytical
methods and identification of critical sea and operating conditions.
The European Union MAXWAVE (2000) project contributed significantly in improving our
understanding of rogue waves; however, some issues are still not well understood as stated by Pastoor et
al (2003). They conducted a nonlinear simulation of a cruise ship in the well known New Year Wave,
measured in 1995 at the Draupner platform. A linear irregular wave was fitted to this real offshore
measurement. By discussing the various phases of the rogue wave encounter they stated that more
knowledge is needed on the spatial and transient behaviour of such wave, as well as its kinematic
properties, in order to enable the construction of a numerical model for accurate ship response
predictions. Others have similarly modelled the Draupner or other rogue waves and assessed the
behaviour of ships or offshore structures in these rogue waves. Guedes Soares et al (2004) presented
nonlinear predictions for the S-175 encountering the Draupner rogue wave showing significantly larger
values than Rule values. Numerical predictions for an FPSO were compared with model experiments.
For this case the predicted and measured bending moments were smaller than Rule values. Fonseca et al
(2005) conducted nonlinear simulations of the S-175 containership for a series of 14 rogue waves as
measured in different places and occasions. Trends of the hull girder bending as a function of rogue
wave properties, such as height, slope and wave length, were then derived.
Clauss et al (2003, 2004 and 2005) studied the response of FPSOs and semi-submersibles in rogue
waves using both numerical methods and model experiments. Clauss et al (2003) modelled the
Draupner wave in the model basin and motions and loads of a semi-submersible were measured. Both
3D frequency and 3D time domain numerical predictions showed reasonable to good agreement with
measurements. Height variations of the rogue wave peak were simulated and the resulting maximum
motions of a semi-submersible showed a nonlinear dependence. Model experiments with a FPSO in the
New Year Wave were conducted by Clauss et al (2004). Three numerical programs were compared with
the experiments: a linear and a nonlinear strip theory (SEAWAY and IST-CODE), and the 3D time
domain panel code WAMIT. The agreement between measurements and predictions was convincing
although the peak values of transfer functions and their associated frequencies were slightly deviating for
the strip theory predictions. Furthermore the longitudinal position of the FPSO was systematically varied
in the tank, by a total of 9 positions, which showed the importance of time and phase information and the
need for precise simulations and model tests. In their latest paper Clauss et al (2005) presented further
work on the semi-submersible and model tests with a smaller FPSO as discussed in their 2004 paper.
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ISSC committee I.2: Loads
Both frequency and time domain predictions were compared with experimental measurements. Good
agreement for motions, splitting and bending moments for the semi-submersible and airgap was
observed.
5.
PROBABILISTIC METHODS
In order to analyse the strength of ship structural members, two pieces of information on wave-induced
loads are generally required. One is the extreme value of wave-induced load under long-term
distribution, which is necessary for large deflection and limit state strength analyses of ship structures.
The other relates to both the long-term distribution and time history of wave-induced loads for a fatigue
strength analysis. Theoretical estimation methods of short and long term distributions for linear waveinduced response is, by and large, established. For example, assuming linear superposition and narrowbanded response spectrum, the short-term distribution of wave-induced loads can be described by
Rayleigh’s distribution function. The long-term distribution is obtained as a weighted sum of the short
term descriptions considering various wave headings, ship speeds and routes. Although linear response
in a given sea state can be obtained in the frequency domain, time domain simulation and/or tank testing
is, in general, required to obtain nonlinear response. Furthermore, unlike the linear case, there is no
theoretical distribution of peak values for the nonlinear wave-induced response. Therefore, development
of approaches to obtain short and long term probability distributions for nonlinear wave-induced load is
continuing, as discussed below and summarised in Table 1 for short-term response.
5.1
Short-term Distribution
Wang and Moan (2004) systematically studied the statistics of nonlinear wave loads on seven ship
models under various short-term sea state and ship speed conditions. The generalized gamma, Weibull,
and generalized Pareto distributions were used to describe the peak value statistics and predict extreme
values. For all ship types, sea state and ship speed conditions, the Weibull distribution appears to be very
suitable for representing the wave load peak value statistics. The fitting of the distribution in the upper
tail area is relatively good, and the statistics uncertainty in the extreme estimation is small. Fonseca and
Guedes Soares (2004a) conducted an experimental program with a containership model advancing in
regular and irregular waves. They presented a more detailed analysis of the statistics of the vertical
responses for three different sea states, and cumulative probability distribution of these responses
together with comparisons with Rayleigh’s distribution. The cumulative distribution of the experimental
vertical motion peaks agree well with Rayleigh’s distribution, and the asymmetries of the positive and
negative peaks are small. The vertical shear force at station 15 (f’wd quarter) and vertical bending
moment at amidships and station 15 have highly asymmetric distributions of peaks, and thus deviate
significantly from Rayleigh’s distribution. In this case sagging loads are larger than hogging loads.
Kapsenberg et al (2003) introduced a reliable method for measuring the excitation of a ship’s hull due to
aftbody slamming impacts in a seakeeping basin. The extreme values of the wave frequency component
of the vertical bending moment, whipping, and total vertical bending moment data in head seas could be
fitted by a 3-parameter Weibull distribution. The peak of whipping vertical bending moment in head
seas occurs together with the peak of sagging bending moment. In following seas the phasing is
different, namely the peak of the whipping bending moment occurs at the same time as the peak of the
hogging bending moment. Baarholm and Jensen (2004) studied the effect of slam-induced whipping on
the design value of the vertical bending moment at amidships. It was assumed that the whipping and
wave-induced responses are independent because this simplifies the establishment of the short-term
distribution. Numerical calculations were performed using a nonlinear, hydroelastic strip theory and
results were presented for the S-175 containership. The exponential distribution gives a good fit to the
whipping maxima and the 3-parameter Weibull distribution was chosen for the wave-induced responses.
Wu and Moan (2004) applied the WINSIR (Wave-Induced ShIp Responses) code, based on strip theory
for high speed vessels, to a high speed pentamaran. The nonlinear simulations of ship motions and wave
loads were carried out in regular and short-crested irregular waves, from head to following sea
ISSC committee I.2: Loads
43
conditions. The short-term probability of exceedances were estimated by fitting the generalized gamma
distribution to the histograms of the peak and trough values extracted from the numerical simulations in
different sea states. Calculated values were compared with model tests in regular and irregular wave
conditions and good agreement was observed .
