Spectral Fatigue Analysis
Methodology for Ships
and Offshore Units
July 2008
Guidance Note
NI 539 DT R00 E
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BV Mod. Ad. ME 545 j - 16 February 2004
GUIDANCE NOTE NI 539
Spectral Fatigue Analysis Methodology
for Ships and Offshore Units
Section 1
July 2008
Spectral Fatigue Analysis Methodology
for Ships and Offshore Units
2
Bureau Veritas
July 2008
Section 1
Spectral Fatigue Analysis Methodology
for Ships and Offshore Units
1
General
1.1
1.2
1.3
2
5
6
July 2008
8
Modeling and boundary conditions
Loading
Hot spot stress RAO
Spectral analysis
6.1
6.2
6.3
8
Modeling and boundary conditions
Loading
Analysis
Fine mesh analysis
5.1
5.2
5.3
7
Introduction
Hydrodynamic model
Analysis
Global structural analysis
4.1
4.2
4.3
5
Wave scatter diagrams
Wave spectrum
Loading conditions
Wave headings
Hydrodynamic analysis
3.1
3.2
3.3
4
Introduction
SFA process
Conditions of analysis
Encountered conditions
2.1
2.2
2.3
2.4
3
5
9
Response spectrum
Spectral moments
Damage calculation
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July 2008
NI 539, Sec 1
SECTION 1
1
SPECTRAL FATIGUE ANALYSIS METHODOLOGY
FOR SHIPS AND OFFSHORE UNITS
General
1.1
1.3
Introduction
1.1.1 The present note provides the methodology to perform a Spectral Fatigue Analysis (SFA).
A spectral fatigue analysis is performed on structural details of
a ship structure or offshore unit to take account of the different
environmental conditions encountered by the structure during
its design life.
Conditions of analysis
1.3.1 Several models have to be prepared: static (still-water)
model corresponding to the loading condition being analysed (draught, weight distribution), hydrodynamic model and
structural model. The objective is to apply to the structural
model the loads obtained from the hydrodynamic analysis.
Therefore, special attention is to be paid to the consistency
between these two models for transfer of loads.
1.3.2 The frequency calculation is carried out regarding
two principal parameters:
1.1.2 In this note, the fluctuating loads studied for fatigue
analysis are the wave-induced loads.
• draught and loading condition
1.1.3 The Spectral Fatigue Analysis methodology described
in this note is based on linear frequency domain analysis.
2
• wave heading.
2.1
1.2
Encountered conditions
Wave scatter diagrams
SFA process
• the long term distribution of stresses resulting from the
action of the cyclic loads applied on the structure
2.1.1 The long-term description of seas encountered by the
ship or at the offshore unit site is usually provided in terms
of scatter diagram(s) of sea-states, giving the number of
observations over a certain period of discrete sea-states,
each being defined by the significant wave height Hs and a
period (e.g. the peak period Tp).
• the fatigue capacity of the structure, characterized by S-N
curves.
2.2
1.2.1 A procedure for fatigue strength assessment requires
determining:
1.2.2 A Spectral Fatigue Analysis includes the following
steps, described in Fig 1:
• Hydrodynamic analysis: external loads induced by the
waves on the ship structure or offshore unit as well as
the resulting motions are determined by a hydrodynamic analysis in frequency domain.
• Structural analysis: loads are transferred to the structural
model. Global analysis on a full or partial structural
model, followed by a very fine mesh analysis provide
the RAOs of stresses (Response Amplitude Operators) at
the location of interest.
• Spectral analysis: the response spectrum at each location
of interest is obtained by the technique of spectral analysis. The short-term distribution of stresses is obtained by
statistics over short-term sea-states, headings and loading conditions of the ship or offshore unit. Long-term distribution of stresses during the design lifetime is then
obtained by summation over the wave scatter diagrams.
• Fatigue damage: the fatigue damage is determined by
the Miner sum, either from the long-term distribution of
stress ranges and appropriate S-N curve or by summation of fatigue damage for each short-term response.
