1. Data Group C: Component Data
This section includes specification of all elementary components to be used for the riser modelling. It is possible to specify more components than are actually used.
The components are labelled with an identifier called “component type
identifier: CMPTYPID
. The maximum number of component types is 500 in
the present version.
For each component a list of data ``attributes'' have to be specified. This list depends on the TYPE CODE given in the data group identifier.
The following component types are included:

FLUID
: Internal fluid flow 
SOIL
: Soil 
SEAF
: Seafloor contact 
DRAG
: Drag chain element 
FIBR
: Fibre rope cross section 
GROW
: Marine growth 
CRS7
: General cross section 
CRS8
: Axisymmetric cross section with axial/torsion strain model
Practical aspects of modelling:

Bending stiffeners are assumed to be modelled by one or more segments with average mass, drag and stiffness properties from the riser and bending stiffener within each segment.

External buoyancy of weight elements that are clamped to the pipe are specified as external wrapping.

The mass of
EXT1
type component is added to the line properties. Drag and mass coefficients are added to those of the line. 
Body and external wrapping can not be specified for segments consisting of the cross section type:
CRS5`
1.1. CRS0  Thinwalled pipe cross section
This crosssection allows for simplified input of circular, homogenous crosssections. The input format is convenient for metallic pipe cross sections.
A thinwalled pipe cross section example is shown below. Subsequent sections give details and further options.
'**********************************************************************
NEW COMPONENT CRS0
'**********************************************************************
' units: Mg kN m C
' icmpty temp
pipe500 20.
'
' diast thst densst thex densex
0.5 0.015 7.85 0.15 0.4
' metkind emod gmod
1 206000E3 79000E3
'
' dh is the hydrodynamic diameter
' icode=2 => dimensionless hydrodynamic force coefficients
' cqx cqy cax cay clx cly icode dh
0.0 0.8 0. 0.60 0. 0. 2 0.9
'
' tb ycurmx
1. 0.4329
1.1.2. Component type identifier
CMPTYPID TEMP ALPHA BETA

CMPTYPID: character(8)
: Component type identifier 
TEMP: real, default: 0
: Temperature at which the specification applies \(\mathrm {[Temp]}\) 
ALPHA: character/real, default: 0
: Thermal expansion coefficient \(\mathrm {[Temp^{1}]}\)
= STEE
: The value \(\mathrm {1.2\times 10^{5}}\) is used 
= TI23
: The value \(\mathrm {9.0\times 10^{6}}\) is used 
These values are applicable for temperatures in Celcius or Kelvin


BETA: character/real, default: 0
: Pressure expansion coefficient \(\mathrm {[1/(F/L^2)]}\)
BETA
gives the expansion of an element with zero effective tension from the difference between the internal and the external pressure. 
= PIPE
: thin walled pipe assumption.BETA
is calculated from the parameters given in Thinwalled pipe cross section_cross (below) as: \(\mathrm {\frac{DIAST(12\nu)}{4THST\times EMOD}}\) where \(\mathrm {\nu=\frac{EMOD}{2GMOD}}1\)

image::um_ii_fig56.svg [title="Axis symmetric pipe cross section",width=456]
1.1.3. Crosssection parameters
DIAST THST DENSST THEX DENSEX R_EXTCNT R_INTCNT

DIAST: real
: Diameter of pipe \(\mathrm {[L]}\)
DIAST > 0
: Outer diameter of pipe 
DIAST < 0
: Inner diameter of pipe


THST: real
: Thickness of pipe \(\mathrm {[L]}\) 
DENSST: real
: Density of pipe material \(\mathrm {[M/L^3]}\) 
THEX: real, default: 0
: Thickness of external coating \(\mathrm {[L]}\) 
DENSEX: real, default: 0
: Density of external coating \(\mathrm {[M/L^3]}\) 
R_EXTCNT: real, default: 0
: Outer contact radius \(\mathrm {[L]}\) 
R_INTCNT: real, default: 0
: Inner contact radius \(\mathrm {[L]}\)
Buoyancy is calculated from the total external diameter
\(\mathrm {DIAST+2\times THEX}\) (For DIAST > 0
) or
\(\mathrm {DIAST+2\times THST+2\times THEX}\) (For
DIAST < 0
).
The outer and inner contact radii of the cross section, R_EXTCNT
and
R_INTCNT
, are used for
* seafloor contact
* pipeinpipe contact
* Tubular contact point specification
The default values of R_EXTCNT
and R_INTCNT
are zero in the present
version.
1.1.4. Material properties
Material constants
MATKIND EMOD GMOD SIGY EMODY/NPAIR HARPAR NCIRC

MATKIND: integer
: Type of material model
MATKIND = 1
: linear material 
MATKIND = 2
: elasticplastic 
MATKIND = 3
: strainstress curve 
MATKIND = 4
: linear material including shear deformation


EMOD: real > 0
: Modulus of elasticity \(\mathrm {[F/L^2]}\) 
GMOD: real > 0
: Shear modulus \(\mathrm {[F/L^2]}\) 
SIGY: real
: Yield stress \(\mathrm {[F/L^2]}\) 
EMODY/NPAIR: real/integer
:
MATKIND = 2
: Slope of strainstress curve for plastic region \(\mathrm {[F/L^2]}\).
EMODY
<EMOD


MATKIND = 3
: Number of user specified strainstress relations
2 ⇐ NPAIR ⇐ 99



HARPAR: real, default: 1
: Hardening parameter for material
0 ⇐ HARPAR ⇐ 1

HARPAR = 1
: Kinematic hardening 
HARPAR = 0
: Isotropic hardening


NCIRC: integer >= 8, default: 16
: Number of integration points along circumference
For MATKIND = 1
or 4
: Only EMOD
and GMOD
are used
For MATKIND = 4
: The shear stiffness is calculated as:
\(\mathrm {GMOD\frac{\pi (D_e^2D_i^2)}{4}0.5}\)
For MATKIND = 3
: NPAIR
input lines of the strainstress curve must
be given Section 1.1_strain.
Strainstress curve (NPAIR input lines to be specified for MATKIND=3)
EPS(I) SIG(I)

EPS(i): real
: Strain for point i on strainstress curve \(\mathrm {[1]}\) 
SIG(i): real
: Stress for point i on strainstress curve \(\mathrm {[F/L^2]}\)
The first point in the stressstrain curve is automatically deduced:
EPS(0) = SIGY/EMOD, SIG(0) = SIGY
. This point is taken as the
proportionality limit of the material, at which the yield/hardening
process starts. EPS(i)
and SIG(i)
are to be given in increasing
order. The gradient of the curve must decrease with increasing strain.
1.1.5. Bendingtorsion geometric coupling specification for MATKIND = 1
or 4
This data group is optional, and can only be applied for MATKIND = 1
or 4
.
BTGC

BTGC: character(4)
: bendingtorsion coupling identifier.
If the BTGC
identifier is present, geometric coupling between torsion
and bending is accounted for.
1.1.6. Damping specification
Identical to input for crosssection type CRS1 except that the local
axial friction model, AXFRC
, is illegal for CRS0, see
Damping specification.
1.1.7. Hydrodynamic load types
Identical to input for crosssection type CRS1 except that the load type HNET is not available, see Hydrodynamic load type.
1.1.8. Aerodynamic force coefficients
Identical to input for crosssection type CRS1, see Aerodynamic load type identification.
1.1.9. Capacity parameter
Identical to input for crosssection type CRS1, see Capacity parameter. :tablecaption: Table :icons: font
1.2. CRS1  Axisymmetric cross section
The following is a CRS1 cross section example. Subsequent sections provide details and further options.
'**********************************************************************
NEW COMPONENT CRS1
'**********************************************************************
' units: Mg kN m C
'cmptypid temp alpha beta
Xaxdmp / / /
'ams ae ai rgyr ast wst dst thst rextcnt rintcnt
0.3 0.0415 0 0.080 / / / / / /
'iea iej igt ipress imf harpar
3 1 1 0 0 0
'
' Axial force/strain of tensioner
' Fx eps=L/L01=x/L0 (L0=1 m, x is tensioner stroke)
1000 0.0 &
1100 5.0 &
1400 10.0
'ei gas
2.84E8 0
'gtminus
2.19E8
'DAMP chtype1 [chtype2 chtype3 chtype4]
DAMP AXDMP
'idmpaxi expdmp
1 1.737
'dmpaxi
30.00
' icode=2 => dimensionless hydrodynamic force coefficients
'cqx cqy cax cay clx cly icode d scfkn scfkt
0 1.0 0 1.0 0 0 2 230E3 1.0 1.0
'tb ycurmx
1600 0.1
1.2.2. Component type identifier
CMPTYPID TEMP ALPHA BETA

CMPTYPID: character(8)
: Component type identifier 
TEMP: real, default: 0
: Temperature at which the specification applies \(\mathrm {[Temp]}\) 
ALPHA: real, default: 0
: Thermal expansion coefficient \(\mathrm {[Temp^{1}]}\) 
BETA: real, default: 0
: Pressure expansion coefficient \(\mathrm {[1/(F/L^2)]}\)
BETA
gives the expansion of an element with zero effective tension from the difference between the internal and the external pressure.

1.2.3. Mass and volume
AMS AE AI RGYR AST WST DST THST R_EXTCNT R_INTCNT

AMS: real
: Mass/unit length \(\mathrm {[M/L]}\) 
AE: real
: External crosssectional area \(\mathrm {[L^2]}\) 
AI: real
: Internal crosssectional area \(\mathrm {[L^2]}\) 
RGYR: real
: Radius of gyration about local xaxis \(\mathrm {[L]}\). Dummy for bar elements, i.e.IEJ = 0
: zero bending stiffness. 
AST: real
: Crosssection area for stress calculations \(\mathrm {[L^2]}\)
The default value is calculated as seen below


WST: real
: Crosssection modulus for stress calculations \(\mathrm {[L^3]}\)
The default value is calculated as seen below


DST: real
: Diameter for stress calculations \(\mathrm {[L]}\)
The default value is calculated as seen below


THST: real
: Thickness for stress calculations \(\mathrm {[L]}\)
The default value is calculated as seen below


R_EXTCNT: real, default: 0
: External contact radius \(\mathrm {[L]}\) 
R_INTCNT: real, default: 0
: Inner contact radius \(\mathrm {[L]}\)
AE
is used to calculate buoyancy.
AI
is used to calculate additional mass of internal fluid if present.
Otherwise AI
is dummy or see below.
Default values of the stress calculation parameters will be calculated
from AE
and AI
if AE > AI
. A homogenous cylinder shaped
crosssection is assumed:

AST
\(\mathrm {=AEAI}\) 
WST
\(\mathrm {=\pi (D_e^4D_i^4)/(32D_e)}\) 
DST
\(\mathrm {=D_e}\) 
THST
\(\mathrm {=(D_eD_i)/2}\)
where \(\mathrm {D_e=\sqrt{\frac{4AE}{\pi }}}\) and \(\mathrm {D_i=\sqrt{\frac{4AI}{\pi }}}\)

The outer and inner contact radii of the cross section, R_EXTCNT
and R_INTCNT
, are used for

seafloor contact
The default values of R_EXTCNT
and R_INTCNT
are zero in the present
version.
1.2.4. Stiffness properties classification
IEA IEJ IGT IPRESS IMF HARPAR

IEA: integer, default: 1
: Axial stiffness code
1  constant stiffness

N  table with N pairs of tensionelongation to be specified

N >= 2


IEJ: integer, default: 0
:
0
 zero bending stiffness 
1  constant stiffness

N  table with N pairs of bending moment  curvature to be specified

N >= 2


IGT: integer, default: 0
: Torsion stiffness code
0
 zero torsional stiffness 
1  constant stiffness

1 nonsymmetric
constant
stiffness 
N  symmetric, (N positive) pairs specified

N general torsion/relation (nonsymmetric) N pairs specified

N >= 2


IPRESS: integer, default: 0
: Pressure dependency parameter related to bending moment
0
 no pressure dependency 
1  linear dependency (not implemented)

NP  NP sets of stiffness properties to be given, corresponding to a table of NP pressure values (not implemented)

2 ⇐ NP ⇐ 10



IMF: integer, default: 0
: Hysteresis option in bending moment/curvature relation
0
 no hysteresis 
1  hysteresis generated by an internal friction moment at reversed curvature


HARPAR: real, default: 0
: Hardening parameter for kinematic/isotropic hardening
0 ⇐ HARPAR ⇐ 1

Only to be given if
IEJ > 1
andIMF = 1

IEJ
and IGT
must both be zero or both greater than zero to assure
stability in the FEM
analysis.
Note that:

IPRESS=0
in this version. 
IMF=0
,IMF=1
is implemented in present version. 
IMF
\(\mathrm {\neq }\)0
should be used with care as the analysis can become unstable.
1.2.5. Bendingtorsion geometric coupling specification
This data group is optional, and will only be applied for IEJ=1
,
IGT=1
, and IMF=0
.
BTGC

BTGC: character(4)
: bendingtorsion coupling identifier.
If the BTGC
identifier is present, geometric coupling between torsion
and bending is accounted for.
1.2.7. Axial stiffness. Case 2, IEA=N
EAF(1) ELONG(1) . . . EAF(N) ELONG(N)

EAF(1): real
: Axial force corresponding to relative elongationELONG(1)
\(\mathrm {[F]}\) 
ELONG(1): real
: Relative elongation () 
.

.

