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Technical Basis ofHydrodynamic Load Analysis
Rio de Janeiro: 24 Feb. 2010
Overview of OSAP 2.0
Gwo-Ang ChangPrincipal Engineer
ABS Corporate Technology
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Outline
Load Generation
Design Wave Calculation
Load Mapping and Balancing
Summary
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3D HydrodynamicAnalysis Model
Geometry and MeshGenerator
HydrodynamicAnalysis Program
FEA Solver
Global Structural FE Model(Coarse Mesh for Yielding and
Panel Buckling Check)
Motion RAOsPressure RAOs
Fluid Velocity (optional)
Global Structural FE Model(Locally Refined Mesh for
Fatigue Check)
Structural Responses(Stress, Strain and Displacement)
OSAP 2.0
User Selected Third-party Applications
Typical Design Workflow Using OSAP
Need LocalFEA
Local FE Modelwith Refined Mesh
Y
N
End
Yielding, Buckling &Fatigue Code Check
Yielding, Buckling &Fatigue Code Check
Global FE Model, Loads,
and Constraints Input
Load Mapping& Balancing
Load Mapping
& BalancingLoad Cases for Strength
& Fatigue Assessment
Design WaveCalculation
Design WaveCalculation
LoadGeneration
LoadGeneration
Critical Responses
RAOs
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OSAP 2.0 Technical Basis
Load Generation
OSAP 2.0 Technical Basis
Load Generation
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OSAP Load Generation Module
Calculate inertia and drag forces for Morison elements
Dynamic forces calculation for mooring or tendons
Sectional forces and moments calculation
Interface with AQWA and WAMIT
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Elements Used for Hydrodynamic Modeling
For WAMIT Model
Panel element
For AQWA Model
Panel element
TUBE element
STUB element
DISC element
PBOY element
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Panel Elements
Hydrostatic pressure
Hydrodynamic pressure
Hydrostatically variant pressure
)( 0ZzgPStatic +=
tPDynamic
=
)( 213 xygP cVariationHydrostati +=
Global Coordinates
Body Coordinates
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Panel Elements
Force and moments in body coordinate systemare calculated by integrating the total pressures
over the body surface
where
: position vector (x,y,z) with respect to thereference point for the moment calculation
: outward normal vector of body surfaceexpressed in the body coordinate system
S : wetted body surface
= S dSnPF
dSnrPMS = )(
r
n
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TUBE and STUB Elements
Circular (TUBE) and non-circular (STUB)Morison elements
Hydrostatic loads Buoyancy forces
Hydrodynamic loads
Drag forces
Inertia forces
Froude-Krylov forces
Diffraction forces
Added-mass forces
Hydrostatic variation
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DISC Elements
A DISC element has no thickness and nomass, but has drag coefficient and added-
mass coefficient in its normal direction No hydrostatic force or Froude-Krylov force
Hydrodynamic loads
Drag forces
Diffraction forces
Added-mass forces
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PBOY Elements
PBOY represents a constant point buoyancy
Hydrostatic forces
Point buoyancy force in either upwards ordownwards direction normal to the mean stillwater line
Hydrodynamic loads
Hydrostatic variation
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Mooring or Tendon Model
For Static Case
Mooring/Tendon loads can be directly definedin OSAP *.STAT files.
Alternatively, mooring/tendon loads can beimported from AQWA-LIBRIUM analysis
results associated with any of the followingloading methods
LINE, NLIN, WNCH, FORC, LNDW (Deck 14)
THRS (Deck 10)
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Mooring or Tendon Model
For Dynamic Case
Mooring/tendons are modeled as masslesslinear springs, with one end attached at thefloater and the other end attached to theseabed.
Total forces/moments due to one spring
+=
ationStaticVarim
ationStaticVarim
m
m
m
M
F
M
F
K
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Linearization of Drag Force
The drag term of the Morison equation can be writtenin a generic linear form:
where is the linearized drag coefficient
Assuming a zero current velocity, the stochastic
linearization of drag force due to a random oscillationin irregular waves is
where is the standard deviation of relative velocity;is the fluid velocity; is the body velocity
OSAP requires the input of a representative sea statefor calculating the linearized drag force.