Ogawa (2003) conducted a series of model tests for a domestic Japanese tanker and a cargo ship in
regular and long-crested irregular waves at head sea condition in order to develop a practical prediction
method for the green water load, as well as volume of water, on the bow deck. The green water at the
stem flows with the same height as its maximum height over the bow top and with a breadth which is
proportional to the maximum height of the water over the bow top. From these results, a relation was
found between the green water load and the square of the maximum height over the bow top. The
probability density function of the maximum value of the green water load can be expressed in terms of
the probability function of the relative water height at the stem, assumed to follow Rayleigh’s
distribution. Therefore, the probability function of the green water load is expressed by the truncated
Rayleigh’s distribution. Fonseca and Guedes Soares (2004b) analysed the results of an experimental
investigation on the shipping of water on the bow of a containership. Model tests were carried out in
head regular and irregular waves of large amplitude, and measurements taken of the absolute vertical
motions, relative motions at the bow, the height of water and the impact pressure on the deck, as well as
the horizontal impact pressure and total force on the first line of containers at the bow. The measured
wave elevation, pitch motions and relative motions were correctly represented by Rayleigh’s distribution.
Heave motion and pressures were better represented by the Weibull distribution, although it is not able to
correctly capture the behaviour of the empirical distributions of the height of water on deck and the
pressure.
TABLE 1 PROBABILITY DISTRIBUTION FUNCTIONS USED FOR NONLINEAR SHORT-TERM RESPONSE.
Authors
Response
Procedure
Wang
and
Moan
(2004)
Fonseca and
Guedes Soares
(2004a)
Kapsenberg et
al (2003)
Wave-induced bending Numerical
moment
simulation
(VWBM)
Wave-induced bending Tank test
moment
Whipping moment & Tank test
Wave-induced bending
moment
Baarholm and Whipping moment & Numerical
Jensen (2004) Wave-induced bending simulation
moment
Wu and Moan
(2004)
Ogawa
(2003)
Fonseca and
Guedes Soares
(2004b)
Belenky et al
(2003)
Ship type
Distribution
function
S-175, SL-7, Tanker, Weibull
Mariner,
Cargo,
Frigate, Destroyer
S-175
unknown
Cruise ship
Weibull
Green water load
Tank test
Exponential
for Whipping,
Weibull
for
WBM
High
speed Generalized
Pentamaran
Gamma
Domestic tanker and Truncated
cargo ship
Rayleigh
Container
Weibull
Parametric Roll
Numerical
simulation
Post-Panamax
class container
Wave-induced bending Numerical
moment
simulation
Green water load
Tank test
S-175
C11 Non-ergodic,
non-normal
distribution
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ISSC committee I.2: Loads
Belenky et al (2003) attempted the ergodicity analysis of irregular roll for a post-Panamax containership
in the regime of parametric resonance in head seas. Statistical data was generated using the LAMP
software, based on potential flow analysis and body-nonlinear hydrodynamics. Using roll variance
estimates for 50 realizations, the non-ergodicity criterion was introduced. The nearly tenfold increase in
the value of non-ergodicity criterion for parametric roll and roll velocity, in comparison to the values for
pitch and heave (which are directly related to the parametric excitation) provides sufficient background
for rejecting the ergodicity hypothesis for roll and roll velocity. The probability distribution of the roll
response from the simulations deviated significantly from the normal distribution. The peak of the
distribution was also significantly sharper.
To improve the efficiency of direct calculations of linear and nonlinear long-term extreme values some
simplified design wave conditions, where the equivalent long-term extreme responses can be generated,
were introduced. Shigemi and Zhu (2003) and Zhu and Shigemi (2003) developed practical estimation
methods of design sea state acting on primary structural members of tankers and bulk carriers based on
linear responses. The dominant short-term sea states, used to generate response values equivalent to the
long-term distributions of stress at 10-8 probability of exceedance, can be represented by a few specific
short-term sea states. These sea states can be identified with good accuracy using response functions of
the following dominant load components, without using stress response functions: (a) Vertical bending
moment ( head sea ), (b) Vertical bending moment ( following sea ), (c) Roll and (d) Wave-induced
hydrodynamic pressure at waterline. They also proposed design regular waves resulting in the same level
of stresses as those induced by irregular waves for the design sea states. They generated a large number
of examples and compared the estimated maximum values between the design regular wave and direct
long-term methods. The results showed good agreement. Iijima et al (2004) introduced the design sea
states for torsional strength assessment of container ship structures. A dominant regular wave condition
for which the torsional response of the container ship becomes maximum was specified. The wave
length is 35% of ship’s length and the wave heading is 120o, 180odenoting head waves. The
aforementioned procedures are adopted for the Class NK rule.
Dietz et al ( 2004 ) proposed the Most Likely Response Wave (MLRW) to estimate the entire nonlinear
extreme response value distribution for a selected operational profile. The ideas by Friis-Hansen and
Nielsen (1995), Taylor et al (1995) and Adegeest et al (1998) were combined, allowing the entire
nonlinear extreme value distribution to be calculated given the amplitude and phase information from
linear transfer functions. Comparison were carried out between the Most Likely Extreme Response
(MLER), which uses the amplitude and phase information from a set of linear transfer functions and can
be used to derive the underlying wave profile, proposed MLRW and brute force simulation for a
Panamax container ship. Good agreement between the MLRW and brute force simulation approaches
was observed. Pastoor et al (2003) presented a summary on calculation procedures for determining
extreme responses of ocean going structures using nonlinear time domain simulations. Model tests were
carried out with a frigate to study the amidships vertical bending moments in random irregular waves and
some conditioned irregular waves, the so-called EMLER (Extended MLER). The sagging bending
moment exceedance probabilities for both cases were shown. Furthermore two functions were fitted to
the random irregular data, namely a Weibull distribution and a Hermit moment model. The response
conditioned experiments showed a good agreement with the random irregular data. Considering the
expected extreme in 3 hours, the differences were small. However, the expected maximum extreme for
10000 vessels, obtained from fitted functions and conditioned results showed large difference. The
authors concluded that safety was dictated by the tail of the distribution and this required accurate
predictions for extreme conditions.