.
The pairs of EAF
and ELONG
must be given in increasing order on a
single input line.
1.2.8. Bending stiffness properties
The amount of input depends upon the parameters IEJ
, IPRESS
and
IMF
according to the table below:

Case: 0,
IEJ
: 0,IPRESS
: 0, Allowed IMFvalues: 0, Data required: None. 
Case: 1a,
IEJ
: 1,IPRESS
: 0, Allowed IMFvalues: 0, Data required:EI, GAs
. 
Case: 1b,
IEJ
: 1,IPRESS
: 0, Allowed IMFvalues: 1, Data required:EI, MF
. 
Case: 2,
IEJ
: 1,IPRESS
: 1, Allowed IMFvalues: 0, Data required: Not implemented. 
Case: 3,
IEJ
: N,IPRESS
: 0, Allowed IMFvalues: 0, 1, Data required:CURV(I): I=1,N. BMOM(I): I=1,N
. 
Case: 4,
IEJ
: N1,IPRESS
: N2, Allowed IMFvalues: 0, Data required: Not implemented.
1.2.9. Bending stiffness. Case 1a, IEJ=1 IPRESS=0 IMF=0
EI GAs

EI: real > 0
: Bending stiffness \(\mathrm {[FL^2]}\) 
GAs: real
: Shear stiffness \(\mathrm {[F]}\)
The shear stiffness, GAs
, is an optional input parameter. Specified
GAs > 0
will include shear deformation. This requires that all
stiffness properties are constant, i.e. IEA = 1
, IEJ = 1
, IGT = 1
1.2.10. Bending stiffness. Case 1b, IEJ=1 IPRESS=0 IMF=1
EI MF SF

EI: real
: Bending stiffness \(\mathrm {[FL^2]}\) 
MF: real
: Internal friction moment, see figure below. \(\mathrm {[FL]}\) 
SF: real, default: 10.
: Internal friction moment stiffness factor. \(\mathrm {[]}\)
The default value of SF
corresponds to the earlier fixed value of
10.0.
1.2.11. Bending stiffness. Case 2, IEJ=1 IPRESS=1 (Not implemented)
EI(1) PRESS(1) EI(2) PRESS(2) MF(1) MF(2)

EI(1): real
: Bending stiffness \(\mathrm {[FL^2]}\) 
PRESS(1): real
: Pressure at which the above values apply \(\mathrm {[F/L^2]}\) 
EI(2): real
: See description above 
PRESS(2):

MF(1): real
: Internal friction moment for pressure PRESS(1) 
MF(2): real
: Internal friction moment for pressure PRESS(2)
PRESS(1) < PRESS(2)
MF(1) and MF(2) dummy for IMF = 0
Values at other pressure levels than PRESS(1)
and PRESS(2)
are
obtained by linear interpolation/ extrapolation.
1.2.12. Bending stiffness description. Case 3 IEJ=N IPRESS=0
Tabulated curvature/bending moment relation. This specification consists
of two different input lines. For IMF
\(\mathrm {\neq }\)
0
cfr. Bending stiffness. Case 4…
Curvature
CURV(1) ... CURV(N)

CURV(1): real
: Curvature values for which bending moment is specified \(\mathrm {[1/L]}\) 
.

.

.

CURV(N)
: To be specified in increasing order
CURV=1/CURVATURE RADIUS
Bending moment, yaxis
BMOMY(1) BMOMY(N)

BMOMY(1): real
: Bending moment around yaxis \(\mathrm {[FL]}\) corresponding to curvature values given above in `Curvature'. 
BMOMY(N)
CURV(1), BMOMY(1)
have to be zero. Positive slope required, i.e.:
BMOMY(I+1) > BMOMY(I)
.
1.2.13. Bending stiffness. Case 4 IEJ=N1, IPRESS=N2 (Not implemented)
This specification consists of three different input lines.
Curvature
CURV(1) ... CURV(N)

CURV(1): real
: Curvature values for which bending moment is specified \(\mathrm {[1/L]}\) 
.

.

.

CURV(N)
: To be specified in increasing order
CURV=1/CURVATURE RADIUS
CURV(1) has to be zero
Pressure
PRESS(1) ... PRESS(N)

PRESS(1): real
: Pressure levels for which bending moment is specified \(\mathrm {[F/L^2]}\) 
PRESS(N)
:
Bending moment, yaxis
BMOMY(1,1) BMOMY(N1,N2)

BMOMY(1,1): real
: Bending moment at curvature I and pressure J \(\mathrm {[FL]}\). 
BMOMY(N1,N2)
BMOMY(1,J), J=1,N2
have to be zero, see also the figure below.
Positive slope with increasing curvature is required, i.e.:
BMOMY(I+1,J) > BMOMY(I,J)
.
1.2.14. Torsion stiffness
No data required for IGT=0
.
Constant torsion stiffness. Case 1 IGT=1
GT GT+

GT: real > 0
: Torsion stiffness \(\mathrm {[FL^2/Radian]}\) 
GT+: real
: D.o. for positive twist. Dummy ifIGT=1
Nonlinear torsion stiffness. Case 2 IGT=N
TMOM(1) TROT(1) . . . TMOM(N) TROT(N)

TMOM(1): real
: Torsion moment \(\mathrm {[FL]}\) 
TROT(1): real
: Torsion angle/length \(\mathrm {[Radian/L]}\) 
.

.

.

TMOM(N)
: 
TROT(N): real
:
If IGT
is positive TMOM(1)
and TROT(1)
have to be zero. TROT
must be given in increasing order.
1.2.15. Damping specification
This data group is optional. It enables the user to specify cross sectional damping properties of the following types:

mass proportional damping

stiffness proportional damping

axial damping properties
Specification of mass and stiffness proportional damping specification will overrule corresponding damping specification given on global level as input to Dynmod data group Time integration and damping parameters.
Data group identifier and selection of damping types
DAMP CHTYPE1 CHTYPE2 CHTYPE3 CHTYPE4

DAMP: character(4)
: Data group identifier (the textDAMP
) 
CHTYPE1: character(5)
:
`=MASPR: Mass proportional damping

`=STFPR: Stiffness proportional damping

`=AXDMP: Local axial damping model

`=AXFRC: Local axial friction model


CHTYPE2: character(5)
: Similar to CHTYPE1 
CHTYPE3: character(5)
: Similar to CHTYPE1 
CHTYPE4: character(5)
: Similar to CHTYPE1
Between one and four damping types may be selected. The order of the damping type selection is arbitrary.
In the following the damping parameters for the selected damping types is described. The input lines have to be given in one block and in the order described below. Skip input for damping types which are not selected.
Parameters for mass proportional damping, if MASPR is specified
A1T A1TO A1B

A1T: real
: Factor for mass proportional damping in axial dofs. 
A1TO: real, default: A1T
: Factor for mass proportional damping in torsional dofs. 
A1B: real, default: A1TO
: Factor for mass proportional damping in bending dofs.
The element stiffness proportional damping matrix is computed by:
\(\mathrm {\boldsymbol{\mathrm {c_m}}=a_{1t}\boldsymbol{\mathrm {m}}_t+a_{1to}\boldsymbol{\mathrm {m}}_{to}+a_{1b}\boldsymbol{\mathrm {m}}_b}\)
where \(\boldsymbol{\mathrm {m}}\) is the local stiffness
matrix and the subscripts t
, to
and b
refer to axial,
torsional and bending contributions, respectively.
Parameters for stiffness proportional damping, if STFPR is specified
A2T A2TO A2B DAMP_OPT

A2T: real
: Factor for stiffness proportional damping in axial dofs. 
A2TO: real, default: A2T
: Factor for stiffness proportional damping in torsional dofs. 
A2B: real, default: A2TO
: Factor for stiffness proportional damping in bending dofs. 
DAMP_OPT: character(4), default: TOTA
: Option for stiffness contribution to Rayleigh damping
= TOTA: Stiffness proportional damping is applied using total stiffness, i.e. both material and geometric stiffness

= MATE: Stiffness proportional damping is applied using material stiffness only

The element stiffness proportional damping matrix is computed by:
\(\mathrm {\boldsymbol{\mathrm {c_k}}=a_{2t}\boldsymbol{\mathrm {k}}_t+a_{2to}\boldsymbol{\mathrm {k}}_{to}+a_{2b}\boldsymbol{\mathrm {k}}_b}\)
where \(\boldsymbol{\mathrm {k}}\) is the local stiffness
matrix and the subscripts t
, to
and b
refer to axial,
torsional and bending contributions, respectively.
Parameters for local axial damping, if AXDMP is specified
The local axial damping model is written:
\(\mathrm {F=C(\varepsilon )\times \dot {\varepsilon }^P\times sign(\dot {\varepsilon })}\)
where:

\(\mathrm {F}\): damping force

\(\mathrm {C}\): damping coefficient (strain dependent)

\(\mathrm {\varepsilon }\): relative elongation

\(\mathrm {\dot {\varepsilon }}\): strain velocity

\(\mathrm {P}\): exponent for strain velocity (P >= 1)
IDMPAXI EXPDMP

IDMPAXI: integer
: Damping coefficient code
= 1: Constant damping coefficient

= N: Table with N pairs of damping coefficient  elongation to be specified.

N >= 2


EXPDMP: real
: Exponent for strain velocity
IDMPAXI = 1
DMPAXI

DMPAXI: real
: Damping coefficient (constant)
IDMPAXI >1
DMPAXI(1) ELONG(1) . . . . . . . . DMPAXI(IDMPAXI) ELONG(IDMPAXI)

DMPAXI(1): real
: Damping coefficient corresponding to relative elongationELONG(1)

ELONG(1): real
: Relative elongation ( )
ELONG
must be given in increasing order for the pairs of DMPAXI
and
ELONG
. All pairs are given on a single input line
Parameters for local axial friction, if AXFRC is specified
FRCAXI(1) ELONG(1) FRCAXI(2) ELONG(2)

FRCAXI(1): real
: Static friction force corresponding to elongationELONG(1)

ELONG(1): real
: Relative elongation ( ) 
FRCAXI(2): real, default: FRCAXI(1)
: Dynamic friction force corresponding to elongationELONG(2)

ELONG(2): real, default: 1.1 x ELONG(1)
: Relative elongation ( )
ELONG(2) > ELONG(1)
1.2.16. Hydrodynamic load type identification, One optional input line
CHLOAD

CHLOAD: character
:= HYDR
 Text to identify hydrodynamic coefficients
Required if nonMorison loads are to be specified 
Load type identification if CHLOAD=HYDR, One input line
CHTYPE

CHTYPE: character
: Hydrodynamic load type
= NONE
: No hydrodynamic load 
= MORI
: Load based on Morisons generalized equation. Sea surface penetration formulation 
= MORP
: AsMORI
, but improved by taking into account partially submerged crosssection 
= MACF
: Load based on MacCamyFuchs potential equations and quadratic drag load 
= POTN
: Potential flow with quadratic drag load coefficients 
= TVIV
: Time domain VIV load. 
= HNET
: Net properties and hydrodynamic added mass coefficients for net

The option POTN currently is under testing. Potential flow
forces are only available for irregular time domain analysis.

The option TVIV is currently under development and some load options are restricted.

Hydrodynamic force coefficients if CHTYPE=MORI or CHTYPE=MORP
Interpretation of hydrodynamic coefficients are dependent on the input
parameter ICODE
. Input of dimensional hydrodynamic coefficient is
specified giving ICODE=1
while input of nondimensional of hydrodynamic
coefficients for circular cross sections is specified giving ICODE=2
.
CHTYPE=MORP is similar to CHTYPE=MORI but with thre key differences:

the load calculated at a crosssection is reduced in proportional with the instantaneous wet portion of the crosssection

the FroudeKrylov term used longitudinal direction in Morison’s equation is replaced by the product of the dynamic pressure and the submerged area at each end of the element.

if the specified value for external area (AE) is zero, neither hydrostatic nor hydrodynamic loads will act on the cross section. Definitions of dimensional/nondimensional hydrodynamic force coefficients for a fully submerged cross section are given below
CQX CQY CAX CAY CLX CLY ICODE D SCFKN SCFKT

CQX: real
: Quadratic drag coefficient in tangential direction
ICODE=1: CQX=CDX
: dimensional drag force coefficient \(\mathrm {[F/((L/T)^2\times L)]}\) 
ICODE=2: CQX=Cdt
: nondimensional drag force coefficient


CQY: real
: Quadratic drag coefficient in normal direction
ICODE=1: CQY=CDY
: dimensional drag force coefficient \(\mathrm {[F/((L/T)^2\times L)]}\) 
ICODE=2: CQY=Cdn
: nondimensional drag force coefficient


CAX: real
: Added mass per unit length in tangential direction
ICODE=1: CAX=AMX
: added mass \(\mathrm {[M/L]}\) 
ICODE=2: CAX=Cmt
: nondimensional added mass coefficient


CAY: real
: Added mass per unit length in normal direction
ICODE=1: CAY=AMY
: added mass \(\mathrm {[M/L]}\) 
ICODE=2: CAY=Cmn
: nondimensional added mass coefficient


CLX: real
: Linear drag force coefficient in tangential direction
ICODE=1: CLX=CDLX
: dimensional linear drag coefficient \(\mathrm {[F/((L/T)\times L)]}\) 
ICODE=2: CLX=CdtL
: nondimensional linear drag force coefficient


CLY: real
: Linear drag force coefficient in normal direction
ICODE=1: CLY=CDLY
: dimensional linear drag force coefficient \(\mathrm {[F/((L/T)\times L)]}\) 
ICODE=2:CLY=CdnL
: nondimensional linear drag force coefficient


ICODE: integer, default: 1
:ICODE
Code for input of hydrodynamic force coefficients
ICODE=1
: Dimensional coefficients 
ICODE=2
: Nondimensional coefficients


D: real, default:
\(\sqrt{\mathrm {\frac{4}{\pi }(AE)}}\): Hydrodynamic diameter of the pipe \(\mathrm {[L]}\).
Default value is calculated from external crosssectional area given as input in data section Mass and volume

Note that the hydrodynamic diameter is used for time domain VIV loads and for marine growth and is a key parameter in
VIVANA
.