uCDLF dLIN 2
1
=
))(8
(2
1sfudLIN uuCDLF
=
ufu su
dC
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Sectional Force/Moment Calculation
External forces applied on Part 1and theinternal forces applied on the cutting plane on
Part 1 side follows Newtons Second Law
M=
+
+
ExternalInternal
ExternalInternal
MM
FF
Part 2Part 1n
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Sectional Force/Moment Calculation
Internal Forces Sectional forces andmoments to be solved
External Forces
Include all the forces applied on the Panel,TUBE, STUB, DISC and PBOY elements as
well as mooring/tendon loads Include the variation of gravity forces (g-effects)
M 6 X 6 mass matrix for Part 1
6 DOF acceleration vector at thereference point&
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Validation Case Study
Longtudinal Shear Force - FLDraft = 23.5m
0
200
400
600
800
1000
1200
1400
1600
1800
0 5 10 15 20 25 30 35 40
period(s)
RAO(KN/m
)
0deg - AGS
30deg - AGS
45deg - AGS
60deg - AGS
90deg - AGS
0deg - ABS
30deg - ABS
45 deg - ABS
60deg - ABS
90deg - ABS
Bending Moment - My
0
20000
40000
60000
80000
100000
120000
0 5 10 15 20 25 30 35 40
period(s)
RAO(KN
-m/m)
0deg - AGS
30deg - AGS
45deg - AGS
60deg - AGS
90deg - AGS0deg - ABS
30deg - ABS
45deg - ABS
60deg - ABS
90deg - ABS
Panel + TUBE Elements
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Validation Case Study
Longtudinal Shear Force - FL
0
200
400
600
800
1000
1200
1400
1600
1800
0 5 10 15 20 25 30 35 40
period(s)
RAO
(KN/m)
0deg - AGS
30deg - AGS
45deg - AGS
60deg - AGS90deg - AGS
0deg - ABS
30deg - ABS
45 deg - ABS
60deg - ABS
90deg - ABS
Bending Moment - My
0
20000
40000
60000
80000
100000
120000
140000
0 5 10 15 20 25 30 35 40
period(s)
RAO
(KN
-m/m)
0deg - AGS
30deg - AGS
45deg - AGS
60deg - AGS
90deg - AGS0deg - ABS
30deg - ABS
45deg - ABS
60deg - ABS
90deg - ABS
DISC + TUBE Elements
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OSAP 2.0 Technical Basis
Design Wave Calculation
OSAP 2.0 Technical Basis
Design Wave Calculation
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Design Waves
What is a design wave?
A means to transfer the responses from a
hydrodynamic model to a global structural FEAmodel
A regular wave that generates the same
magnitude of critical response in the structure How to calculate a design wave?
Deterministic approach
Stochastic approach
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Design Wave Analysis Deterministic Approach
Calculate RAOs of critical responses (loads andaccelerations)
Define regular wave steepness S and maximum wave height Calculate the maximum response, Rmax, and the period,
Tmax, and heading where Rmax occurs
Design wave period = Tmax, the period where Rmaxoccurs
Design wave heading = wave heading where Rmaxoccurs
Design wave height = H(Tmax)
NjTRAOTH
MAXRj
j,1,)(
2
)(
max
=
= S
gTTH
j
j 2)(
2
=
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Design Wave Analysis Stochastic Approach
Short term approach
Use waves from a specified return period contour
(for example, 100-year return wave contour) Use multiple 100-year return waves
The maximum response is the design criticalresponse.
Long term approach
Predict based on the statistics of the wave scatterdiagram at the site
The long term response is predicted to a probabilityof exceedence based on the specified return period(for example 10-8.7 for 100-year return period).
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Design Wave Analysis Stochastic Approach
Using Short Term Approach (Available in OSAP)
Calculate RAOs of critical responses (loads and accelerations)
Derive wave energy spectrum (Sw)
Calculate response spectrum
Predict most probable extreme response (Rmax) for each seastate
Determine the maximum Rmax among all sea states
Calculate the design wave height curve (LF load factor )
Select design wave height
=== 02
00max_ )(2)
10800ln(2 dSmm
mT
TmR RnnZ
Z
j
)()]([)(2 WR SRAOS =
NjRMAXR j ,1),( max_max ==
LFTRAO
RTHD
)(
2)( max=
))(min( THH DD =
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Design Wave Analysis Stochastic Approach
Load Factor
CSDUs had been designed based on the deterministic
method of approach for many years before thestochastic method of approach was used. Thus, mostof the experience gained by the industry are from thedeterministic design
The stochastic design predicts lower values than thedeterministic design. To accept the stochasticallypredicted values, the industry suggests load factors forcalibrating the stochastic value in line with thedeterministic value
Site specific factors
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Design Wave Analysis Stochastic Approach
Using Long Term Approach
Repeat the short term prediction for each sea state inthe wave scatter diagram
Assume the short term response to follow the Rayleighdistribution
Take each sea states joint probability of occurrence
into account to calculate the total number ofoccurrences for each response amplitude
Assume the distribution of all the response amplitudesto follow the Weibull distribution
Predict the long term response to a probability ofexceedence based on the specified return period
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Wave Return Period
For MODUs
Owner/designer to specify the design wave
conditions.