5.2
Long-term Distribution
Time domain simulation required to obtain nonlinear response involves analyses which are rather timeconsuming. Therefore, a simplified method for the estimation of the extreme wave-induced value in the
long-term distribution with specific probability of exceedance is necessary to improve efficiency. Folso
and Rizzuto (2003) introduced the concept of the equivalent waves. This is, by definition, an
approximation, as complex wave patterns giving rise to a linear extreme response in the long-term
ISSC committee I.2: Loads
45
distribution are modelled with a simplified geometry. The difference from reality is even greater if the
simplified wave is sinusoidal, whose characteristics are very different from those of extreme sea waves.
The aim of an equivalent wave is neither to model the geometry of extreme sea waves, nor to provide
means to check the ship structure against the envelope of extreme responses it is exposed to during its
life. Calculations were carried out for a 128m Ro-Ro fast ferry. The analysis of the proposed test case
appears to indicate that a set of 3 or 4 equivalent waves is sufficient to cover the chosen responses; in
particular head, beam and bow quartering waves with different wave lengths are found to be
representative.
Minoura and Naito (2004) proposed a stochastic process model for the long-term statistics of ship
responses. The correlation between significant wave height and standard deviation of ship responses at
sea was investigated. Analysing the monitored ship response data on board a container ship and a bulk
carrier for 3 years, it was observed that these standard deviations have three stochastic properties, namely
the Markov property, regression to equilibrium and linearity of fluctuation. The stochastic process model
based on these properties is given by the stochastic differential equations, and the probability density
function is obtained by the Fokker-Plank equation. The long-term prediction of ship response based on
this model was derived and compared to monitored data, showing good agreement. Shin et al (2004b)
presented a methodology for calculating the correlation factors to combine the long-term dynamic stress
components of ship structures from various loads in irregular seas. The methodology is based on the
theory of stationary ergodic narrow-banded Gaussian process. The total combined stress in short-term
sea states is expressed as a linear summation of the component stresses with the corresponding
combination factors. The long-term total stress is similarly expressed by linear summation of component
stresses with appropriate combination factors. The combination factors strongly depend on wave
heading and period in short-term sea states and are not sensitive to the selected probability of exceedance
level of the stress in the long-term sense.
Baarholm and Jensen (2004) performed a long-term analysis accounting for both nonlinearity and
transient elasticity effects on the vertical bending moment at amidships. The contour line method was
applied to obtain the long-term extreme value. The results were compared with predictions obtained
using the following simplified methods : (a) linear Sikora, (b) linear closed-form, (c) nonlinear closedform and (d) classification rules. The contour line approach was shown to give satisfactory results for
the cases studied in this work. Kawabe et al (2005) estimated the probability distribution of the
nonlinear extreme wave bending moment considering the limiting wave condition that a ship can
navigate. Deck wetness, bottom slamming and pitching angle were selected as the parameters for the
limiting wave condition. For the sagging condition, the distribution of extreme bending moment
obtained by nonlinear analysis (assuming the most severe short-term wave condition) is about 10% lower
than that obtained by linear analysis (assuming a long-term wave-induced distribution). The
corresponding value for the hogging condition is 40- 50% (lower).
6.
UNCERTAINTY ANALYSIS
The notion of uncertainty analysis being a permanent part of experimental and computational fluid
dynamics is maturing, and more published experimental and computational results are enhanced by
statements about uncertainty in the outcome. Experimentalists generally approve of the methodologies
and procedures recommended in estimates of experimental uncertainty. The International Towing Tank
Conference (ITTC 2005) recommends to its technical committees further development of methods and
procedures for uncertainty analysis for a wide range of experiments and full-scale measurements, taking
into account the usual bias errors and precision errors, fairing of curves etc. The need to develop
practical methodologies for extrapolating the uncertainty to full-scale predictions was also identified.
The approach to uncertainty in simulations is maturing as well. For example a significant number of
publications on RANS applications are complemented by uncertainty analyses. However, the majority of
practical applications are still based on strip theory and panel methods and more research is needed to
develop/attest uncertainty analysis techniques for these numerical approaches (ITTC 2005). Even though
the basic approach to uncertainty analysis appears to be uniform, the terminology is not always used
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ISSC committee I.2: Loads
consistently; it is not always clear what terms “error” or “uncertainty” mean in some applications. For
the purpose of this write-up, the terms applied by authors are used to report on particular publications.
6.1
Uncertainty in Measurements - Model and Full-scale
Uncertainty analysis procedure for model-scale tests appears to have become the routine practice; hence,
relevant information is rarely published, unless unconventional experiments or tests dedicated to
validation of numerical codes are involved. For the uncertainty analysis of full-scale trials, approaches
deviating from presently accepted methods and consideration or discussion of any new unconsidered
error sources are encouraged and would be a welcome addition to our present level of knowledge. Fullscale trials are essential for correlation with model-scale measurements and estimation of modelling
errors in calculated results. Nevertheless, it is rather difficult to find in the open literature results from
full-scale trials. Moreover, papers reporting full-scale trials do not usually include uncertainty analyses;
however, they do discuss relevant issues of concern. Cumming (2005) reported on the difficulty in
interpretation of sea conditions due to superposition of low frequency swell and high frequency new
waves coming from different relative directions. Detailed information on full-scale wave measurements
and relevant uncertainty is vital for proper preparation of model tests and setting up simulations
Statistical information on sea state is not always sufficient for direct comparisons between computational
and model and full-scale data.
Ma et al (2004) presented experimental uncertainty using two methods: ITTC and GUM (Guide to the
Expression of Uncertainty in Measurement). Analyses were conducted to estimate uncertainty in captive
model tests, measuring centrifugal force, carried out in a circular ship basin. The primary difference
between the two methods was that the ITTC approach categorizes uncertainty as systematic and random
and the GUM approach divides it into Type A and Type B uncertainties. Type A uncertainty can be
evaluated using statistical methods based on multiple tests and Type B uncertainty can be estimated by
means other than statistical. Type A and Type B uncertainties do not necessarily correspond to precision
(repeatability) and fixed (bias) uncertainties. The author concluded that the GUM method was effective
for cases of low confidence level and recommends this method for practical use. Olivieri et al 2003
presented an investigation into the flow around a fast displacement ship hull model. The boundary layer
and wake flow parameters were measured using a five-hole Pitot probe at Froude number 0.28 and
Reynolds number 1.2x107. The final outcome was presented as a pressure coefficient and velocity
components measured at three locations along the hull. The reported total uncertainty in the pressure
coefficient was larger than those for the velocity components. In all cases the systematic uncertainty was
the dominating element of the total experimental uncertainty. The collected data will be used to validate
a CFD model.