July 2008
Wave spectrum
2.2.1 Each sea-state is described by a wave energy spectrum
of appropriate shape for the voyage or site under consideration (e.g. Pierson-Moskowitz, JONSWAP, Ochi Hubble).
2.2.2 To take account of confused short-crested seas, the
total wave energy spectrum may be split according to wave
direction as follow:
S (ω, θ) = S (ω) G (ω, θ)
Where S(ω) is the wave spectrum and G(ω,θ) the directional
spreading function, characterizing the directional distribution of the wave energy around the mean direction.
2.3
Loading conditions
2.3.1 Offshore units
The loading conditions that may be considered for SFA of
offshore units may be the ones described in NR445 Rules
for Offshore Units.
Representative loading conditions of the loading/unloading
sequences may be selected from the loading manual or
from operating data. Each loading condition being characterized by the levels in oil and water ballast tanks and the
associated draught.
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NI 539, Sec 1
Figure 1 : SFA process
( $ $
) * !
!"#
%& $ $
' 2.3.2 Oil tankers
The loading conditions that may be considered for SFA of
oil tankers are the full load and ballast conditions, as
described in IACS Common Structural Rules for Double
Hull Oil Tankers or NR467 Rules for Steel Ships as the case
may be.
2.3.3 Bulk carriers
The loading conditions that may be considered for SFA of
bulk carriers are the homogeneous, normal ballast, heavy
ballast and eventually alternate conditions (depending on
bulk carrier notation), as described in IACS Common Structural Rules for Bulk Carriers or NR467 Rules for Steel Ships
as the case may be.
2.3.4 Other ships
The loading conditions that may be considered for SFA of
other ships are the ones described in NR467 Rules for Steel
Ships.
2.4
Wave headings
2.4.1 The range of headings to be considered depends on
the type of ship or offshore unit.
6
For a trading ship or a spread moored unit, the range of
headings has to cover 360°.
When the offshore unit is turret moored, the wave headings
of interest can be generally taken in the range [-90°, 90°]
from “head sea”. The range of wave headings may be determined more precisely by performing a heading study. In this
case, the environmental conditions (wave current, wind) are
to be combined as described in NI493 Classification of
Mooring Systems for Permanent Offshore Units, Appendix 2.
When swell and wind seas are independant, both conditions are to be computed separately.
2.4.2 A heading interval in the range of 15° to 22° will be
adequate to get accurate directional response using directional spectrum.
The heading interval is often taken as 45°, in relation with
commonly available directional information. This is however not sufficient to catch the directional response of the
structure to waves (e.g. horizontal wave bending moment)
and precludes the use of directional spectrum to describe
waves.
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NI 539, Sec 1
3
Hydrodynamic analysis
3.1
The size of elements may be constant but needs to be
refined near the waterline, at the end parts of the model and
at the location of sharp corners.
Introduction
3.1.1 The objective of the hydrodynamic analysis is to evaluate by direct calculations RAOs of wave-induced loads
(e.g. motions, accelerations, wave pressures and hull girder
loads such as bending moments and shear forces), for the
environmental conditions during the ship trading routes or
at the site where the offshore unit will operate.
3.1.2 The hydrodynamic analysis is to be carried out using
a recognised software, such as Hydrostar of the Society. In
particular, the use of a software based on three dimensional
potential flow based diffraction radiation theory is required.
Any other software is to be documented.
3.2
Hydrodynamic model
3.2.1 General
The model should take into account the following effects:
• The ship or unit forms with appendices (e.g. skeg), if any
• The weight distribution of the loading conditions
described in [3.2.2], including lightship distribution
• The connections with the seabed if any.
For each loading condition, the hydrodynamic model is to
be consistent with the loading manual in terms of mass distribution, inertia, trim, still water bending moments and
shear forces.
3.2.4 Number of elements
The wetted surface of the ship or unit should be modeled by
a sufficient number of elements.
The number of elements is to be taken between 700 to 1500
for a half hull. A greater number of elements normally does
not influence the results.