50-year or 100-year return storms arecommonly selected by the Owners and
designers. For Floating Production Installations
Part 5B of ABS Guide for Building and Classing
Floating Production Installations(2009) 100 year return storm is required.
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Maximum Wave Height limit
For MODUs
For severe storm conditions, owner defined 1/10 wave
slope and the maximum wave height limit is typicallyused for worldwide operation except North Sea
For normal drilling conditions, owner defined 1/14 regularwave slope and the maximum wave height limit isnormally used
Although, the MODU rules no longer mentions the 1/10wave slope, the designers still choose the 1/10 waveslope
For Floating Production Installations
Wave height limit is not required to be defined by owner.
Site specific scatter diagram is required.
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Critical Responses for Twin-Hull Semis
Prying force
Summation of all transverse forces on a vertical plan
cut through the centerline.
The maximum occurs at beam seas when wave lengthis approximately equal to 2 times the distance betweenthe outer edge of the lower hulls.
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Critical Responses for Twin-Hull Semis
Torsional moments
Summation of all torsional moments on a vertical plan
cut through the centerline.
The maximum occurs at diagonal seas when wavelength is approximately equal to the diagonal distancebetween the lower hull ends.
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Critical Responses for Twin-Hull Semis
Longitudinal shear force
Summation of all longitudinal forces on a vertical plan
cut through the centerline. The maximum value occurs at diagonal seas when
wave length is approximately equal to 1.5 times thediagonal distance of the lower hull ends.
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Critical Responses for Twin-Hull Semis
Transverse racking forces
Summation of all transverse inertia forces due to the
mass of the deck and upper columns. The maximum occurs at beam sea in shallow draft.
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Critical Responses for Twin-Hull Semis
Longitudinal racking force
Summation of all longitudinal inertia forces due to the
mass of the deck and upper columns. The maximum value occurs at head seas in shallow
draft.
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Critical Responses for Twin-Hull Semis
Vertical accelerations
Summation of all vertical inertia forces due to the mass
of the deck and upper columns. The maximum value occurs at head seas in shallow
draft.
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Critical Response for Ring Pontoon Semis and TLPs
Prying/Squeezing loads between columns
Critical value diagonal seas, with a wave
length slightly more than twice the diagonalcolumn centerline spacing.
A second important case beam/head seas
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Critical Response for Ring Pontoon Semis and TLPs
Torsional moments (about transverse andlongitudinal axis)
Longitudinal shear forces between parallelpontoons
Transverse, longitudinal and vertical
accelerations of deck masses
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OSAP Output of Design Wave Curves
Zoom-in View
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OSAP 2.0 Technical Basis
Load Mapping
OSAP 2.0 Technical Basis
Load Mapping
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OSAP Load Mapping Module
Capability of mapping pressures, forces, andinternal tank loads from a hydro model to a FEAmodel
Functions of assisting load balancing
Interface with ANSYS and NASTRAN
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Load Mapping Procedure
OSAP
Load Generation
Translate FEModel
Model MeshMapping
Load Mapping
FEA LoadInterface
FEA Input toNASTRAN or
ANSYS
FE ModelTank Models
FE MassConstraints
HydrodynamicAnalysis Model
Motion RAOsForce RAOSPressure RAOsDesign WavesStatic Loads
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Supported Hydro Model Mesh Type
Five Types of Hydrodynamic Element
Panel element
TUBE element
STUB element
DISC element
PBOY element
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Supported FE Model Mesh Type
For Stiffeners Rod or beam
Truss element (rod element in NASTRAN or
link in ANSYS) with axial stiffness and aconstant cross-sectional area.