Stern et al (2005) discussed a statistical approach for estimating a systematic error of measurements in a
towing tank facility. The approach is based on M different measurements, in different facilities or using
different measuring systems, at the same N order level experiment. The process will generate a
population of NxM samples allowing for application of probabilistic methods for estimate of systematic
error intervals at required confidence level. An example of resistance test repeated at three different
facilities using two model sizes and conducted at three Froude numbers is shown. For high speed tests,
the facility bias for larger (1/24.8) and smaller (1/46.6) scale models was estimated at 2.9% and 9.3%,
respectively.
Faltinsen et al (2002) presented an experimental and theoretical investigation into global hydroelastic
effects due to wet-deck slamming on a high speed catamaran in regular head seas. A three-segment
model was used and vertical shear forces and bending moments, and motions were measured. The
authors reported that comparison between predictions and experimental measurements was satisfactory.
They identified sources of experimental error contributing to the comparison error, such as the spatial
variation of incident waves, an unintended small mean roll angle, an incident wave direction slightly
different from a head sea, and inaccuracies in measurement of trim angle, sinkage, wet deck height and
mass distribution. The most important theoretical error sources were associated with the hydrodynamic
loads on the side hulls and neglecting nonlinear side hull effects. The authors did not offer quantitative
ISSC committee I.2: Loads
47
estimates of errors or uncertainties. Fonseca and Guedes Soares (2004a) reported on estimates of
uncertainty in the second and third order harmonics of vertical load responses obtained from model-scale
experiments on a segmented model of a containership. The analyses were based on pairs of repeated
runs in regular waves of different frequencies and a comparison of the normalized responses. The
authors concluded that the dispersion of the first harmonics was very small but increased for the second
and third order harmonics of the vertical bending moment responses.
6.2
Verification and Validation of Numerical Codes
Verification and validation (V&V) is required to determine the accuracy of numerical codes. To perform
the validation it in necessary to take into account both experimental and numerical uncertainties. To
estimate numerical errors and/or uncertainties, iterative and parameter convergence studies must be
conducted. These are carried out using multiple solutions and systematic parameter refinement by
varying one parameter while holding all others constant. Input parameters subject to convergence study
are grid spacing, time step and artificial dissipation. Convergence studies require a minimum of three
solutions to evaluate convergence with respect to input parameters corresponding to fine, medium and
coarse grid solutions. Three convergence cases are possible: (i) monotonic convergence, (ii) oscillatory
convergence and (iii) divergence. For monotonic convergence the generalized Richardson extrapolation
can be used to obtain errors or uncertainties. In the case of oscillatory convergence, uncertainties are
estimated by bounding the oscillations with maxima and minima. For the case of divergence, errors and
uncertainties cannot be estimated. In general, the accuracy of the estimates depends on the solution’s
vicinity to the asymptotic range. The last report of this committee (ISSC 2003) identified estimates for
the modelling uncertainty based on the difference (or comparison error) E between the experimental
result and the simulation value, as well as relevant errors and uncertainties. Accordingly, validation can
be achieved at two levels, UE (uncertainty in E) or UV (validation uncertainty); for the former EUE and
for the latter, and more practical approach, EUV.
Past experience indicates that CFD predictions carried out by various individuals conducted using similar
tools result in a large scatter of the results. Pelletier et al (2003) presented an approach to increase the
confidence in CFD predictions and to develop good CFD practices. The authors discussed and presented
samples of an adaptive method to perform systematic grid refinement studies in order to achieve
solutions independent of meshing. They also discussed the application of sensitivity analysis to obtain
information on parameters most influencing the solution and where in the domain the errors tend to
occur. The flow sensitivities were defined as the partial derivatives of the solution with respect to the
parameters of interest. The sensitivity analysis can also be useful as a design optimisation tool because it
offers the potential to reduce the number of design parameters. In their conclusions the authors
underlined that the combination of mesh adaptation and uncertainty with sensitivity analysis could be a
powerful tool for verification and validation of CFD simulations. International benchmark workshops
for CFD applications for ship flow are useful in this respect. Larsen et al (2003) presented a summary of
the investigation of the most recent workshop. 20 organizations participated in investigating three test
cases of total resistance coefficient. The authors presented conclusions of the meeting including
discussion of each code's uncertainty using a verification and validation approach. Most participants
used verification as part of the computational procedures but only half of them presented quantitative
estimates. For successful validation cases reported, UV levels vary from 3% to 15%. This paper also
underlined the user factor in uncertainty estimates; the same code run by two different users showed up
to 55% difference.
Schellin et al (2003) investigated the application of linear frequency domain and nonlinear time domain
methods to predict wave induced global loads for a high speed ferry and round bilge fast mono-hulls. To
evaluate the numerical methods and to specify the limits of application, the predictions were compared to
data obtained from systematic model tests. The measured responses included a higher order nonlinear
load component. The experimental data was not supplemented by a formal uncertainty analysis. The
authors merely state that the scatter of the first order harmonics of the measured responses was
approximately 2% and indicate that the scatter of the second and third order harmonics increased but was
small relative to the mean values. With respect to V&V analysis for predictions, the authors indicated
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ISSC committee I.2: Loads
that the most influential parameters were selected to ensure adequate accuracy. They concluded that both
numerical methods complemented each other as the time domain method covered areas where the
frequency domain method was not valid. Maury et al (2003) compared two different methods of
calculation for the Green's function with forward speed, when used in panel methods for seakeeping and
loads calculations. The computational results were evaluated against experimental results obtained from
model tests of two Series 60 models with 0.6 and 0.8 block coefficients. The authors identified and
estimated experimental errors, to some degree. The validation presented was mostly through qualitative
comparison of computed and measured results.