SCFKN: real, default: 1
: Scaling factor for the FroudeKrylov term in Morison’s equation in normal direction 
SCFKT: real, default: 1
: Scaling factor for the FroudeKrylov term in Morison’s equation in tangential direction. Only the values 0.0 and 1.0 are permitted.
Definition of hydrodynamic force coefficients
The tangential force which is a friction force per unit length acting in local xaxis, \(\mathrm {Ft}\) is computed by:
\(\mathrm {Ft=CDX\times VRELX\times VRELX+CDLX\times VRELX}\)
The drag force per unit length acting normal to the local xaxis, \(\mathrm {F_n}\), is computed by assuming that the instantaneous drag force direction is parallel to the instantaneous transverse relative velocity component:
\(\mathrm {F_n=CDY(VRELY^2+VRELZ^2)+CDLY\times \sqrt{VRELY^2+VRELZ^2}}\)
where:

\(\mathrm {CDX,CDY}\): are the dimensional quadratic drag force coefficients in local x and ydirections (i.e. tangential and normal directions)

\(\mathrm {CDLX,CDLY}\): are the dimensional linear drag force coefficients in local x and ydirections

\(\mathrm {VRELX,VRELY,VRELZ}\): are relative water velocities in local x,y and zdirections
The nondimensional hydrodynamic force coefficients for a circular cross section are defined according to the following expressions:

\(\mathrm {CDX=\frac{1}{2}\rho S_WC_{dt}}\)

\(\mathrm {CDY=\frac{1}{2}\rho DC_{dn}}\)

\(\mathrm {CDLX=\rho \sqrt{gS_W}\times S_W^2C^L_{dt}}\)

\(\mathrm {CDLY=\rho \sqrt{gD}\times D^2C^L_{dt}}\)

\(\mathrm {AMX=\rho \frac{\pi D^2}{4}C_{mt}}\)

\(\mathrm {AMY=\rho \frac{\pi D^2}{4}C_{mn}}\)
where:

\(\mathrm {\rho }\): water density

\(\mathrm {g}\): acceleration of gravity

\(\mathrm {S_W}\): cross sectional wetted surface \(\mathrm {(=\pi D)}\)

\(\mathrm {D}\): hydrodynamic diameter of the pipe

\(\mathrm {C_{dt}}\): nondimensional quadratic tangential drag coefficient

\(\mathrm {C_{dn}}\): nondimensional quadratic normal drag coefficient

\(\mathrm {C^L_{dt}}\): nondimensional linear tangential drag coefficient

\(\mathrm {C^L_{dn}}\): nondimensional linear normal drag coefficient

\(\mathrm {C_{mt}}\): nondimensional tangential added mass coefficient

\(\mathrm {C_{mn}}\): normal added mass coefficient

(\(\mathrm {C_{mn}}\) is normally equal to 1.0 for a circular cross section)

Note that if the specified value for external area (AE) is zero, neither hydrostatic nor hydrodynamic loads will act on the cross section
Hydrodynamic force coefficients if CHTYPE=MACF
MacCamyFuchs frequencydependent hydrodynamic loads on a stationary
vertical circular cylinder will be applied for CHTYPE=MACF
.
MacCamyFuchs forces are precomputed based on the element position
after static calculation. MacCamyFuchs forces are only available for
irregular time domain analysis.
Quadratic drag may also be applied on crosssections with MacCamyFuchs loading.
Hydrodynamic force coefficients
CQX CQY CAX ICODE D

CQX: real
: Quadratic drag coefficient in tangential direction
ICODE=1: CQX=CDX
: dimensional drag force coefficient \(\mathrm {[F/((L/T)^2\times L)]}\) 
ICODE=2: CQX=Cdt
: nondimensional drag force coefficient


CQY: real
: Quadratic drag coefficient in normal direction
ICODE=1: CQY=CDY
: dimensional drag force coefficient \(\mathrm {[F/((L/T)^2\times L)]}\) 
ICODE=2: CQY=Cdn
: nondimensional drag force coefficient


CAX: real, default: 0.0
: Added mass per unit length in tangential direction
ICODE=1: CAX=AMX
: added mass \(\mathrm {[M/L]}\) 
ICODE=2: CAX=Cmt
: nondimensional added mass coefficient


ICODE: integer
: Code for input of hydrodynamic drag coefficients
ICODE=1
: Dimensional coefficients 
ICODE=2
: Nondimensional coefficients


D: real, default:
\(\sqrt{\mathrm {\frac{4}{\pi }(AE)}}\): Hydrodynamic diameter of the pipe \(\mathrm {[L]}\).
Default value is calculated from external crosssectional area given as input in data section Mass and volume

Simplified radiation force
The horizontal radiation loads is based on an added mass coefficient and a damping coefficient.
CAY DAMP IRACOD

CAY: real, default: 0.0
: Added mass per unit length in normal direction
IRACOD=1: CAY=AMY
: added mass \(\mathrm {[M/L]}\) 
IRACOD=2: CAY=Cmn
: nondimensional added mass coefficient


DAMP: real, default: 0.0
: Damping in normal direction
IRACODE=1: DAMP=CDa
: dimensional damping coefficient \(\mathrm {[F/((L/T)\times L)]}\) 
IRACODE=2: DAMP=CDan
: nondimensional damping coefficient


IRACODE: integer, default: 1
: Code for input of simplified radiation force coefficients
IRACODE=1
: Dimensional coefficients 
IRACODE=2
: Nondimensional coefficients

The nondimensional hydrodynamic added mass coeffcient and the damping coefficient are defined according to the following expressions:

\(\mathrm {CDa=\rho \sqrt{gD}\times D^2CD_{an}}\)

\(\mathrm {AMY=\rho \frac{\pi D^2}{4}C_{mn}}\)
The input CHTYPE=MACF is extended in Riflex 4.13 and is not compatible with earlier versions of Riflex. 
Hydrodynamic force coefficients if CHTYPE=POTN
Frequencydependent added mass, radiation damping, and excitation forces
based on the first order potential flow solution will be applied for
CHTYPE=POTN
. The radiation and diffraction coefficients are to be
given by a separate input file specified under the data group
Potential flow library specification.
Quadratic drag may also be applied on crosssections with potential flow loading.
CQX CQY ICODE D SCFKT

CQX: real
: Quadratic drag coefficient in tangential direction
ICODE=1: CQX=CDX
: dimensional drag force coefficient \(\mathrm {[F/((L/T)^2\times L)]}\) 
ICODE=2: CQX=Cdt
: nondimensional drag force coefficient


CQY: real
: Quadratic drag coefficient in normal direction
ICODE=1: CQY=CDY
: dimensional drag force coefficient \(\mathrm {[F/((L/T)^2\times L)]}\) 
ICODE=2: CQY=Cdn
: nondimensional drag force coefficient


ICODE: integer, default: 1
:ICODE
Code for input of hydrodynamic force coefficients
ICODE=1
: Dimensional coefficients 
ICODE=2
: Nondimensional coefficients


D: real, default:
\(\sqrt{\mathrm {\frac{4}{\pi }(AE)}}\): Hydrodynamic diameter of the pipe \(\mathrm {[L]}\).
Default value is calculated from external crosssectional area given as input in data section Mass and volume


SCFKT: real, default: 1
: Scaling factor for the FroudeKrylov term in Morison’s equation in tangential direction. Only the values 0.0 and 1.0 are permitted.
Hydrodynamic force coefficients if CHTYPE=TVIV
Under implementation. Some load options are restricted.
CQX CQY CAX CAY CLX CLY ICODE D SCFKN SCFKT
See the description above for Hydrodynamic force coefficients.
Time domain VIV load options and coefficients, 2 or 3 input lines.
CHTVIV NMEM CHH

CHTVIV: character(8)
: Time domain VIV load option
= CF
: Crossflow VIV loads only 
= CFIL
: Crossflow and inline VIV loads calculated independently. Restricted option 
= IL
: Inline VIV loads only. Restricted option


NMEM: integer > 0, default: 500
: Number of time steps used in calculation of standard deviation 
CHH: real >= 0, default: 0.0
: Higher harmonic load coefficient (nondimensional). Restricted option
Crossflow VIV load coefficients. The following input line is given if
CHTVIV is CF
or CFIL
:
CV FNULL FMIN FMAX

CV: real >= 0
: Vortex shedding force coefficient for the (instantaneous) crossflow load term (nondimensional) 
FNULL: real > 0
: Natural crossflow vortex shedding frequency (nondimensional) 
FMIN: real > 0
: Minimum crossflow vortex shedding frequency (nondimensional) 
FMAX: real > FMIN
: Maximum crossflow vortex shedding frequency (nondimensional)
Independently calculated inline load coefficients. Restricted option.
The following input line is given if CHTVIV is CFIL
or IL
:
CVIL FNULIL FMINIL FMAXIL

CVIL: real >= 0
: Vortex shedding force coefficient for the (instantaneous) inline load term (nondimensional) 
FNULIL: real > 0
: Natural inline vortex shedding frequency (nondimensional) 
FMINIL: real > 0
: Minimum inline vortex shedding frequency (nondimensional) 
FMAXIL: real > FMINIL
: Maximum inline vortex shedding frequency (nondimensional)
The VIV parameters are nondimensional and independent of ICODE .

VIV parameters for pure CF are shown in Table 1. 
Flow conditions 
Structure type 
Parameters 








Constant current 
Bare riser section 
1.3 
1.0 
1.0 
0.13 
0.10 
0.26 

Buoyancy section (L_{b}/L_{r}=1/2) 
Bare riser 
1.2 
0.9 
1.0 
0.18 
0.10 
0.22 

Buoyancy element 
0.08 
0.3 
1.0 
0.10 
0.05 
0.15 

Buoyancy section (L_{b} /L_{r}=1/1) 
Bare riser 
0.8 
1.2 
1.0 
0.18 
0.10 
0.26 

Buoyancy element 
0.5 
0.6 
1.0 
0.10 
0.05 
0.15 

Vessel motion induced VIV 
Bare riser & buoyancy section 
0.8 
1.2 
1.0 
0.216 
0.10 
0.26 
L_{b}/L_{r} is the ratio between the length of the buoyancy element and the bare riser section, see Figure 7. 
Net properties and hydrodynamic added mass coefficients if CHTYPE=HNET
A complete net is normally modelled bye a set of segments where each segment represents a net panel, and is specified by a cable/bar cross section with equivalent properties.
The net properties and hydrodynamic added mass coefficients are specified for segment end 1. The derived drag and lift coefficients and the specified added mass coefficients are scaled according to the actual net width which is found by linear interpolation between specified net width at segment end 1 and segment end 2. This also applies to the specified unit mass and external area.
CHTYPE=HNET may only be used with bar elements (No bending and torsional stiffness to be specified)

The net load model requires that the net plane is defined. The net plane is the plane containing the updated local element Xaxis and the fixed reference vector specified in the input group LOCAL ELEMENT AXIS. 
If the specified value for external area (AE) is zero, neither hydrostatic nor hydrodynamic loads will act on the cross section 
Net and segment properties
SN WIDTH1 WIDTH2 REDVEL

SN: real >= 0 ⇐1
: Solidity ratio (the ratio between thread area and net area) \(\mathrm {[]}\) 
WIDTH1: real >= 0
: Net width at segment end 1 \(\mathrm {[L]}\) 
WIDTH2: real >= 0
: Net width at segment end 2 \(\mathrm {[L]}\) 
REDVEL: real >= 0 ⇐ 1
: Reduced current velocity factor (the ratio between reduced current speed and ambient current speed due to upstream net shadowing effects \(\mathrm {[]}\)
Note that only one of the input variables WIDTH1
or WIDTH2
can be
specified with the value 0.
The drag and lift coefficient \(\mathrm {[F/((L/T)^2\times L^2)]}\) are calculated based on the net solidity (SN) according to the following equations:
Direction independent drag force coefficient:

\(\mathrm {C_{D0}=\frac{1}{2}\rho \times 0.04}\)
Direction dependent drag force coefficient:

\(\mathrm {C_{D1}=\frac{1}{2}\rho \times (0.04+SN1.24SN^2+13.7SN^3)cos(\alpha)}\)
Direction dependent lift force coefficient:

\(\mathrm {C_l=\frac{1}{2}\rho \times (0.57SN3.54SN^2+10.1SN^3)sin(2\alpha})\)
where:

\(\mathrm {\rho }\): is the water density

\(\mathrm {SN}\): is the net solidity ratio

\(\mathrm {\alpha }\): angle between the flow direction and the net normal vector in the direction of the flow
Note that the equations for drag and lift coefficients are valid for the
solidity ratio range [0.13,0.32]
, see netloads in the Theory manual.
Hydrodynamic force coefficients
CAX CAY ICODE D

CAX: real
: Added mass per length, tangential direction \(\mathrm {[M/L]}\)
ICODE=1: CAX=AMX
: added mass \(\mathrm {[M/L]}\) 
ICODE=2: CAX=Cmt
: nondimensional added mass coefficient