3.3
Analysis
3.3.1 General
The hydrodynamic analysis is based on linear theory. The
motions are calculated without taking into account non-linearities due to intermittent wetting effect in the splash zone,
flare and water on deck.
The motion analysis will account for such loads as the
external loads by incident and diffracted wave, the inertial
loads, the hydrodynamic added mass and damping loads
and the hydrostatic restoring forces.
3.3.2 Range of frequencies
A range of wave frequencies of 0,1 to 1,5 rad/s is normally
sufficient.
30 to 35 wave frequencies is adequate. 20 is a minimum.
A refinement around the ship resonance frequency is recommended.
3.2.2 Weight distribution
The inertia matrices necessary to the hydrodynamic analysis
can be derived from the mass model. The mass model has
to reflect the steel weight distribution, the weight distribution of cargo and ballast and the weight distributions of others items (e.g. topside structures for offshore units)
3.3.3 Rolling damping
Roll motion is sensible to roll damping. The viscous part of
roll damping may be calibrated by model tests or estimated
by semi-empiric formulation.
For a full structural model, the mass matrix is obtained from
the structural model which includes a description of the
mass distribution.
• Linear damping coefficients:
For a three holds structural model, the mass matrix of the
modeled part is obtained in the same way as for the full ship
structural model. The mass matrix of the fore and aft parts
have to be evaluated as well, so that the aggregate mass
matrix of all 3 parts is matching the global mass matrix.
In the case where no value is available, the following roll
damping may be considered:
• taken between 5% and 8% of the critical damping
for tankers, bulk carriers and LNG carriers
• taken between 3% and 5% of the critical damping
for container ship
• Quadratic damping coefficient :
• 0,5ρCdB4L
where:
Any inaccuracy on mass matrix may result in either an
unbalance of the structural model or incorrect end shear
forces and/or bending moments.
3.2.3 Dimension of panels
In the cylindrical part of the ship or offshore unit, the wave
length must be properly described: 6 to 10 points over one
wave length. For this reason, the following relationship may
be satisfied:
L w ave
L pa ne l ≤ ----------10
where:
2
gT
L w ave = -------2π
T
July 2008
: Shortest encountered wave period.
ρ
: Sea water density, in t/m3
Cd
B
: Adimensional drag coefficient, whose
value depends on hull shape, may be
taken within the range [0,08 ; 0,1] for
offshore units and [0,06 ; 0,08] for ships
: Ship or unit breadth, in m
L
: Ship or unit length, in m.
3.3.4 Results
The results provided by the hydrodynamic calculations are
the RAOs of loads (e.g. external pressures, motions...) for
the different combinations of frequencies, headings and
loading conditions. The next step is to determine the structural behaviour of the ship or of the offshore unit under
these conditions.
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NI 539, Sec 1
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4.1
Global structural analysis
4.2.4 Internal tank pressure and cargo loads
The pressure in internal tank or cargo hold is deduced from
the tank accelerations.
Modeling and boundary conditions
4.1.1 General
The structural model may be a full model, or includes several cargo holds (generally 3), centered on the area of interest for the fatigue analysis.
Attention is to be paid for the mesh on the waterline area,
for the considered loading conditions. In this area, the
height of panels is to be reduced. A panel height equal to
ordinary stiffener spacing may be used.
4.1.2 Full model
In the case of a full model, modeling and boundary conditions are to be in accordance with NR467 Rules for Steel
Ships , Pt B, Ch 7, App 3, [2].
4.1.3 Three holds model
In the case of a three holds model and depending on the
ship or unit type, modeling and boundary conditions are to
be in accordance with:
• Rules for Offshore Units (NR445)
• CSR for Oil Tankers (NR523)
• CSR for Bulk Carriers (NR522)
4.2.5 Inertia loadings
The inertia loading is generated from the accelerations acting on the steel mass of the structure, and other masses.
4.2.6 Hull girder loads for three holds models
In the case of a three holds model, hull girder bending
moments and shear forces are to be determined to represent
the ends of the model, and are used as boundary conditions.