More and more RANS based methods are being applied to simulate ship motions (e.g. see sections 2.1.3,
4.1, 4.2 and 4.3). They require increased robustness and more detailed experimental data for validation
purposes. Rhee and Makarov (2005) presented a validation study of a free surface wave flow around
surface piercing cylindrical structures. The volume of fluid method implemented in a Navier-Stokes
solver was used to calculate the free surface wave patterns and velocity distributions around a surface
piercing NACA 0024 hydrofoil and a circular cylinder. The validation process included a qualitative
comparison of the computed and measured data without modelling and experimental uncertainties being
considered. However, spatial grid convergence studies were conducted to find a grid independent
solution and to demonstrate the improvement in convergence to the solution when a finer grid was
applied. The time step dependency was not tested, since the solution stability was of greater concern
than its accuracy. Bunnik and Huijsmans (2005) discussed the validation process for a numerical wave
tank. Two approaches were tested, one based on potential flow theory and the other on a Volume of
Fluid algorithm and Navier-Stokes solver. The validation was conducted using data from wave tank
facilities. The waves were generated reflecting variations of significant wave height, modal period and
water depth. Measurements taken at 7 tank locations were compared with predicted results. A grid
convergence study was carried out to identify grid independent solutions. Weymouth et al (2005)
conducted a study to demonstrate that RANS methods can be used to correctly simulate the vertical plane
responses, including parameters such as added mass and damping. The authors conducted an uncertainty
analysis of simulated pitch and heave motion responses of a Wigley hull form using the CFDSHIPIOWA code. For the verification part, grid spacing and time step convergence studies were carried out to
estimate numerical errors. The resistance force and pitch and heave motion coefficients were considered.
For the validation investigation the calculated results were compared to experimental data, the latter
having an estimated uncertainty of approximately 2.5%. The resistance force and pitch motion results
were validated at uncertainty levels UV = 4.45% and 2.5% respectively, i.e. EUV; the heave motion
was not validated because the error E=6.56% and the uncertainty UV=6.52%. Simonsen and Stern
(2003) applied the CFDSHIP-IOWA code to a manoeuvring problem to compute the hydrodynamic
forces and moments acting on the hull. They used both the bare and appended hulls of the Esso Osaka
tanker for their investigation. The free surface effects were neglected and a k- turbulence model was
applied. Experiments were conducted at a Froude number of 0.063. The bare hull results were validated
at UV levels between 4.2% and 9.3%. For the appended hull, in oblique flow and flow with deflected
rudder, the level of validation for rudder forces and hull forces was achieved at UV levels between 3.4%
and 37.2%. They concluded that, although the validation levels were not satisfactory for all considered
cases, the method is applicable for hydrodynamic analysis of hull forces with varying rudder and drift
angles.
7.
FATIGUE LOADING
In a fatigue analysis the whole operational profile of a ship is required to obtain all stress cycles that will
be encountered during the service time. The most frequent cyclic loads have the most significant effects
on the fatigue strength of the hull structure. For conventional ship types usually linear frequency domain
methods for calculation of wave-induced loads are sufficient to predict fatigue strength, by applying
stochastic procedures to estimate life time fatigue accumulation. For example linear spectral methods
can be used, requiring transfer functions of stress responses to be determined in several operational and
environmental conditions. This is rather tedious if several structural details need to be analysed.
Simplified methods have been developed to represent the long-term distributions of stresses or loads
ISSC committee I.2: Loads
49
applying stochastic methods based on, for example Weibull-distribution. Application of linear
procedures is basically straightforward but includes several sources of uncertainties, such as calculations
of loads and structural responses as well as predictions of the life time operational and environmental
conditions. Huther et al (2004) discussed the uncertainties and simplifications in fatigue prediction
methods, including loads and stresses, and fatigue strength and failure criteria. They concluded that
progress has been made but validation of the calculation methods and results was still needed.
Component based spectral fatigue analysis was applied by Han et al (2004). Linear combination of
stress components were defined for hull girder loads and external and internal pressures. The so-called
influence coefficients were defined as stress per unit load. The method was applied to a LNG carrier,
together with a more complete spectral method where combined stresses were determined directly from a
FE analysis. Stress RAOs obtained from the component spectral analysis correlated rather well with the
full FE results. However, the component stresses can be difficult to determine if the stress distribution in
the structural detail is complicated and the stresses are due to loads from different sources.
Linear methods are not always sufficient to estimate fatigue strength of ships. For example, external
hydrodynamic pressure variations about the still water level and sagging and hogging loads can be
significant. These need to be analysed using nonlinear methods to obtain reliable fatigue loading for
strength analyses. In addition high frequency loads, such as springing and whipping can be important
and linear approaches are not always sufficient in this respect. In offshore structures second order loads
are usually significant and can be important in determining fatigue strength.
Influence of nonlinearities in loads for estimating fatigue damage was studied by Cariou and Jancart
(2003). Sagging and hogging nonlinearities were considered and fatigue damage predictions were based
on time domain simulations. They found that sagging and hogging has large influence on fatigue
damage and nonlinear loads gave considerably larger fatigue damage than linear predictions. The
nonlinear effects were due to Froude-Krylov and hydrostatic restoring forces, while radiation and
diffraction were assumed to be linear. On the other hand, model tests carried out for a fast mono-hull
showed that calculations tended to overestimate vertical bending moments (Schellin et al 2003). The
calculation model used also included nonlinear effects due to Froude-Krylov and hydrostatic restoring
forces and the authors suggested that not accounting for radiation and diffraction effects possibly
contributed to overestimated wave loads in several cases. Storhaug et al (2003) presented results from
full-scale measurements for a conventional large ocean going ship. The main emphasis in the
measurements was to investigate springing and whipping loads. Fatigue damage was estimated using
rainflow counting and wave frequency contribution was obtained using low-pass filtering in the
measured time series. It was concluded that springing was the main contribution to fatigue in ballast
condition. This was partly explained by the prevailing head sea conditions whilst on the ballast journey.
The effects of slamming and associated whipping loads on the fatigue life of a high speed vessel were
discussed by Thomas et al (2005). Data collected during full-scale trials showed that small slam events
had little or no influence on overall fatigue life. The overall reduction of fatigue life, due to slamming
ranged from 55% to 98%. For example, a change in wave height from 2m to greater than 2.5m in head
seas could reduce the expected fatigue life from 32 years down to 3 years. As a result the authors caution
designers to take into account the likely ship operational profile, to ensure that adequate fatigue life is
inherent within the structural design.
Effects of low cycle fatigue on ships were investigated by Urm et al (2004). Typical loading conditions
inducing maximum stress ranges were presented for oil tankers. In addition recommendations were
given for the minimum number of cycles for different type of ships.