CAY: real
: Added mass per length, normal direction \(\mathrm {[M/L]}\)
ICODE=1: CAY=AMY
: added mass \(\mathrm {[M/L]}\) 
ICODE=2: CAY=Cmn
: nondimensional added mass coefficient


ICODE: integer, default: 1
:ICODE
Code for input of hydrodynamic force coefficients
ICODE=1
: Dimensional coefficients 
ICODE=2
: Nondimensional coefficients


D: real, default:
\(\sqrt{\mathrm {\frac{4}{\pi }(AE)}}\): Equivalent hydrodynamic diameter to be used for nondimensional added mass coefficients \(\mathrm {[L]}\).
Default value is calculated from external crosssectional area given as input in data section Mass and volume

1.2.17. Aerodynamic load type identification, One optional input line
CHLOAD

CHLOAD: character
:= WIND
 Text to identify wind coefficients
Load type identification if CHLOAD=WIND, One input line
CHTYPE

CHTYPE: character
: Type of load coefficients
= MORI
: Morisonlike loading, Drag term

Drag coefficients if CHTYPE=MORI, One input line
CDXAERO CDYAERO ICODE D

CDXAERO: real
: Quadratic drag coefficient in tangential direction
ICODE=1: CDXAERO=CDXa
: dimensional drag force coefficient \(\mathrm {[F/((L/T)^2\times L)]}\) 
ICODE=2: CDXAERO=Cdta
: nondimensional drag force coefficient


CDYAERO: real
: Quadratic drag coefficient in normal direction
ICODE=1: CDYAERO=CDYa
: dimensional drag force coefficient \(\mathrm {[F/((L/T)^2\times L)]}\) 
ICODE=2: CDYAERO=Cdna
: nondimensional drag force coefficient


ICODE: integer, default: 1
: Code for input of aerodynamic force coefficients
ICODE=1
: Dimensional coefficients 
ICODE=2
: Nondimensional coefficients


D: real, default:
\(\sqrt{\mathrm {\frac{4}{\pi }(AE)}}\): Aerodynamic diameter of the pipe \(\mathrm {[L]}\).
Default value is calculated from external crosssectional area given as input in data section Mass and volume

Dummy for
ICODE=1

The tangential force which is a friction force per unit length acting in local xaxis, \(\mathrm {F_t}\) is computed by:
\(\mathrm {F_t=CDXa\times VRELX\times VRELX}\)
The drag force per unit length acting normal to the local xaxis, \(\mathrm {F_n}\), is computed by assuming that the instantaneous drag force direction is parallel to the instantaneous transverse relative velocity component:
\(\mathrm {F_n=CDYa(VRELY^2+VRELZ^2)}\)
where:

\(\mathrm {CDXa,CDYa}\): are the dimensional quadratic drag force coefficients in local x and ydirections (i.e. tangential and normal directions)

\(\mathrm {VRELX,VRELY,VRELZ}\): are relative wind velocities in local x,y and zdirections
The nondimensional aerodynamic force coefficients for a circular cross section are defined according to the following expressions:

\(\mathrm {CDXa=\frac{1}{2}\rho _aS_WC_{dta}}\)

\(\mathrm {CDYa=\frac{1}{2}\rho _aDC_{dna}}\)
where:

\(\mathrm {\rho _a}\): air density

\(\mathrm {S_W}\): cross sectional perimeter \(\mathrm {(=\pi D)}\)

\(\mathrm {D}\): aerodynamic diameter of the pipe

\(\mathrm {C_{dta}}\): nondimensional quadratic tangential drag coefficient

\(\mathrm {C_{dna}}\): nondimensional quadratic normal drag coefficient
1.3. CRS2  Double symmetric cross section
1.3.2. Component type identifier
CMPTYPID TEMP

CMPTYPID: character(8)
: Component type identifier 
TEMP: real
: Temperature at which the specification applies
Dummy in present version

1.3.3. Mass and volume
AMS AE AI RGYR

AMS: real
: Mass per unit length \(\mathrm {[M/L]}\) 
AE: real
: External crosssectional area \(\mathrm {[L^2]}\) 
AI: real
: Internal crosssectional area \(\mathrm {[L^2]}\) 
RGYR: real
: Radius of gyration about local xaxis \(\mathrm {[L]}\)
AE
is used to calculate buoyancy.
AI
is used to calculate additional mass of internal fluid if present.
Otherwise AI
is dummy.
Note that the mass center is located along the local Xaxis, i.e. at the origin of the local Y and Zaxes.
1.3.4. Stiffness properties classification
IEA IEJ IGT IPRESS

IEA: integer, default: 0
: Axial stiffness code
1  constant stiffness

N  table with N pairs of tensionelongation to be specified

N >= 2


IEJ: integer, default: 0
:
0
 zero bending stiffness 
1  constant stiffness

N  table with N pairs of bending moment  curvature to be specified.

N >= 2


IGT: integer, default: 0
: Torsion stiffness code
0
 zero torsional stiffness 
1  constant stiffness

1 nonsymmetric ``constant'' stiffness

N  symmetric, N (positive) pairs specified

N general torsion/relation (nonsymmetric) N pairs specified

N >= 2


IPRESS: integer, default: 0
: Pressure dependency parameter related to bending moment
0
 no pressure dependency 
1  linear dependency (not implemented)

NP  NP sets of stiffness properties to be given, corresponding to a table of NP pressure values (not implemented)

2 ⇐ NP ⇐ 10


Normally IEJ
and IGT
should both be zero or both greater than zero
to assure stability in the FEM
analysis.
IPRESS=0
in this version of the program.
1.3.5. Bendingtorsion geometric coupling specification
This data group is optional, and will only be applied for IEJ=1
and
IGT=1
.
BTGC

BTGC: character(4)
: bendingtorsion coupling identifier.
If the BTGC
identifier is present, geometric coupling between torsion
and bending is accounted for.
1.3.7. Axial stiffness. Case 2 IEA=N
EAF(1) ELONG(1) . . . EAF(N) ELONG(N)

EAF(1): real
: Axial force corresponding to relative elongationELONG(1)
\(\mathrm {[F]}\) 
ELONG(1): real
: Relative elongation () 
.

.

.

EAF(N): real
: 
ELONG(N): real
:
The pairs of EAF
and ELONG
must be given in increasing order. See
also the figure Axial force corresponding to relative elongation.
1.3.8. Bending stiffness properties
The amount of input depends upon the parameters IEJ
and IPRESS
according to the table below:

Case: 0,
IEJ
: 0,IPRESS
: 0, Data required: None. 
Case: 1,
IEJ
: 1,IPRESS
: 0, Data required:EJY, EZJ, MFY, MF2
. 
Case: 2,
IEJ
: 1,IPRESS
: 1, Data required: Not implemented. 
Case: 3,
IEJ
: N,IPRESS
: 0, Data required:CURV(I): I=1,N. BMOMY(I): I=1,N. BMOMZ(I)

Case: 4,
IEJ
: N1,IPRESS
: N2, Data required: Not implemented.
Thus, the following data are required for the respective cases:
1.3.9. Bending stiffness. Case 1, IEJ=1 IPRESS=0
EJY EJZ GAsZ GAsY

EJY: real > 0
: Bending stiffness around local yaxis \(\mathrm {[FL^2]}\) 
EJZ: real > 0
: Bending stiffness around zaxis \(\mathrm {[FL^2]}\) 
GAsZ: real
: Shear stiffness in Zdirection \(\mathrm {[F]}\) 
GAsY: real
: Shear stiffness in Ydirection \(\mathrm {[F]}\)
The shear stiffness, GAsZ
and GAsY
, are optional input parameters.
Specified GAsZ>0
and GAsY>0
will include shear deformation. This
requires that all stiffness properties are constant, i.e. IEA = 1
,
IEJ = 1
, IGT = 1
.
Note that the shear center is located along the local Xaxis, i.e. at the origin of the local Y and Zaxes.
1.3.10. Bending stiffness. Case 2, IEJ=1 IPRESS=1 (Not implemented)
EJY(1) EJZ(1) PRESS(1) EJY(2) EJZ(2) PRESS (2)

EJY(1): real
: Bending stiffness around local yaxis \(\mathrm {[FL^2]}\) 
EJZ(1): real
: Bending stiffness around local zaxis \(\mathrm {[FL^2]}\) 
PRESS(1): real
: Pressure at which the above values apply \(\mathrm {[F/L^2]}\) 
EJY(2): real
: Bending moments corresponding to 2nd pressure level, see description above 
EJZ(2): real
: 
PRESS(2): real
:
PRESS(1) < PRESS(2)
Values at other pressure levels than PRESS(1)
and PRESS(2)
are
obtained by linear interpolation/ extrapolation.
1.3.11. Bending stiffness description. Case 3 IEJ=N IPRESS=0
This specification consists of three different input lines.
Curvature
CURV(1) ... CURV(N)

CURV(1): real
: Curvature values for which bending moment is specified \(\mathrm {[1/L]}\) 
.

.

.

CURV(N): real
: To be specified in increasing order
CURV=1/CURVATURE RADIUS
Bending moment, yaxis
BMOMY(1) . . . BMOMY(N)

BMOMY(1): real
: Bending moment around local yaxis \(\mathrm {[FL]}\) 
.

.

.

BMOMY(N): real
Bending moment, zaxis
BMOMZ(1) . . . BMOMZ(N)

BMOMZ(1): real
: Bending moment around local zaxis \(\mathrm {[FL]}\) 
.

.

.

BMOMZ(N): real
CURV(1), BMOMY(1)
and BMOMZ(1)
have to be zero. See also the figure
Bending moment around yaxis as function of curvature.
1.3.12. Bending stiffness. Case 4 IEJ=N1, IPRESS=N2 (Not implemented)
This specification consists of four different input lines.
Curvature
CURV(1) ... CURV(N)

CURV(1): real
: Curvature values for which bending moments are specified \(\mathrm {[1/L]}\) 
.

.

.

CURV(N): real
: To be specified in increasing order
CURV=1/CURVATURE RADIUS
CURV(1) has to be zero. See also the figure Bending moment around yaxis as function of curvature.
Pressure
PRESS(1) ... PRESS(N)

PRESS(1): real
: Pressure levels for which bending moments are specified \(\mathrm {[F/L^2]}\) 
.

.

.

PRESS(N): real
:
1.3.13. Torsion stiffness
1.3.14. Damping specification
Identical to input for crosssection type CRS1, see data group Damping specification.
1.3.15. Hydrodynamic load type identification, One input line
CHLOAD

CHLOAD: character
:= HYDR
 Text to identify hydrodynamic load type
Note: Required if nonMorison loads are to be specified
Load type identification for CHLOAD=HYDR, One input line
CHTYPE

CHTYPE: character
: Hydrodynamic load type
= NONE
: No hydrodynamic load 
= MORI
: Load based on Morisons generalized equation. Sea surface penetration formulation 
= MORP
: AsMORI
, but improved by taking into account partially submerged crosssection 
= MACF
: Load based on MacCamyFuchs potential equations and quadratic drag load 
= POTN
: Load based on input of force transfer functions and retardation fuctions from 3rd party programs and quadratic drag load (Under development)

Note that the option POTN
currently is under testing. Potential flow
forces are only available for irregular time domain analysis.
Hydrodynamic force coefficients if CHTYPE=MORI or CHTYPE=MORP, submerged cross section
CHTYPE=MORP is similar to CHTYPE=MORI but with three key differences:

the load calculated at a crosssection is reduced in proportional with the instantaneous wet portion of the crosssection.

the FroudeKrylov term used longitudinal direction in Morison’s equation is replaced by the product of the dynamic pressure and the submerged area at each end of the element. The external area for this purpose is assumed to be circular.