Beam element with axial, torsional and bi-directional shear and bending stiffness.
For Plates plate or shell
Membrane plate element (i.e., plane-stresselement) with bi-axial and in-plane shearstiffness and constant thickness.
Bending plate element with in-plane stiffnessas the membrane element plus out-of-planebending stiffness and constant thickness.
L d M i M i
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Load Mapping Matrix
Mooring/TendonForce
PBOY
DISC
STUB
TUBE
Panel
NodeBeamRod/LinkPlate/Shell
FE Model Mesh TypeHydro Model Meshor Load Type
L d M i F ti
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Automatic Mapping function for external wet surface
OSAP automatically searches the matching FE structuremodel with the elements in hydro model within a given
tolerance. The hydro model needs closely match the FE structure
model to generate accurate load mapping.
Mapped FE model is loaded with hydro loads for all
supported hydro elements Option load mapping function for internal tank
User needs to define tank boundary in FE structuremodel
OSAP will find the FE tank boundary, calculate tankpressure on the boundary, map the pressure load andtransfer the load back to the FE tank boundary foranalysis.
Load Mapping - Functions
L d M i P
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Load Mapping - Pressure
Hydro pressures on diffraction panels are mappedto the matching plate elements in FE model.
To smooth the pressures on FE plate elements,the following procedure is implemented
Calculate the nodal pressure in FE model using thepressures on the matching hydro panel.
Calculate the FE plate element pressures byaveraging nodal pressures in each element
Calculate pressure induced nodal forces using the
element area weighted average method for eachFE node.
Wave profile is not taken into account.
L d M i F
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Load Mapping - Force
Morison forces on TUBE and STUB in a hydro modelare mapped to the matching plate elements or lineelements in structure FEM using linear interpolation.
Loads on a DISC element in hydro model is mapped toa group of matching plate elements in structure FEMusing the similar averaging process for pressuremapping.
Loads on a PBOY in hydro model is mapped to thenode of structure FE closest to the PBOY location.
Loads on a mooring/tendon in hydro model is mapped
to the node of structure FEM closest to themooring/tendon attachment location.
Load Mapping Inertia Loads
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Load Mapping - Inertia Loads
Nodal Acceleration
where= acceleration at a node
= translation acceleration at a node
= node coordinate with respect to the reference point
= rotational acceleration about the reference point= gravity acceleration
= vertical direction unit vector
Nodal Inertial Force
m is the nodal mass
)()( 00 kgrraa
++=
a
0a
0rr
g
k
amF
=
Load Mapping Internal Tank Pressures
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Load Mapping - Internal Tank Pressures
Dynamic internal tank pressure is the motion-relatedload components due to rigid body motion and inertialcomponents.
Total Pressure at tank boundary points
2/1222
0))()()(( zzyyxxt agagaghPP +++=
where
P = total internal tank pressure at a tank boundary point
P0 = value of the pressure relief valve setting
= density of fluid cargo or ballast
ht = total pressure head in the direction of total
instantaneous acceleration vector
ax, ay, az = longitudinal, vertical and lateral instantaneousacceleration
gx, gy, gz = longitudinal, vertical and lateral instantaneous gravity
Load Mapping Internal Tank Pressures
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Load Mapping - Internal Tank Pressures
Static Internal Tank Pressure in Filled Tanks
ghPP t+= 0
Load Mapping Load Balancing
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Load Mapping Load Balancing
The unbalanced forces for each load caseneed to be determined and resolved.
OSAP provides extensive output informationfor load balance conditions of each load case.
Functions of applying displacement
constraints and mass points are available inOSAP.
Automatic load balancing is not implementedin OSAP.
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OSAP 2.0 Technical Basis
Summary of
Hydrodynamic Load Analysis
OSAP 2.0 Technical Basis
Summary of
Hydrodynamic Load Analysis
Summary
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Summary
In OSAP, Morison loads can be calculated and mapped tothe structural FE model using a rational approach.
In OSAP, dynamic forces exerted by mooring or tendons can
be calculated and transferred to structure FEM
In OSAP, sectional forces and moments due tohydrodynamic loads can be accurately calculated at anydefined section, which is very important on determining the
maximum global response at specified sections A robust algorithm is implemented in OSAP to map the
hydrodynamic and hydrostatic loads from the hydro model tostructural FE model.
The loaded FE model is ready to be solved by eitherNASTRAN or ANSYS.
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