Luo et al (2003) analysed critical connections of a truss spar to hull sections applying time domain and
frequency domain approaches to determine loads and fatigue strength. Wave frequency and low
frequency motions are both important for Spar type structures and the authors concluded that fatigue
damage was underestimated about 20% to 50% if only wave frequency contributions were taken into
account. Lu et al (2003) performed fatigue analysis of heave plates in truss spars. Time domain
approach was applied to predict pressure loads on the heave plates and rainflow counting was used to
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ISSC committee I.2: Loads
determine fatigue damage. It was shown that heave plate pressures were dominated by inertial forces and
fatigue damage could be significant, notwithstanding the location of the heave plates being well below
the water surface. Mikkola et al (2003) also performed similar calculations for a truss spar. Rayleigh
and rainflow distributions of bending moment range M, at the cross section of spar hard tank and truss
section, from time domain simulations are presented in Figure 9. Rayleigh’s distribution is based on the
standard deviation of the response obtained from the time history. The second order contribution is
rather small and both Rayleigh and rainflow counting result in the same type of distribution. Although
Rayleigh’s distribution can give good predictions for the response ranges, typically the Rayleigh fatigue
model results in conservative predictions for fatigue strength. Usually time domain approaches are time
consuming if several sea states have to be analysed to obtain reliable prediction for fatigue strength. A
practical approach to reduce the number of sea states in analyses was also presented by Mikkola et al
(2003). They applied interpolation polynomials to define fatigue loading in wave height and period
space. This method was used to predict fatigue strength for global motion induced loads for truss spars.
It was shown that the interpolated results fitted well with results obtained from direct numerical
simulations.
Figure 9: Load cycle histogram for the global bending moment at spar hull cross section between the
truss and hard tank sections (Mikkola et al 2003).
8.
RULES DEVELOPMENT FOR SHIPS
Up to the fifties, classification assessment of ship’s strength was mainly based on past experience, static
and quasi-static wave profile loads, as the natural forces and behaviour of the sea were deemed at the
time to be largely unpredictable. This rule and minimum standards framework ensured safety for
existing ship types but was more difficult to apply to new types of ships. Furthermore, the requirements
referring to the ship’s structure scantlings had tabular form and were not expressed in non-dimensional
format, normally derived from the principles of structural mechanics. At the time the ship structure was
appraised in terms of separate structure members. It was conservatively assumed that if each structure
member satisfied the minimum requirements then the whole hull structure would be safe. On larger
ships, the verification of deck cross section was additionally required. Nevertheless, trends to optimise
the fleet led to new ship types reflecting the diversity of carried cargo and means of loading and
ISSC committee I.2: Loads
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unloading. The safety standards applied at the time appeared to be inadequate to the new types of ships.
Classification societies started to develop new safety standards in response to this new situation.
Safety standards in the present rules correspond to the division of the hull structure strength into hull
girder, zone (hold) and local problems, i.e. 3 problems in total. Theoretically 4 criteria , namely yielding
of the structure material, buckling of the structure, fatigue of structure details and ultimate strength, have
to be applied to each problem, effectively resulting in 12 problems. In practice, the ultimate strength
criterion, in current rules, is only applied to certain structures (e.g. bulkheads) and the fatigue strength
criterion is applied only to the design requirements of some structural connections (e.g. for connections
of longitudinals); thus, reducing the number of problems. In the yield check the allowable stress is
divided into components, i.e. the criterion for hull girder, zone and local strength components. However,
the decomposition of the allowable stress into components is not simple. This is mainly due to the fact
that class rules require application of different wave loads, in the form of formulae, which are likely to
occur once in a ship’s lifetime. These loads do not appear “simultaneously”; there is a phase shift
between them. Therefore, summing the stresses in a particular structural member (e.g. bottom
longitudinal) resulting from the application of the rule load components (for example, wave bending
moments, wave pressure and ship’s accelerations) results in a value greater than that caused by
superposition of the loads taking into account their phase shift. The proper combination of the stress
components is important for deriving the total stress value, giving rise to the question : “How can one
combine the dynamic load components, determined either by the rules formulae or predicted separately
through the use of suitable software?”.
Decades of applying such rules and ship structure casualties, notably affecting the structure of bulk
carriers and tankers and mainly due to uncertainties in wave loads determination, gave rise to the
development and implementation, sometimes retroactively, of new requirements in direct reaction to
such casualties. This unsatisfactory state of regulations for ships’ structure triggered both:
 the development of Common Structural Rules for Oil Tankers (JTP) and Bulk carriers (JBP) by
IACS (2004a, b), which have recently been presented to the industry for comments, and
 the development of the Goal Based New Ship Construction Standards (GBS) by IMO (2004 a, b,
c), namely MSC 78/26, MSC 79/26 and MSC 80/6.
The proposed Common Rules are intended to embrace more aspects of safety, such as ultimate strength,
fatigue strength and strength in damaged conditions, than the presently binding rules. Design loads - the
most uncertain aspect affecting safety - are in the form of a combination of static and dynamic, local and
global loads and they “consider the most unfavourable combination of load effects”, as given by JTP
(IACS 2004a).
The requirements referring to the dynamic load components (wave bending moments and shear forces,
external sea pressures, internal dynamic pressures, ship motion and accelerations) are presented in the
form of formulae. The loads for scantling requirements and strength assessment are at the probability
level of 10-8 (10-4 being the reference level for fatigue strength), as given by JTP and JBP. The load
combination factors are given as tabulated values and are calculated by application of the equivalent
design wave approach , as also given by JTP and JBP (IACS 2004a, b).
Shigemi and Zhu (2003), and Zhu Shigemi (2003) developed methods for practical estimation of the
design loads which, based on the following definitions:
 design sea state (irregular wave) is the sea state that generates response value equivalent to the
long-term prediction of stress,
 design regular wave is the regular wave that generates response values equivalent to the response
values generated by the design irregular wave, and
 design loads are loads generated by the design regular wave and used to design the hull structure.