If the specified value for external area (AE) is zero, neither hydrostatic nor hydrodynamic loads will act on the cross section.
Definitions of dimensional hydrodynamic force coefficients for a fully submerged cross section are given below
CDX CDY CDZ CDTMOM AMX AMY AMZ AMTOR CDLX CDLY CDLZ SCFKN SCFKT

CDX: real
: Drag force coefficient for local xdirection \(\mathrm {[F/((L/T)^2\times L)]}\) 
CDY: real
: Drag force coefficient for local ydirection \(\mathrm {[F/((L/T)^2\times L)]}\) 
CDZ: real
: Drag force coefficient for local zdirection \(\mathrm {[F/((L/T)^2\times L)]}\) 
CDTMOM: real
: Drag force coefficient for local xrotation. Not used in present version. 
AMX: real
: Added mass per length in xdirection \(\mathrm {[M/L]}\) 
AMY: real
: Added mass per length in ydirection \(\mathrm {[M/L]}\) 
AMZ: real
: Added mass per length in zdirection \(\mathrm {[M/L]}\) 
AMTOR: real
: Added mass for local xrotation \(\mathrm {[ML^2/L]}\) Not used in present version. 
CDLX: real, default: 0
: Linear drag force coefficients in local xdirection \(\mathrm {[F/((L/T)\times L)]}\) 
CDLY: real, default: 0
: Linear drag force coefficients in local ydirection \(\mathrm {[F/((L/T)\times L)]}\) 
CDLZ: real, default: 0
: Linear drag force coefficients in local zdirection \(\mathrm {[F/((L/T)\times L)]}\) 
SCFKN: real, default: 1
: Scaling factor for the FroudeKrylov term in Morison’s equation in normal direction 
SCFKT: real, default: 1
: Scaling factor for the FroudeKrylov term in Morison’s equation in tangential direction. Only the values 0.0 and 1.0 are permitted.
The drag forces per unit length acting in the local coordinate system are computed as:

\(\mathrm {F_x=CDX\times VRELX\times VRELX+CDLX\times VRELX}\)

\(\mathrm {F_y=CDY\times \sqrt{VRELY^2+VRELZ^2}\times VRELY+CDLY\times VRELY}\)

\(\mathrm {F_z=CDZ\times \sqrt{VRELY^2+VRELZ^2}\times VRELZ+CDLZ\times VRELZ}\)
where:

\(\mathrm {CDX,CDY,CDZ}\): are the input quadratic drag force coefficients in local x, y and zdirections

\(\mathrm {CDLX,CDLY,CDLZ}\): are the input linear drag force oefficients in local x, y and zdirections

\(\mathrm {VRELX,VRELY,VRELZ}\): are relative water velocities in local x, y and zdirections
The input quadratic drag force coefficients \(\mathrm {CDX}\), \(\mathrm {CDY}\) and \(\mathrm {CDZ}\) will normally be calculated as:

\(\mathrm {CDX=\frac{1}{2}\rho S_{2D}C_{dx}}\)

\(\mathrm {CDY=\frac{1}{2}\rho B_yC_{dy}}\)

\(\mathrm {CDZ=\frac{1}{2}\rho B_zC_{dz}}\)
where:

\(\mathrm {\rho }\): water density

\(\mathrm {S_{2D}}\): cross sectional wetted surface

\(\mathrm {B_y,B_z}\): projected area per. unit length for flow in local y and zdirection, respectively

\(\mathrm {C_{dx},C_{dy},C_{dz}}\): nondimensional drag coefficients in local x, y and zdirections, respectively
The input added mass per. unit length \(\mathrm {AMX}\), \(\mathrm {AMY}\) and \(\mathrm {AMZ}\) can be calculated as:

\(\mathrm {AMX=\rho AC_{mx}}\)

\(\mathrm {AMY=\rho AC_{my}}\)

\(\mathrm {AMZ=\rho AC_{mz}}\)
where:

\(\mathrm {\rho }\): water density

\(\mathrm {A}\): cross sectional area

\(\mathrm {C_{mx},C_{my},C_{mz}}\): nondimensional added mass coefficients in local x, y and zdirections, respectively
Hydrodynamic force coefficients if CHTYPE=MACF
MacCamyFuchs frequencydependent hydrodynamic loads on a stationary
vertical circular cylinder will be applied for CHTYPE=MACF
.
MacCamyFuchs forces are precomputed based on the element position
after static calculation. MacCamyFuchs forces are only available for
irregular time domain analysis.
Quadratic drag may also be applied on elements with MacCamyFuchs loading. McCamy Fuchs assumes that the crosssection is circular, so a single transverse quadratic drag coefficient is given (CDZ will be set to CDY).
CQX CQY ICODE D

CQX: real
: Quadratic drag coefficient in tangential direction
ICODE=1: CQX=CDX
: dimensional drag force coefficient \(\mathrm {[F/((L/T)^2\times L)]}\) 
ICODE=2: CQX=Cdt
: nondimensional drag force coefficient


CQY: real
: Quadratic drag coefficient in normal direction
ICODE=1: CQY=CDY
: dimensional drag force coefficient \(\mathrm {[F/((L/T)^2\times L)]}\) 
ICODE=2: CQY=Cdn
: nondimensional drag force coefficient


ICODE: integer
: Code for input of hydrodynamic drag coefficients
ICODE=1
: Dimensional coefficients 
ICODE=2
: Nondimensional coefficients


D: real, default:
\(\sqrt{\mathrm {\frac{4}{\pi }(AE)}}\): Hydrodynamic diameter of the pipe \(\mathrm {[L]}\).
Default value is calculated from external crosssectional area given as input in data section Mass and volume

Hydrodynamic force coefficients if CHTYPE=POTN
Frequencydependent added mass, radiation damping, and excitation forces
based on the first order potential flow solution will be applied for
CHTYPE=POTN
. The radiation and diffraction coefficients are to be
given by a separate input file specified under the data group
Potential flow library specification.
Quadratic drag may also be applied on crosssections with potential flow loading.
CQX CQY CQZ ICODE D SCFKT

CQX: real
: Quadratic drag coefficient in local xdirection
ICODE=1: CQX=CDX
: dimensional drag force coefficient \(\mathrm {[F/((L/T)^2\times L)]}\) 
ICODE=2: CQX=Cdt
: nondimensional drag force coefficient


CQY: real
: Quadratic drag coefficient in local ydirection
ICODE=1: CQY=CDY
: dimensional drag force coefficient \(\mathrm {[F/((L/T)^2\times L)]}\) 
ICODE=2: CQY=Cdn
: nondimensional drag force coefficient


CQZ: real
: Quadratic drag coefficient in local zdirection
ICODE=1: CQZ=CDZ
: dimensional drag force coefficient \(\mathrm {[F/((L/T)^2\times L)]}\) 
ICODE=2: CQZ=Cdn
: nondimensional drag force coefficient


ICODE: integer, default: 1
:ICODE
Code for input of hydrodynamic force coefficients
ICODE=1
: Dimensional coefficients 
ICODE=2
: Nondimensional coefficients


D: real, default:
\(\sqrt{\mathrm {\frac{4}{\pi }(AE)}}\): Hydrodynamic diameter \(\mathrm {[L]}\).
Default value is calculated from external crosssectional area given as input in data section Mass and volume


SCFKT: real, default: 1
: Scaling factor for the FroudeKrylov term in Morison’s equation in tangential direction. Only the values 0.0 and 1.0 are permitted.
1.3.16. Aerodynamic load type identification, One optional input line
CHLOAD

CHLOAD: character
:= WIND
 Text to identify wind coefficients
1.3.17. Load type identification, One optional input line
CHTYPE

CHTYPE: character
: Type of wind load coefficients
= MORI
: Morisonlike loading, Drag term 
= AIRC
: Air foil cross section to be specified (Not implemented) 
= AIRF
: Air foil cross section, Refers to a air foil library file

CHTYPE=MORI: Morisonlike aerodynamic drag, One input line
CDXAERO CDYAERO CDZAERO

CDXAERO: real
: Dimensional quadratic drag coefficient for local xdirection \(\mathrm {[F/((L/T)^2\times L)]}\) 
CDYAERO: real
: Dimensional quadratic drag coefficient for local ydirection \(\mathrm {[F/((L/T)^2\times L)]}\) 
CDZAERO: real
: Dimensional quadratic drag coefficient for local zdirection \(\mathrm {[F/((L/T)^2\times L)]}\)
The drag forces per unit length acting in the local coordinate system are computed as:  \(\mathrm {F_x=CDXAERO\times VRELX\times VRELX}\)  \(\mathrm {F_y=CDYAERO\times VRELY\times \sqrt{VRELY^2+VRELZ^2}}\)  \(\mathrm {F_z=CDZAERO\times VRELZ\times \sqrt{VRELY^2+VRELZ^2}}\)
where:

\(\mathrm {CDXAERO,CDYAERO,CDZAERO}\): are the input quadratic drag force coefficients in local x, y and zdirections

\(\mathrm {VRELX,VRELY,VRELZ}\): are relative wind velocities in local x, y and zdirections
The input quadratic drag force coefficients \(\mathrm {CDX}\), \(\mathrm {CDY}\) and \(\mathrm {CDZ}\) will normally be calculated as:

\(\mathrm {CDXAERO=\frac{1}{2}\rho _{air}S_{2D}C_{dx}}\)

\(\mathrm {CDYAERO=\frac{1}{2}\rho _{air}B_yC_{dy}}\)

\(\mathrm {CDZAERO=\frac{1}{2}\rho _{air}B_zC_{dz}}\)
where:

\(\mathrm {\rho _{air}}\): air density

\(\mathrm {S_{2D}}\): cross sectional surface area

\(\mathrm {B_y,B_z}\): projected area per. unit length for flow in local y and zdirection, respectively

\(\mathrm {C_{dx},C_{dy},C_{dz}}\): nondimensional drag coefficients in local x, y and zdirections, respectively
If the component is part of a wind turbine tower line, only the CDY
component is used for tower shadow computation.
CHTYPE=AIRF: Coefficients on file. ID and chord length, One input line
CHCOEF CHORDL YFC ZFC ROTFAX

CHCOEF: character(32)
: Air foil coefficient identifier. Must be found on the air foil library file 
CHORDL: real
: Chord length of foil section. \(\mathrm {[L]}\)
It is used to scale the air foil load coefficients.


YFC: real, default: 0
: Ycoordinate of foil origin \(\mathrm {[L]}\) 
ZFC: real, default: 0
: Zcoordinate of foil origin \(\mathrm {[L]}\) 
ROTFAX: real, default: 0
: Inclination of foil system \(\mathrm {[deg]}\)
The blade coordinate system and origin coincides with the elastic (local) \(\mathrm {(X_L,Y_L,Z_L)}\) coordinate system. The aerodynamic coordinate system \(\mathrm {(X_{AF},Y_{AF})}\) is located at (YFC,ZFC) referred to the local coordinate system, and is rotated about the blade x axis by the angle ROTFAX, as indicated in the figure below. The \(\mathrm {X_L}\) axis is pointing into the paper plane, while the \(\mathrm {Z_{AF}}\) is pointing out of plane. Note that the air foil coefficients has to be referred to the aerodynamic coordinate system as indicated by the corresponding angle of attack in the figure. For airfoil elements that are part of a wind turbine blade, the local \(\mathrm {X_L}\)axis is pointing towards the blade tip.
Normally, the arodynamic twist and the structural twist are given as one input. The input is given as twist of the elastic local coordinate system (see Line and segment specification ). ROTFAX
should normally be 0
.
In coupled analysis, a SIMO
wind type with IWITYP >= 10
must be used
if the case contains elements with wind force coefficients that are not
on the blades of a wind turbine.
1.4. CRS7  General cross section
1.4.2. Component type identifier
CMPTYPID TEMP ALFA

CMPTYPID: character(8)
: Component type identifier 
TEMP : real
: Temperature at which the specification applies
Dummy in present version


ALPHA: real
: Thermal expansion coefficient \(\mathrm {[Temp^{1}]}\)
Dummy in present version

1.4.3. Mass
YECC_MASS ZECC_MASS

YECC_MASS: real
: Mass center coordinate \(\mathrm {Y_m}\) in beam element system \(\mathrm {[L]}\) 
ZECC_MASS: real
: Mass center coordinate \(\mathrm {Z_m}\) in beam element system \(\mathrm {[L]}\)
AMS RGYR

AMS : real
: Mass per unit length \(\mathrm {[M/L]}\) 
RGYR: real
: Radius of gyration about mass center \(\mathrm {(Y_m,Z_m)}\) \(\mathrm {[L]}\)
1.4.4. Buoyancy
YECC_BUOY ZECC_BUOY

YECC_BUOY: real
: Buoyancy center Ycoordinate in beam element system \(\mathrm {[L]}\)
Dummy in present version. Bouyancy center set equal to mass center.


ZECC_BUOY: real
: Buoyancy center Zcoordinate in beam element system \(\mathrm {[L]}\)
Dummy in present version. Bouyancy center set equal to mass center.

AE AI

AE: real
: External crosssectional area \(\mathrm {[L^2]}\)
Basis for calculation of buoyancy


AI: real
: Internal crosssectional area \(\mathrm {[L^2]}\)
Dummy in present version

1.4.6. Area center and principal axes
The area center is the crosssection point where the axial force acts through. The principal axes are formally determined from the requirement \(\int_AV\,W\,\,\mathrm {d}A=0\), where \(\mathrm {V}\) and \(\mathrm {W}\) denote the principal coordinates and \(\mathrm {A}\) is the crosssection area. The orientation of the principal axes is defined in terms of a positive Xrotation \(\mathrm {\theta }\) relative to the beam element YZcoordinate system as shown in the figure General crosssection
YECC_AREACENT ZECC_AREACENT THETA

YECC_AREACENT: real
: Area center coordinate \(\mathrm {Y_a}\) in beam element system \(\mathrm {[L]}\) 
ZECC_AREACENT: real
: Area center coordinate \(\mathrm {Z_a}\) in beam element system \(\mathrm {[L]}\) 
THETA: real
: Orientation \(\mathrm {\theta }\) of principal axes V and W [deg.]. See figure General crosssection.
1.4.7. Shear center
The shear center represents the attack point of the shear forces.
YECC_SHEARCENT ZECC_SHEARCENT

YECC_SHEARCENT: real
: Shear center coordinate \(\mathrm {Y_s}\) in beam element system \(\mathrm {[L]}\) 
ZECC_SHEARCENT: real
: Shear center coordinate \(\mathrm {Z_s}\) in beam element system \(\mathrm {[L]}\)
1.4.9. Bending stiffness
The bending stiffness refers to the principal axes V and W, see figure General crosssection.
EJV EJW

EJV: real > 0
: Bending stiffness about principal Vaxis \(\mathrm {[FL^2]}\) 
EJW: real > 0
: Bending stiffness about principal Waxis \(\mathrm {[FL^2]}\)
1.4.10. Shear stiffness
The shear stiffness refers to the principal axes V and W, see figure General crosssection.
GAsW GAsV

GAsW: real
: Shear stiffness in principal Wdirection \(\mathrm {[F]}\) 
GAsV: real
: Shear stiffness in principal Vdirection \(\mathrm {[F]}\)
The shear stiffness, GAsW
and GAsV
, are optional input parameters.
Specified GAsW>0
and GAsV>0
will include shear deformation.
1.4.11. Torsion stiffness
GT