4.3
Analysis
4.3.1 When structural analysis takes into account still water
and dynamic effects, an additional still water calculation is
to be performed for each loading condition.
Loading
4.2.1 General
Wave pressures and inertia loads obtained from the hydrodynamic analysis are to be transferred from the hydrodynamic model into the structural model. Hydrodynamic and
structural models have to be consistent, both in geometry
and in the description of mass.
Under the assumptions of a linear spectral analysis, overall
loading for each combination of frequency, wave heading
and loading is harmonic and can be described by real and
imaginary parts.
4.2.2 Wave pressure loads
The sea pressure obtained from the hydrodynamic analysis
has to be transferred to the structural model of the ship or
offshore unit.
In the case the mesh of the hydrodynamic model and the
structural model are the same, the sea pressure may be
taken directly from the hydrodynamic analysis and applied
to finite elements.
4.2.3 Intermittent wetting
In linear diffraction-radiation analysis, hydrodynamic pressure is obtained over the wetted surface at rest as a harmonic pressure variation at each point. Therefore, the
pressure on the side shell between the surface at rest and a
wave crest is not modeled, and in a wave through below the
surface at rest, an unrealistic negative pressure is generated.
Intermittent wetting effect, in the free surface area, is to be
taken into account by means of an additional pressure loading on the side shell.
8
Non-linearities induced by pressure distribution in internal
tank and cargo hold is to be avoided as fatigue calculation
is performed in the frequency domain.
4.3.2 The RAOs of displacements of the global calculation
are extracted in the area of fatigue interest as boundary conditions for the fine mesh analysis.
• Rules for Steel Ships (NR467).
4.2
A quasi-static approximation may be used, under the
assumption of small movements of the ship or offshore unit,
where the pressure is defined based on the intensity and
angular variations of the total acceleration, including gravity.
5
5.1
Fine mesh analysis
Modeling and boundary conditions
5.1.1 Depending on the ship or unit type, fine mesh modeling and boundary conditions are to be in accordance with:
• Rules for Offshore Units (NR445)
• CSR for Oil Tankers (NR523)
• CSR for Bulk Carriers (NR522)
• Rules for Steel Ships (NR467).
5.2
Loading
5.2.1 The fine mesh is to be loaded with the same loads
than those applied in the global model in [4.2].
5.3
Hot spot stress RAO
5.3.1 Depending on the ship or unit type, the hot spot
stress RAO may be calculated according to:
• Rules for Offshore Units (NR445)
• CSR for Oil Tankers (NR523)
• CSR for Bulk Carriers (NR522)
• Rules for Steel Ships (NR467).
5.3.2 When structural analysis takes into account still water
and dynamic effects, an additional fine mesh calculation in
still water condition is to be performed for each loading
condition to get the still water hot spot stress at location of
interest.
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NI 539, Sec 1
For each loading condition, this stress is to be deduced to the
real and imaginary hot spot stresses calculated for the different load cases (combinations of frequency and heading).
5.3.3 On the free surface area, the hot spot stresses RAO
are to be corrected to take account of the intermittent wetting effect.
The RAO correction may be based on an additional stress,
function of an additional loading and combined with the
Relative Wave Elevation (RWE) calculated at each frequency.
6
Spectral analysis
6.1
• Mean zero-up-crossing period of the stress response:
m
T z = 2 π -------0
m2
6.2.2 In the case of a ship with an advance speed V, the
spectral moments are given by:
∞
Mn =
∫ω
n
e
⋅ S ( ω ) dω
0
Where ωe is the encountered frequency calculated as:
ω ⋅ V ⋅ cos θ
ω e = ω – -------------------------------g
2
Response spectrum
6.1.1 A linear modeling of the ship is assumed for fatigue.
The structural response is then described by a superposition
of the response of all regular wave components, leading to a
frequency analysis.
6.3
Damage calculation
The response spectrum is given as follow:
6.3.1 Short-term distribution
For a ship or offshore unit, the stress range is generally
assumed narrow banded and assumed to be Rayleigh distributed during each short-term loading state.