The values of stresses estimated with the use of these proposed design loads are claimed to be equivalent
to the long-term predictions of stresses for typical load cases (see section 5). In the design regular wave
approach the dominant load is determined for wave heading angle, wave period and height values which
produce a maximum response. The dominant load is computed for each load case. Then the load
combination factors, representing the relationship between responses to dominant and secondary loads,
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ISSC committee I.2: Loads
are determined (Shin et al 2004b). This regular wave approach has been widely used in local scantling
and FE analysis of ship structure. An irregular wave approach is more appropriate in combining
load/stress components for fatigue assessment. Shin et al (2004b) presented a consistent and complete
method for the combination factors in multiple sea states. The formulation is exact when applied to a
single random sea. To determine the load combination factors in long term the probability of the sea
state occurring was taken into account.
Direct methods of determining the loads acting on a ship and its structural response are based on
hydrodynamic and structural mechanic theories. The actual shape of the ship, mass distribution,
randomness of the sea and loading conditions are taken into account in these theories. Theoretically, an
infinite number of loads acting on the ship should be considered; in practical calculations, however, a
sufficient but finite number of representative cases is implemented. Most important of all, the actual
phase shifts between loads are determined in the evaluation of the stresses on the structure. Therefore, it
is questionable whether:
 the simple formulae approximating the amplitudes of wave load components - with the assumed
probability of exceeding thereof,
 the phase shifts between loads in the form of factors, and
 the small number of load cases assumed in the simplified methods
can approximate the randomness of the sea and ship operations that is represented in its mathematical
models by a family of functions (stochastic approach).
The Maritime Safety Committee of IMO has commenced the development of Goal Based Standards,
which was initiated in 2002. So far this Committee has formulated (IMO 2004 a, b, c):
 the goals, which assume that “ships are to be designed and constructed for a specified designed
life to be safe and environmentally friendly when properly operated and maintained under the
envisaged operating and environmental conditions, in intact and foreseeable damage conditions,
throughout their life”, and
 the functional requirements which, amongst others, refer to the design life, environmental
conditions, fatigue life, structural strength and residual strength.
The problem of quantification of the functional requirements is under discussion.
9.
CONCLUSIONS
9.1
Environmental Loads on Ships
Strip methods, due to their robustness and efficiency, are still in use and this is likely to continue for the
next few years. The nonlinear developments of this method make it suitable for special hull forms, fast
ships and large motion applications, such as roll. It has been noted that in such circumstances they may
provide more reliable results than 3D methods.
Methods using the zero forward speed Green’s function, with corrections for forward speed, are quite
mature and provide good results which are of the same level of accuracy as strip methods. The 3D
Green’s function method with forward speed, due to its inherent numerical complexities, continues to
attract attention. Development of reliable and efficient numerical schemes is essential for this method to
compete with strip theory and the 3D Green’s function without forward speed in the prediction of
motions and loads in common design practice. In addition there are issues, such as irregular frequencies
and the influence of steady flow. Progress has been made in dealing with all these aspects but further
work is required, especially in obtaining load predictions from the methods developed.
Accounting for the influence of geometrical nonlinearities on wave-induced motions and loads in the 3D
domain is, in the main, carried out using the body-nonlinear time-domain Green’s function and the
Rankine source methods. The former has limitations due to the linearised free surface condition, the
latter is versatile but rather time consuming. Remarkable advance has been achieved by studies based on
ISSC committee I.2: Loads
53
CFD and particle methods; however, improvement is still needed for higher resolution and reduction of
computational time. There is a need for a more comprehensive validation of such numerical methods.
Hydroelasticity approaches using modal decomposition based on dry modes and linear frequency domain
analysis for the steady state hydrodynamic forces represent a good compromise between accuracy and
computational demand. The first flexural mode is, generally, responsible for at least ninety per cent of
the total whipping contribution to the amidships vertical bending moment. To this end even very simple
models with one degree of freedom are capable of predicting the whipping contribution fairly accurately
provided that the impact force is accurately described. In this respect rigid body approximations, either
theoretical or experimental, are capable of determining this impact force.
There are clearly two schools of thought regarding modelling of elastic deformations of ships: the fully
flexible model using a material with a low Young’s modulus and thin structural elements and the
segmented model with a flexible backbone. The former is clearly more complex and, hence, more
expensive; however, a real scaled version of the ship is not fully achievable and it is practically
impossible to construct the model with all structural details so that local measurements in the model can
directly be transferred to values for the real ship. The latter approach relies on the assumption that the
interaction between the loads on the model and the deformation is sufficiently achieved using a
discretisation of the flexibility of the hull into a limited number of segments. There is a direct relation
between the ambition of the experimental programme, e.g. the number of deformation modes that are
deemed relevant, and the number of segments. There is presently no proof of the validity of this
assumption and the accuracy of the experiments that is lost when limiting the number of segments.
Use of hull monitoring systems is beginning to establish itself, although there is still a long way to go.
The design of some of these systems is quite comprehensive in collecting a wealth of full-scale data, that
can be used for verifying/validating theoretical methods and model test measurements. There are two
issues that require attention: the unavailability of such information in the open literature and the
uncertainty associated with data relating to environmental/operational conditions. The former is also an
issue for customised model tests.
3D Green’s function and Rankine source methods are, in general, applied to predict the response of
multi-hulled vessels and high speed craft in waves. Many of the theoretical formulations have been
validated using vertical plane responses derived from experiments. Efforts should be focussed to
obtaining suitable benchmark data in oblique waves, especially for multi-hulled vessels.
Large amplitude roll motions have become a significant problem since new hull forms characterized by
large alterations of righting lever were introduced. Excessive accelerations may occur leading to cargo
loss or damage, when this is combined with large values of initial metacentric height. This is the typical
case of parametric roll in head seas. The vessel may suddenly capsize, when this is combined with low
initial metacentric height values and stern quartering seas. This can be due to loss of stability, parametric
roll or a combination of the two. Experimental and numerical investigations are used to simulate this
problem, the latter consisting by and large of nonlinear strip theories with a limited number of degrees of
freedom. On the numerical side there is room for improvement of predictions. On the experimental side
efforts can be targeted on irregular seas and the whole range of headings.
The simulation of ship operations in ice is improving. Experimental and full-scale data are required for
better understanding of the physics of ice-hull interactions, and for validation of numerical codes.
Development and application of plasticity based limit states could generate more cost-effective and safer
ships. Future work needs to be directed towards improved numerical models of ice evolution and ice
contact. The design models and rules must find a way to reflect the true nature of ice loads.