GT: real > 0
: Torsion stiffness \(\mathrm {[FL^2/Radian]}\)
For a circular crosssection the torsion stiffness is given by the polar moment of inertia. Note that this is not the case for noncircular crosssections.
1.4.12. Bendingtorsion geometric coupling
This data group is optional.
BTGC

BTGC: character(4)
: bendingtorsion coupling identifier.
If the BTGC
identifier is present, geometric coupling between torsion
and bending is accounted for.
1.4.13. Damping specification
Identical to input for crosssection type CRS1, see data group Damping specification.
The stiffness matrix used as basis for the Rayleigh damping includes only the material stiffness matrix. The geometric stiffness matrix is not included as this would introduce damping of the rigid body motion for CRS7.
1.4.14. Hydrodynamic load type identification, One input line
CHLOAD

CHLOAD: character
:= HYDR
 Text to identify hydrodynamic coefficients
Note: Required if nonMorison loads are to be specified
Load type identification for CHLOAD=HYDR, One input line
CHTYPE

CHTYPE: character
: Hydrodynamic load type
= NONE
: No hydrodynamic load coefficients 
= MORI
: Slender element hydrodynamic coefficients

Hydrodynamic force coefficients if CHTYPE=MORI
CDX CDY CDZ CDTMOM AMX AMY AMZ AMTOR CDLX CDLY CDLZ SCFKN SCFKT

CDX: real
: Drag force coefficient for local xdirection \(\mathrm {[F/((L/T)^2\times L)]}\) 
CDY: real
: Drag force coefficient for local ydirection \(\mathrm {[F/((L/T)^2\times L)]}\) 
CDZ: real
: Drag force coefficient for local zdirection \(\mathrm {[F/((L/T)^2\times L)]}\) 
CDTMOM: real
: Drag force coefficient for local xrotation. Not used in present version. 
AMX: real
: Added mass per length in xdirection \(\mathrm {[M/L]}\) 
AMY: real
: Added mass per length in ydirection \(\mathrm {[M/L]}\) 
AMZ: real
: Added mass per length in zdirection \(\mathrm {[M/L]}\) 
AMTOR: real
: Added mass for local xrotation \(\mathrm {[ML^2/L]}\) 
CDLX: real, default: 0
: Linear drag force coefficients in local xdirection \(\mathrm {[F/((L/T)\times L)]}\) 
CDLY: real, default: 0
: Linear drag force coefficients in local ydirection \(\mathrm {[F/((L/T)\times L)]}\) 
CDLZ: real, default: 0
: Linear drag force coefficients in local zdirection \(\mathrm {[F/((L/T)\times L)]}\) 
SCFKN: real, default: 1
: Scaling factor for the FroudeKrylov term in Morison’s equation in normal direction 
SCFKT: real, default: 1
: Scaling factor for the FroudeKrylov term in Morison’s equation in tangential direction. Only the values 0.0 and 1.0 are permitted.
The drag forces per unit length acting in the local coordinate system are computed as:

\(\mathrm {F_x=CDX\times VRELX\times VRELX+CDLX\times VRELX}\)

\(\mathrm {F_y=CDY\times VRELY\times VRELY+CDLY\times VRELY}\)

\(\mathrm {F_z=CDZ\times VRELZ\times VRELZ+CDLZ\times VRELZ}\)
where:

\(\mathrm {CDX,CDY,CDZ}\): are the input quadratic drag force coefficients in local x, y and zdirections

\(\mathrm {CDLX,CDLY,CDLZ}\): are the input linear drag force coefficients in local x, y and zdirections

\(\mathrm {VRELX,VRELY,VRELZ}\): are relative water velocities in local x, y and zdirections
The input quadratic drag force coefficients \(\mathrm {CDX}\), \(\mathrm {CDY}\) and \(\mathrm {CDZ}\) will normally be calculated as:

\(\mathrm {CDX=\frac{1}{2}\rho S_{2D}C_{dx}}\)

\(\mathrm {CDY=\frac{1}{2}\rho B_yC_{dy}}\)

\(\mathrm {CDZ=\frac{1}{2}\rho B_zC_{dz}}\)
where:

\(\mathrm {\rho }\): water density

\(\mathrm {S_{2D}}\): cross sectional wetted surface

\(\mathrm {B_y,B_z}\): projected area per. unit length for flow in local y and zdirection, respectively

\(\mathrm {C_{dx},C_{dy},C_{dz}}\): nondimensional drag coefficients in local x, y and zdirections, respectively
The input added mass per. unit length \(\mathrm {AMX}\), \(\mathrm {AMY}\) and \(\mathrm {AMZ}\) can be calculated as:

\(\mathrm {AMX=\rho AC_{mx}}\)

\(\mathrm {AMY=\rho AC_{my}}\)

\(\mathrm {AMZ=\rho AC_{mz}}\)
where:

\(\mathrm {\rho }\): water density

\(\mathrm {A}\): cross sectional area

\(\mathrm {C_{mx},C_{my},C_{mz}}\): nondimensional added mass coefficients in local x, y and zdirections, respectively
1.4.15. Aerodynamic load type identification, One optional input line
CHLOAD

CHLOAD: character
:= WIND
 Text to identify wind coefficients
1.4.16. Load type identification, One optional input line
CHTYPE

CHTYPE: character
: Type of wind load coefficients
= MORI
: Morisonlike loading, Drag term 
= AIRC
: Air foil cross section to be specified (Not implemented) 
= AIRF
: Air foil cross section, Refers to a air foil library file

CHTYPE=MORI: Morisonlike aerodynamic drag, One input line
CDXAERO CDYAERO CDZAERO

CDXAERO: real
: Dimensional quadratic drag coefficient for local xdirection \(\mathrm {[F/((L/T)^2\times L)]}\) 
CDYAERO: real
: Dimensional quadratic drag coefficient for local ydirection \(\mathrm {[F/((L/T)^2\times L)]}\) 
CDZAERO: real
: Dimensional quadratic drag coefficient for local zdirection \(\mathrm {[F/((L/T)^2\times L)]}\)
The drag forces per unit length acting in the local coordinate system are computed as:

\(\mathrm {F_x=CDXAERO\times VRELX\times VRELX}\)

\(\mathrm {F_y=CDYAERO\times VRELY\times \sqrt{VRELY^2+VRELZ^2}}\)

\(\mathrm {F_z=CDZAERO\times VRELZ\times \sqrt{VRELY^2+VRELZ^2}}\)
where:

\(\mathrm {CDXAERO,CDYAERO,CDZAERO}\): are the input quadratic drag force coefficients in local x, y and zdirections

\(\mathrm {VRELX,VRELY,VRELZ}\): are relative wind velocities in local x, y and zdirections
The input quadratic drag force coefficients \(\mathrm {CDX}\), \(\mathrm {CDY}\) and \(\mathrm {CDZ}\) will normally be calculated as:

\(\mathrm {CDXAERO=\frac{1}{2}\rho _{air}S_{2D}C_{dx}}\)

\(\mathrm {CDYAERO=\frac{1}{2}\rho _{air}B_yC_{dy}}\)

\(\mathrm {CDZAERO=\frac{1}{2}\rho _{air}B_zC_{dz}}\)
where:

\(\mathrm {\rho _{air}}\): air density

\(\mathrm {S_{2D}}\): cross sectional surface area

\(\mathrm {B_y,B_z}\): projected area per. unit length for flow in local y and zdirection, respectively

\(\mathrm {C_{dx},C_{dy},C_{dz}}\): nondimensional drag coefficients in local x, y and zdirections, respectively
If the component is part of a wind turbine tower line, only the CDY
component is used for tower shadow computation.
CHTYPE=AIRF: Coefficients on file. ID and chord length, One input line
CHCOEF CHORDL YFC ZFC ROTFAX

CHCOEF: character(32)
: Air foil coefficient identifier. Must be found on the air foil library file 
CHORDL: real
: Chord length of foil section. \(\mathrm {[L]}\)
It is used to scale the air foil load coefficients.


YFC: real, default: 0
: Ycoordinate of foil origin \(\mathrm {[L]}\) 
ZFC: real, default: 0
: Zcoordinate of foil origin \(\mathrm {[L]}\) 
ROTFAX: real, default: 0
: Inclination of foil system \(\mathrm {[deg]}\)
The blade coordinate system and origin coincides with the elastic (local) \(\mathrm {(X_L,Y_L,Z_L)}\) coordinate system. The aerodynamic coordinate system \(\mathrm {(X_{AF},Y_{AF})}\) is located at (YFC,ZFC) referred to the local coordinate system, and is rotated about the blade x axis by the angle ROTFAX, as indicated in the figure below. The \(\mathrm {X_L}\) axis is pointing into the paper plane, while the \(\mathrm {Z_{AF}}\) is pointing out of plane. Note that the air foil coefficients has to be referred to the aerodynamic coordinate system as indicated by the corresponding angle of attack in the figure. For airfoil elements that are part of a wind turbine blade, the local \(\mathrm {X_L}\)axis is pointing towards the blade tip.
Note that suppliers of wind turbine blades normally give the foil twist relative to the the areodynamic coordinate system, i.e. as twist around the \(\mathrm {Z_{AF}}\) axis.
Definition of foil center and inclination of foil system in the local cross section (strength
In coupled analysis, a SIMO
wind type with IWITYP >= 10
must be used
if the case contains elements with wind force coefficients that are not
on the blades of a wind turbine.
1.5. CRS8  Axisymmetric cross section with axial/torsion strain model and hysteresis effects in bending/cuvature relation
1.5.2. Component type identifier
Identical to input for crosssection type CRS1 , see Component type identifier for CRS1.
1.5.3. Mass and volume
Identical to input for crosssection type CRS1 , see Mass and volume for CRS1.
1.5.4. Stiffness properties classification
IEAIGT

IEAIGT: integer, default: 1
: Axial and torsional stiffness code
1  constant stiffness

N  table with N >= 3 pairs of tensionelongation and momentrotation to be specified

1.5.6. Axial stiffness. Case 2, IEAIGT=N
EAF(1) ELONG(1) . . . EAF(N) ELONG(N)

EAF(1): real
: Axial force corresponding to relative elongationELONG(1)
\(\mathrm {[F]}\) 
ELONG(1): real
: Relative elongation () 
.

.

.
The pairs of EAF
and ELONG
must be given in increasing order on a
single input line.
1.5.8. Bending stiffness.
EI MF SF

EI: real
: Bending stiffness \(\mathrm {[FL^2]}\) 
MF: real
: Internal friction moment, see figure below. \(\mathrm {[FL]}\) 
SF: real, default: 10.
: Internal friction moment stiffness factor. \(\mathrm {[]}\)
The default value of SF
corresponds to the earlier fixed value of
10.0.
1.5.9. Torsion stiffness
Constant torsion stiffness. Case 1 IGT=1
GT BETA

GT: real > 0
: Torsion stiffness \(\mathrm {[FL^2/Radian]}\) 
BETA: real
: Tension/torsion coupling parameter \(\mathrm {[L]}\)
Nonlinear torsion stiffness. Case 2 IEAIGT=N
TMOM(1) TROT(1) BETA(1). . . TMOM(N1) TROT(N1) BETA(N1) TMOM(N) TROT(N)

TMOM(1): real
: Torsion moment \(\mathrm {[FL]}\) 
TROT(1): real
: Torsion angle/length \(\mathrm {[Radian/L]}\) 
BETA(1): real
: Tension/torsion coupling parameter \(\mathrm {[L]}\) 
.

.

TMOM(N1): real

TROT(N1): real
: 
BETA(N1): real
: 
TMOM(N): real
: 
TROT(N): real
:
TROT
and TMOM
must be given in increasing order. BETA(1)
is constant in the range TROT(1)
< = TROT
< TROT(2)
,
BETA(2)
constant in the range TROT(2)
< = TROT
< TROT(3)
etc. Consequently BETA(N) is not to be specified.
1.5.10. Damping specification
Identical to input for crosssection type CRS1 , see Damping specification for CRS1.
1.5.11. Hydrodynamic load types
Identical to input for crosssection type CRS1, see Hydrodynamic load type identification for CRS1.
1.5.12. Aerodynamic force coefficients
Identical to input for crosssection type CRS1, see Aerodynamic load type identification for CRS1.
1.5.13. Capacity parameter
Identical to input for crosssection type CRS1, see Capacity parameter for CRS1.
1.6. BODY  Description of attached bodies
1.6.2. Component type identifier
CMPTYPID

CMPTYPID: character(8)
: Component type identifier
A body is a component that may be attached at supernodes and segment interconnection points. The following essential properties should be observed:

The
BODY
is directly attached to a nodal point and has no motion degrees of freedom by itself. 
The
BODY
component serves to add concentrated masses (inertia force), weight or buoyancy forces to the system.
1.6.3. Mass and volume
AM AE

AM: real
: Mass \(\mathrm {[M]}\) 
AE: real
: Displacement volume \(\mathrm {[L^3]}\)
1.6.4. Hydrodynamic coefficients
ICOO CDX CDY CDZ AMX AMY AMZ

ICOO: character(5)
: Coordinate system code
ICOO=GLOBAL
: Coefficients refer to global coordinate system 
ICOO=LOCAL
: Coefficients refer to local coordinate system of neighbour elements in the actual line


CDX: real
: Drag force coefficient in Xdirection \(\mathrm {[F/(L/T)^2)]}\) 
CDY: real
: Drag force coefficient in Ydirection \(\mathrm {[F/(L/T)^2)]}\) 
CDZ: real
: Drag force coefficient in Zdirection \(\mathrm {[F/(L/T)^2)]}\) 
AMX: real
: Added mass in Xdirection \(\mathrm {[M]}\) 
AMY: real
: Added mass in Ydirection \(\mathrm {[M]}\) 
AMZ: real
: Added mass in Zdirection \(\mathrm {[M]}\)
The drag forces acting in the global/local coordinate system are computed as:

\(\mathrm {F_x=CDX\times VRELX\times VRELX}\)

\(\mathrm {F_y=CDY\times VRELY\times VRELY}\)

\(\mathrm {F_z=CDZ\times VRELZ\times VRELZ}\)
where:

\(\mathrm {CDX,CDY,CDZ}\): are the input drag force coefficients in global/local x, y and zdirections, respectively

\(\mathrm {VRELX,VRELY,VRELZ}\): are relative water velocities in global/local x, y and zdirections respectively
The input quadratic drag force coefficients \(\mathrm {CDX}\), \(\mathrm {CDY}\) and \(\mathrm {CDZ}\) will normally be calculated as:

\(\mathrm {CDX=\frac{1}{2}\rho B_xC_{dx}}\)

\(\mathrm {CDY=\frac{1}{2}\rho B_yC_{dy}}\)

\(\mathrm {CDZ=\frac{1}{2}\rho B_zC_{dz}}\)
where:

\(\mathrm {\rho }\): water density

\(\mathrm {B_x,B_y,B_z}\): projected area for flow in global/local y and zdirection

\(\mathrm {C_{dx},C_{dy},C_{dz}}\): nondimensional drag coefficients in global/local x, y and zdirections
1.7. CONB  Description of ball joint connectors
This component can be used to model balljoint, hinges and universal
joints. The component has zero length, and adds 6 degrees of freedom to
the system model. The forces due to mass and weight are assumed to act
at the nodal point at which the component is specified. Note that this
component can not be used in branch lines in standard systems, or in
combination with bar elements. Should also be used with care at
supernodes with user defined boundary conditions for rotations in AR
system to avoid singularities in the FEM
solution procedure.
1.7.3. Mass and volume
AM AE

AM: real
: Mass \(\mathrm {[M]}\) 
AE: real
: Displacement volume \(\mathrm {[L^3]}\)
1.7.4. Hydrodynamic coefficients
ICOO CDX CDY CDZ AMX AMY AMZ

ICOO: character
: Coordinate system code
ICOO=GLOBAL
: Coefficients refer to global coordinate system 
ICOO=LOCAL
: Coefficients refer to local coordinate system of neighbour elements in the actual line


CDX: real
: Drag force coefficient in Xdirection \(\mathrm {[F/(L/T)^2)]}\) 
CDY: real
: Drag force coefficient in Ydirection \(\mathrm {[F/(L/T)^2)]}\) 
CDZ: real
: Drag force coefficient in Zdirection \(\mathrm {[F/(L/T)^2)]}\) 
AMX: real
: Added mass in Xdirection \(\mathrm {[M]}\) 
AMY: real
: Added mass in Ydirection \(\mathrm {[M]}\) 
AMZ: real
: Added mass in Zdirection \(\mathrm {[M]}\)
The drag forces acting in the global/local coordinate system are computed as:

\(\mathrm {F_x=CDX\times VRELX\times VRELX}\)

\(\mathrm {F_y=CDY\times VRELY\times VRELY}\)

\(\mathrm {F_z=CDZ\times VRELZ\times VRELZ}\)
where:

\(\mathrm {CDX,CDY,CDZ}\): are the input drag force coefficients in global/local x, y and zdirections, respectively

\(\mathrm {VRELX,VRELY,VRELZ}\): are relative water velocities in global/local x, y and zdirections respectively
The input quadratic drag force coefficients \(\mathrm {CDX}\), \(\mathrm {CDY}\) and \(\mathrm {CDZ}\) will normally be calculated as:

\(\mathrm {CDX=\frac{1}{2}\rho B_xC_{dx}}\)

\(\mathrm {CDY=\frac{1}{2}\rho B_yC_{dy}}\)

\(\mathrm {CDZ=\frac{1}{2}\rho B_zC_{dz}}\)
where:

\(\mathrm {\rho }\): water density

\(\mathrm {B_x,B_y,B_z}\): projected area per. unit lengt for flow in global/local y and zdirections, respectively

\(\mathrm {C_{dx},C_{dy},C_{dz}}\): nondimensional drag coefficients in global/local x, y and zdirections, respectively
1.7.5. Degrees of freedom
IRX IRY IRZ

IRX: integer, default: 0
: Rotation freedom code, xaxis 
IRY: integer, default: 0
: Rotation freedom code, yaxis 
IRZ: integer, default: 0
: Rotation freedom code, zaxis
1
 Fixed (no deformation) 
0
 Free (zero moment)

x, y and zaxes refer to local coordinate system of the neighbour element in the line where the ball joint is specified.
1.8. FLEX  Description of flexjoint connectors
This component can be used to model ball joints, hinges and universal
joints with specified rotational stiffness. It will introduce one extra
element with zero length at the segment end to which it is attached, and
add 6 degrees of freedom to the system model. The translation dofs of
freedom are suppressed by use of linear constraint equations. Note that
this component can not be used in branch lines in standard systems, or
in combination with bar elements. It should also be used with care at
supernodes with user defined boundary conditions for rotations in AR
system to avoid singularities in the FEM
solution procedure.
In present version, flexjoint connectors may only be used for nonlinear static and dynamic analysis.
1.8.3. Mass and volume
AM AE RGX RGY RGZ CRX CRY CRZ

AM: real, default: 0
: Mass \(\mathrm {[M]}\) 
AE: real, default: 0
: Displacement volume \(\mathrm {[L^3]}\) 
RGX: real, default: 0
: Radius of gyration around local xaxis \(\mathrm {[L]}\) 
RGY: real, default: 0
: Radius of gyration around local yaxis \(\mathrm {[L]}\) 
RGZ: real, default: 0
: Radius of gyration around local zaxis \(\mathrm {[L]}\) 
CRX: real, default: 0
: Damping coeff. Rotational velocity around local xaxis \(\mathrm {[FLT/deg]}\) 
CRY: real, default: 0
: Damping coeff. Rotational velocity around local yaxis \(\mathrm {[FLT/deg]}\) 
CRZ: real, default: 0
: Damping coeff. Rotational velocity around local zaxis \(\mathrm {[FLT/deg]}\)
1.8.4. Hydrodynamic coefficients
CDX CDY CDZ AMX AMY AMZ AMXROT AMYROT AMZROT

CDX: real, default: 0
: Drag coeff. in local xdirection \(\mathrm {[F/(L/T)^2)]}\) 
CDY: real, default: 0
: Drag coeff. in local ydirection \(\mathrm {[F/(L/T)^2)]}\) 
CDZ: real, default: 0
: Drag coeff. in local zdirection \(\mathrm {[F/(L/T)^2)]}\) 
AMX: real, default: 0
: Added mass in local xdirection \(\mathrm {[M]}\) 
AMY: real, default: 0
: Added mass in local ydirection \(\mathrm {[M]}\) 
AMZ: real, default: 0
: Added mass in local zdirection \(\mathrm {[M]}\) 
AMXROT: real, default: 0
: Added mass rotation around local xdirection \(\mathrm {[FL\times T^2]}\) 
AMYROT: real, default: 0
: Added mass rotation around local ydirection \(\mathrm {[FL\times T^2]}\) 
AMZROT: real, default: 0
: Added mass rotation around local zdirection \(\mathrm {[FL\times T^2]}\)
The tangential drag force, the force acting in local xaxis, is computed by:
\(\mathrm {FX=CDX\times VRELX\times VRELX}\)
The drag force acting normal to the local xdirection, is assumed to act in the same direction as the relative velocity transverse component and are computed according to:

\(\mathrm {FY=CDY\times \sqrt{VRELY^2+VRELZ^2}\times VRELY}\)

\(\mathrm {FZ=CDY\times \sqrt{VRELY^2+VRELZ^2}\times VRELZ}\)
1.8.5. Stiffness properties classification
IDOF IBOUND RAYDMP

IDOF: character(4)
: Degree of freedom
IDOF = IRX
: Rotation around local xaxis 
IDOF = IRY
: Rotation around local yaxis 
IDOF = IRZ
: Rotation around local zaxis 
IDOF = IRYZ
: Rotation around bending axis


IBOUND: integer
: Constraint
IBOUND = 1
: Fixed (Legal if 2 of 3 dofs are fixed) 
IBOUND = 0
: Free. Not available withIDOF = IRYZ

IBOUND = 1
: Constant stiffness 
IBOUND > 1
: Table withIBOUND
pairs of moment  rotational angle to be specified


RAYDMP: real
: Stiffness proportional damping coefficient
3 or 2 input lines to be specified: IRX, IRY, IRZ
or IRX, IRYZ
x, y and zaxes refer to the local coordinate system of the element to which the flex joint is attached. This is similar to the ball joint connector as illustrated in the figure Rotation freedom for a ball joint component.
1.8.6. Stiffness data
Stiffness data are to be given in the sequence IRX, IRY
and IRZ
or
IRX
and IRYZ
. Stiffness data are to be omitted for IBOUND ⇐ 0
Linear stiffness
IBOUND = 1
, One input line
STIFF

STIFF: real
: stiffness with respect to rotation \(\mathrm {[FL/deg]}\)
Nonlinear stiffness; IBOUND > 1
IBOUND > 1
, IBOUND input lines
MOMENT ANGLE

MOMENT: real
: Moment corresponding to rotational angle \(\mathrm {[FL]}\) 
ANGLE: real
: Rotational angle \(\mathrm {[deg]}\)
MOMENT
and ANGLE
must be given in increasing order. Linear
extrapolation will be used outside the specified range of values.
For dofs IRX, IRY
and IRZ
, both negative and positive values should
be given.
For dof IRYZ
, MOMENT
and ANGLE
have to be greater or equal to
zero. To avoid convergence problems, the first pair should be 0.0, 0.0.
1.9. FLUID  Specification of internal fluid flow
1.9.3. Fluid flow characteristics
RHOI VVELI PRESSI DPRESS IDIR

RHOI: real
: Density \([\mathrm {M/L^3}]\) 
VVELI: real
: Volume velocity \([\mathrm {L^3/T}]\) 
PRESSI: real
: Pressure at fluid inlet end \([\mathrm {F/L^2}]\) 
DPRESS: real
: Pressure drop \([\mathrm {F/L^3}]\) 
IDIR: integer, default: 1
: Flow direction code
1: Inlet at supernode end 1 of the line

2: Inlet at supernode end 2 of the line

The pressure drop is assumed to be uniform over the line length. For further clarification of pressure definition, confer Theory Manual.
In this version only RHOI
is used to calculate weight and mass for
static and dynamic analysis. The other parameters are used for
calculating wall force (flange force) only depending on output option
(OUTMOD
)
1.10. EXT1  External wrapping
This component can be used to model additional weight or buoyancy modules attached to a riser line. The specified additional weight and buoyancy are used to adjust the average properties of the segment.
1.10.3. Mass and volume
AMS AE RGYR FRAC

AMS: real
: Mass per unit length \(\mathrm {[M/L]}\) 
AE: real
: Buoyancy volume/length \(\mathrm {[L^2]}\) 
RGYR: real
: Radius of gyration around local xaxis \(\mathrm {[L]}\) 
FRAC: real
: Fraction of the segment that is covered \(\mathrm {[1]}\)
0 ⇐ FRAC ⇐ 1

The resulting properties of the segment with external wrapping are:
Mass / length:

\(\mathrm {AMS_{res}=AMS_{cs}+AMS_{ext}\times FRAC}\)
Resulting radius of gyration:

\(\mathrm {RGYR_{res}=(AMS_{cs}\times RGYR_{cs}^2+AMS_{ext}\times RGYR_{ext}^2\times FRAC)/(AMS_{cs}+AMS_{ext}\times FRAC)}\)
Resulting external area for buoyancy:

\(\mathrm {AE_{res}=AE_{cs}+AE_{ext}\times FRAC}\)
Where:

cs denotes the original cross section properties; i.e. without wrapping.

ext denotes the properties of the wrapping given in this data group.

res denotes the resulting average segment properties
1.10.4. Hydrodynamic coefficients
CDX CDY AMX AMY CDLX CDLY

CDX: real
: Drag force coefficient in tangential direction \(\mathrm {[F/((L/T)^2\times L)]}\) 
CDY: real
: Drag force coefficient in normal direction \(\mathrm {[F/((L/T)^2\times L)]}\) 
AMX: real
: Added mass per length in tangential direction \(\mathrm {[M/L]}\) 
AMY: real
: Added mass per length in normal direction \(\mathrm {[M/L]}\) 
CDLX: real, default: 0
: Linear drag force coefficients in tangential direction \(\mathrm {[F/((L/T)\times L)]}\) 
CDLY: real, default: 0
: Linear drag force coefficients in normal direction \(\mathrm {[F/((L/T)\times L)]}\)
The coefficients specified for the external wrapping are added directly to the coefficients specified for the pipe.
The drag forces per unit length acting in the local xdirection is computed as:

\(\mathrm {F_x=(CDX_R+FRAC\times CDX)VRELX\times VRELX+(CDLX_R+FRAC\times CDLX)VRELX}\)
In the case of an axis symmetric cross section the drag force per unit length, \(\mathrm {F_n}\), acting normal to the local xaxis is computed by assuming that the instantaneous drag force direction is parallel to the instantaneous transverse relative velocity component