S σ ( ω H s, T z, θ ) = H σ ( ω θ ) ⋅ S η ( ω Hs , T z )
6.3.2
2
Hσ (ω,θ) is the stress range transfer function obtained for
each loading condition, whose values depend on the wave
frequency and on the heading angle. It contains all the
RAOs of stresses.
When directional spreading is considered according to
[2.2], the stress response is obtained as:
Short-term damage for a single slope S-N
curve
For a single slope S-N curve, the damage corresponding to
one sea-state spectrum (Hs, Tz) is given as follow:
m
T
m
D = ------------- ⋅ ( 2 2m 0 ) ⋅ Γ ⎛ ----- + 1⎞
⎝2
⎠
K ⋅ Tz
where:
S σ ( ω H s, T z, θ ) = H σ ( ω θ ) ⋅ S η ( ω Hs , T z ) ⋅ G ( ω, θ )
K,m
: S-N curve parameters of the single slope S-N
curve
6.1.2
T
: Reference duration
m0
: Spectral moment of order 0
Γ
: Gamma function.
2
Mean stress effect
The response spectrum may be corrected to take account of
the less damaging effect of the compressive part of the stress
range, for each loading condition if any.
The correction requires the mean stress calculation at location of interest for each loading condition.
Depending on the ship or unit type, Mean stress effect correction may be carried out according to:
• Rules for Offshore Units (NR445)
m
T
m
D = ------------- ⋅ ( 2 2m 0 ) ⋅ μ ⋅ Γ ⎛⎝ ----- + 1⎞⎠
K ⋅ Tz
2
where:
• CSR for Oil Tankers (NR523)
μ
• CSR for Bulk Carriers (NR522)
• Rules for Steel Ships (NR467).
6.2
6.3.3 Short-term damage for a two slopes S-N curve
For a two slopes S-N curve, the damage corresponding to
one sea-state spectrum (Hs, Tz) is given as follow:
Spectral moments
6.2.1 The spectral moments of order n of the stress process
are given by:
⎧K
⎫
m′ – m
m
m′
Γ 1 + ----- ;A + ⎨ ----- ( 2 2m0 )
γ 1 + ------ ;A ⎬
2
K′
2
⎩
⎭
μ = -------------------------------------------------------------------------------------------------------------------m
⎛
⎞
Γ 1 + ----⎝
2⎠
A
∞
Mn =
∫ω
n
0
Assuming that the stress process is stationary and Gaussian,
the statistical parameters of the stress process are obtained
from the spectral moments as follow:
RMS =
July 2008
m0
: Coefficient taken equal to:
SQ ⎞ 2
A = ⎛ -----------------⎝ 2 2m ⎠
0
⋅ S ( ω ) dω
• RMS (Root Mean Square):
: Coefficient taking account of the change of
slope in the S-N curve, taken equal to:
K, m
: Parameters of the S-N curve above change of
slope
K’, m’
: Parameters of the S-N curve below change of
slope
T
: Reference duration
m0
: Spectral moment of order 0
Bureau Veritas
9
NI 539, Sec 1
Γ[X+1] : Complete Gamma function
The long-term damage is given as follow:
Γ[X+1;ν]: Incomplete Gamma function
D =
γ[X+1;ν] : Γ[X+1]- Γ[X+1;ν]
i
j
k
⋅ D i jk
ij k
SQ
: Stress range at change of slope on the S-N
curve.
6.3.4
Long-term damage
The long-term damage is the sum of the short-term damages, weighted by the probability of occurence of each
loading state, considering the number of stress cycles in this
loading state.
10
∑ Pr ⋅ Pr ⋅ Pr
where:
Pri
: Joint-Probability of (Hs, Tz) of the considered
sea-state in the scatter diagram
Prj
Prk
: Probability of occurence of each wave heading
: Probability of occurence of the considered
loading condition
: Short-term damage calculated in [6.3.2] or
[6.3.3].
Dijk
Bureau Veritas
July 2008