9.2
Environmental Loads on Offshore Structures
First and second order solutions continue to be in use in estimating wave loads on fixed and floating
offshore structures. The major development relates to multi-body interactions and the gap resonance
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ISSC committee I.2: Loads
between hulls. The aim is to produce a computationally efficient method, hence the idealisation of the
hull(s) and surrounding fluid is very important, e.g. use of inner/outer domains; near-, middle- and farfield, flexible lid or gap dissipation area etc. Use of RANS related methods is rather sparse. More
experimental evidence would be welcome for verification purposes.
Coupled floater-mooring global response is the main issue of interest, with particular focus on cable
touchdown, drag damping arising from the mooring/cable system and the snap- and slack impact loads.
Furthermore, emphasis is placed on the degree of coupling and the nonlinear dynamic behaviour of
mooring lines. Instability of the floater - mooring system is beginning to gain ground as an important
aspect of dynamic behaviour. Another area of interest relates to riser clashing.
Vortex shedding induced vibrations continue to challenge engineers and scientists. Experimentation,
semi-empirical models and CFD-based models are employed to produce engineering results for design of
risers, steel catenaries, pipelines and spars just to mention a few typical systems. CFD-based models
require more work on validation and on speeding up computations for these to become engineering
tools. Early strategy to avoid the lock-in regime altogether is no longer feasible and it is necessary to
master the transition zone. Monitoring projects are in operation or under way; one hopes that at least
some of their findings will reach the open literature.
9.3
Loads due to Impacts and Extreme Events
Numerical solutions of the water entry problems are typically based on the boundary element method and
the free surface is updated using mixed Eulerian-Lagrangian approach. Use of CFD in ship slamming
problems is increasing. It should be noted, however, that methods applied in local slamming problems
are mostly based on simple geometries, such as 2D wedges. Development of methods suitable for 3D
bodies is progressing, but the shapes used are relatively simple. Experience is still lacking with ship like
hull forms and more complex geometries, e.g. convex bodies such as bow flare type geometries.
Furthermore rather few results are presented for slamming induced structural responses and stresses.
Although our understanding of sloshing is advancing, some issues require more attention. The
understanding and modelling of hydroelastic effects of sloshing impacts is still in an early phase. The
accuracy and practical applicability of CFD for local flow phenomena needs further development. More
work is also required to resolve the problem of scaling from model tests. Ultimately full-scale
measurements inside a LNG tank would be most desirable to support our understanding of these issues.
A number of approaches, ranging from hydrostatic and semi-empirical methods to smoothed particle
hydrodynamics and use of RANS codes, have been applied to simulate green water on deck with
reasonable degree of success. Several applications focussed on identifying deck geometries to mitigate
the effects of green water. More experimental evidence is required to assess the success of the methods
used.
Accurate modelling of freak waves is a vital precondition for the simulation or experimental testing of
structures in rogue waves. Furthermore an improved understanding of their occurrence, i.e. when, where
and how often, is a significant factor in making them part of a design load procedure. Cooperation
between meteocean researchers, hydrodynamicists and design load specialists is needed in this respect.
9.4
Probabilistic Methods
For the strength assessment of ship structural members, it is necessary to estimate the maximum value of
wave-induced load during the ship’s operating period. As in the severest sea state condition the ship
response is nonlinear, there are many theoretical and/or experimental methods for estimating the
probability distribution of nonlinear response in the irregular short-term wave condition with very large
significant wave height. It was shown that the statistical distributions depend on the type of ship and
ship response. New methods, such as MLRW, MLER and EMLER, for estimating the entire nonlinear
extreme response value distribution for a selected operational profile were proposed. These, however,
ISSC committee I.2: Loads
55
have to be verified with further numerical simulations and experiments before becoming established
tools. Some simplified methods for the estimation of the linear extreme wave-induced value in the longterm distribution with specific probability of exceedance were proposed. However, a complete long-term
distribution of the nonlinear response is still outstanding.
9.5
Uncertainty Analysis
With respect to experimental uncertainties, the use of a standardized approach and terminology is
required to keep the process transparent, uniform and compatible, as well as practical. The validation
process is usually based on integrated quantities, such as ship responses, which could carry some
unaccounted errors. Validation based on measurements, such as pressure, could provide more insight
into relevant hydrodynamic processes. Furthermore, effort should be focussed on generating suitable
benchmark measurements for loads.
Verification and Validation studies routinely accompany computations based on RANS and FE codes.
The situation for 2D and 3D potential flow based codes is unsatisfactory and should be remedied.
Furthermore the “user” factor should also be taken into account. Our search revealed that validations
deemed successful were achieved at different levels of uncertainty. This indicates the need to establish
target levels for acceptable uncertainty (experimental and numerical) to provide guidelines for developers
and users.
9.6
Fatigue Loading
Linear methods in fatigue loading are well known and their use is becoming more common in fatigue
analyses of ship and offshore structures. Further studies and validation of these methods are still
required to increase the reliability of fatigue predictions. It is not always possible, especially for ships, to
obtain accurate data for environmental loading and operational conditions, resulting in rather large
uncertainties in fatigue predictions. Nonlinear loads for ships, such as hydrodynamic pressure, whipping
and springing, sagging and hogging bending moments, and second order wave loads for offshore
structures are shown to be important. Nonlinear procedures need to be further investigated and
developed in order to include nonlinear loads in fatigue analyses in a reliable manner.
9.7
Rules Development for Ships
In the design regular wave approach the load combination factors represent the relationship between the
dominant (maximized in specific wave conditions) and the lower order loads. It is questionable,
however, whether such an approach can approximate the randomness of the sea and ship operations.
Developments, such as the Goal Based New Ship Construction Standards by IMO, are intended to define
the safety level for ship structure. They are intended to be used to verify whether the classification rules,
IMO requirements and administration requirements implemented to an individual ship ensure the defined
safety level.
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ISSC committee I.2: Loads
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ISSC committee I.2: Loads
Krüger, S., Hinrichs, R. and Cramer, H. (2004). Performance Based Approaches for the evaluation of
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Moe, G., Teigen, T., Simantiras, P., Willis, N. and Lie, H. (2004). Predictions and Model Tests of an
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Olagnon, M. and Prevosto, M. (2004). (Editors) Rogue Waves Workshop, IFREMER France,
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Storhaug, G., Vidic-Perunovic, J., Rudinger, F., Holtsmark, G., Bloch Helmers, J. and Gu, X. (2003).
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