\(\begin{array}{l}\mathrm {F_n=(CDY_R+FRAC\times CDY)(VRELY^2+VRELZ^2)}\\+\mathrm {(CDLY_R+FRAC\times CDLY)\sqrt{VRELY^2+VREZ^2}}\end{array}\)
In the case of a cross section with 2 symmetry planes the drag force per unit length in the local y and z directions are computed as:

\(\mathrm {F_y=(CDY_R+FRAC\times CDY)VRELY\times VRELY+(CDLY_R+FRAC\times CDLY)VRELY}\)

\(\mathrm {F_z=(CDZ_R+FRAC\times CDZ)VRELZ\times VRELZ+(CDLZ_R+FRAC\times CDLZ)VRELZ}\)
Where:

\(\mathrm {CDX_R,CDY_R,CDZ_R}\): are the input quadratic drag force coefficients of the riser in local x,y and zdirections

\(\mathrm {CDLX_R,CDLY_R,CDLZ_R}\): are the input linear drag force coefficient of the riser in local x,y and zdirections

\(\mathrm {CDX,CDY}\): are the input quadratic drag force coefficients of the external wrapping in local x and ydirections

\(\mathrm {CDLX,CDLY}\): are the input linear drag force coefficients of the external wrapping in local x andydirections

\(\mathrm {VRELX,VRELY,VRELZ}\): are relative water velocities in local x, y and zdirections
For an axis symmetric pipe with external wrapping the input drag force coefficient in normal direction can be calculated as:

\(\mathrm {CDY=\frac{1}{2}\rho (DC_{dn}D_RC_{dnR})}\)
The added mass per unit length in normal direction can be calculated as:

\(\mathrm {AMY=\rho \frac{\pi }{4}(D^2C_{mn}D_R^2C_{mnR})}\)
where:

\(\mathrm {\rho }\): water density

\(\mathrm {D}\): outer diameter of the external wrapping

\(\mathrm {D_R}\): outer diameter of the pipe

\(\mathrm {C_{dn}}\): normal drag coefficient

\(\mathrm {C_{dnR}}\): normal drag coefficient of the pipe

\(\mathrm {C_{mn}}\): normal added mass coefficient of the external wrapping

\(\mathrm {C_{mnR}}\): normal added mass coefficient of the pipe
1.11. CRS5  Partly submerged general shaped cross section
This cross section is used for floating structural members. It can only be used for elements with local zaxis approximately parallel the global zaxis pointing in the same direction. The roll and pitch angles are restricted to 30\(\mathrm {^{\circ}}\) as a practical upper limit. The stiffness properties are based on two symmetry planes, while area and hydrodynamic force coefficients are calculated based on the cross section description represented by offset points symmetric with regard to the vertical (z) axis. For hydrodynamic load computation the element is divided into subelements specified in data section Segment specification. NSEG input lines. The cross section can only be used when consistent formulation is applied (see STAMOD: External, static loads) and for nonlinear dynamic analysis with regular waves.
1.11.2. Component type identifier
Identical to Component type identifier for CRS2.
1.11.3. Mass and volume
Identical to Mass and volume.
1.11.4. Stiffness properties classification
Identical to Stiffness properties classification for CRS2
1.11.5. Axial stiffness. Case 1, IEA=1
Identical to Axial stiffness. Case 1
1.11.6. Axial stiffness. Case 2, IEA=N
Identical to Axial stiffness. Case 2
1.11.7. Bending stiffness. Case 1, IEJ=1 IPRESS=0
Identical to Bending stiffness. Case 1
1.11.8. Bending stiffness. Case 2, IEJ=1 IPRESS=1 (not implemented)
Identical to Bending stiffness. Case 2
1.11.10. Bending stiffness. Case 4 IEJ=N1, IPRESS=N2 (not implemented)
Identical to Bending stiffness. Case 4 IEJ=N1
1.11.11. Damping specification
Identical to Damping specification for CRS2
1.11.12. Hydrodynamic force coefficients
CDX CDY CDZ CDTMOM AMX

CDX: real
: Drag force coefficient per length, tangential \(\mathrm {[F/((L/T)^2\times L)]}\) 
CDY: real
: Drag force coefficient per length, local yaxis \(\mathrm {[F/((L/T)^2\times L)]}\) 
CDZ: real
: Drag force coefficient per length, local zaxis \(\mathrm {[F/((L/T)^2\times L)]}\) 
CDTMOM: real
: Drag coefficient around local xaxis
Dummy in present version.


AMX: real
: Added mass per length, tangential \(\mathrm {[M/L]}\)
All hydrodynamic force coefficients applies to fully submerged cross section. That is, the actual coefficients are proportional to submerged volume. The drag force coefficients are to be scaled according to consistent units used, see Unit names and gravitational constant.
The tangential drag force which is a friction force acting along the local xdirection is calculated according to:  \(\mathrm {F_t=CDX\times (A_{sub}/A_{tot})\times V_{x,rel}\times V_{x,rel}}\)
The viscous normal force per unit length is calculated using the drag
force term in Morison’s equation and assuming the drag force direction
is parallel the instantaneous relative velocity transverse component: 
\(\mathrm {F_y=CDY\times (A_{sub}/A_{tot})\times \sqrt{V^2_{y,rel}\times V^2_{z,rel}}\times V_{y,rel}}\)

\(\mathrm {F_z=CDZ\times (A_{sub}/A_{tot})\times \sqrt{V^2_{y,rel}\times V^2_{z,rel}}\times V_{z,rel}}\)
where:  \(\mathrm {A_{sub}}\): is instantaneous cross section submergence  \(\mathrm {A_{tot}}\): is total external areal of the cross section  \(\mathrm {V_{x,rel}}\): is relative water velocity in local xdirection  \(\mathrm {V_{y,rel}}\): is relative water velocity in local ydirection  \(\mathrm {V_{z,rel}}\): is relative water velocity in local zdirection
1.11.13. Description of cross section shape
NOB NSUB NROLL NDFS

NOB: integer
: Number of offset points to describe the cross section shape.
Only one half of the shape is described due to assumed symmetry about local zaxis.

3 ⇐ NOB ⇐ 20


NSUB: integer, default: 20
: Number of points of submergence in table of submerged volume as function of submergence and roll angle. 
NROLL: integer, default: 20
: Number of roll angles in table of submerged volume as function of submergence and roll angle. 
NDFS: integer, default: 20
: Number of points of submergence in table of added mass and poten tial damping as function of submergence.
The submerged cross section area is calculated for a number of
submergence positions and relative roll angles in the range (0

\(\mathrm {\pi }\)/2
). The instantaneous submerged area is
found by linear interpola tion for points lying between those given in
the table.
Tables of twodimensional added mass and potential damping as function of submergence are calculated using the Frank.closefit technique. The instantaneous added mass and damping are found by linear interpolation for points lying between those given in the tables.
1.11.14. Offset points
INB YB ZB

INB: integer
: Offset point number 
YB: real
: Local ycoordinate for offset pointINB

ZB: real
: Local zcoordinate for offset pointINB
Only one half of the cross section shape is modelled due to the assumed symmetry about local zaxis.
The offset points must be given in increasing order with decreasing
value of the zcoordinate. YB
and ZB
are referred to the principal
local axis. YB >= 0
and first and last value of YB
has to be zero,
see the figure below.
1.11.15. Capacity parameter
Identical to Capacity parameter for CRS2
1.12. CONTACT  Contact point of roller type
Available for elastic contact surface description only.
The local coordinate system \(\mathrm {(X_L,Y_L,Z_L)}\) of the elastic contact surface is indicated. The \(\mathrm {X_L}\)axis is pointing into the paper plane.
The contact point may contain several rollers.
The rollers are located in the \(\mathrm {Y_LZ_L}\)plane of
the element to which the contact point is attached. Besides the
location, each roller is described by its length, which may be infinite,
by its stiffness and dash pot damping. The location and orientation of a
roller is defined by a point and an inclination angle referred in the
local coordinate system of the contact surface element. A roller of
finite length is shown in the figure below. The roller origin (starting
point) is defined by the point \(\mathrm {(Y_R,Z_R)}\) and the
inclination angle (ROTX
) is defined by a clockwise rotation around the
contact surface \(\mathrm {X_L}\)axis.
Roller with finite length located in the local coordinate system of an element contributing to the elastic contact surface.
The \(\mathrm {X_L}\)axis is pointing into the paper plane.
1.12.3. Number of rollers
NROLLS

NROLLS: integer
: Number of rollers
The following 3 data groups (Location and orientation
, Stiffness
properties
and Spring stiffness, Case 1 or 2
) must be given in blocks
for each of the NROLLS
roller.
1.12.4. Location and orientation of roller axis
ROTX YR ZR RLENG

ROTX: real, default: 0
: Direction of roller axis. (Clockwise around the \(\mathrm {X_L}\)axis of the actual surface plane) \(\mathrm {[deg]}\) 
YR: real, default: 0
: Ycoordinate of roller origin \(\mathrm {[L]}\) 
ZR: real, default: 0
: Zcoordinate of roller origin \(\mathrm {[L]}\) 
RLENG: real, default: 0
: Length of roller \(\mathrm {[L]}\)
= 0
means infinite length

In case of infinite roller length, YR
and ZR
describe coordinates of
an arbitrary point on the roller principal axis.
1.12.5. Stiffness properties classification and damping
IKS DAMP

IKS: integer
: Stiffness code1
1 : Constant spring compression stiffness

N : Table with N pairs of pressure force  displacements to be specified

N > 2



DAMP: real, default: 0
: Dash pot damping coefficient \(\mathrm {[FT/L]}\)
1.12.6. Spring stiffness, Case 1 IKS = 1
STIFFR RADROL

STIFFR: real
: Spring compression stiffness \(\mathrm {[F/L]}\) 
RADROL: real
: Radius of roller \(\mathrm {[L]}\)
The figure below describes the interpretation of contact force in case
that IKS=1
. The spring is active when the distance between the
principal axis of the roller and the pipe is less than
\(\mathrm {\Delta _0=RADROl+RTUBE}\). The external radius of
the tube, RTUBE
, is calculated from the external area of the cross
section of the element in contact with the roller.
1.12.7. Spring stiffness, Case 2 IKS > 2
FS(1) ZS(1) ... FS(N) ZS(N)

FS(1): real < 0
: Pressure force corresponding to compressionZS(1)
\(\mathrm {[F]}\) 
ZS(1): real
: Spring compression \(\mathrm {[L]}\) 
.

.

.
ZS(i)
must be given in increasing order.
The figure below describes the interpretation of contact force in case
that IKS>2
. The specified stiffness characteristics is moved to
account for the external radius of the tube, RTUBE
. The external
radius of the tube, RTUBE
, is calculated from the external area of the
cross section of the element in contact with the roller.
The three data groups Location and orientation
, Stiffness properties
and Spring stiffness, Case 1 or 2
are to be repeated NROLLS
times.
1.13. Tensioner
Available for elastic contact surface description only.
The function of the tensioner is to grip and apply tension to the
pipeline during the lay operation. In dynamic analysis the tensioner
accounts for the pipeline pay out or pay in to prevent large
oscillations in the pipeline tension. This is modelled as a dynamic
boundary condition with respect to the applied axial force, eg. the
applied load is T0
plus/minus a dead band range. Outside the dead band
range the load is constant. The applied load which acts in the
longitudinal direction of the tube, is formulated as a discrete element
load. During static analysis the tensioner applies a constant load,
T0
, to the pipeline.
1.13.3. Characteristics of tensioner
T0 TMAX TMIN DELTA SIGNX

T0: real
: Applied load during static analysis \(\mathrm {[F]}\) 
TMAX: real
: Maximum load transmitted from the tensioner \(\mathrm {[F]}\) 
TMIN: real
: Minimum load transmitted from the tensioner \(\mathrm {[F]}\) 
DELTA: real
: Pipeline displacement through the tensioner for a load variation of:TMAXTMIN
\(\mathrm {[L]}\) 
SIGNX: real, default: 1
: Direction of applied load referring to local xaxis of the element going through the tensioner \(\mathrm {[]}\)
SIGNX = 1.0
: The load will act in local xaxis direction 
SIGNX = 1.0
: The load will act opposite local xaxis

The stiffness characteristics of the tensioner will be derived from
DELTA
as: STIFF = (TMAXTMIN)/DELTA
1.14. Tubular contact component
This component is available for elastic contact surface description only.
1.14.3. Specification of contact force characteristics
RCONT CHDIR IKS DAMP STIFFR FRICST FRICDY CHAXI CHROT VELLIM

CONT: real
: Contact radius \(\mathrm {[L]}\) 
CHDIR: character
: Contact direction:INWARDS
orOUTWARDS

IKS: integer
: Stiffness code for radial contact force
= 1
Constant contact compression stiffness 
= N
Table with N pairs of contact force  displacement to be specified


RELDAM: real
: = Desired relative damping level at estimated eigen period in the pipe, pipe and contact spring system (see below) \(\mathrm {[1]}\). Damping is only applied in the radial direction. Not used in static analysis. 
DAMP: real
: Dash pot damping coefficient \(\mathrm {[FT/L]}\). Damping is only applied in the radial direction. Not used in static analysis. 
STIFFR: real
: Spring stiffness associated with static friction coefficientFRICST
, \(\mathrm {[F/L]}\). The spring stiffness is applied in the ring and axial directions until the spring force exceeds the static friction force. Not used in static analysis. Dummy ifCHAXI = OFF
. 
FRICST: real
: Static friction coefficient \(\mathrm {[1]}\). Not used in static analysis. Dummy ifCHAXI = OFF
. 
FRICDY: real
: Dynamic sliding friction coefficient \(\mathrm {[1]}\).FRICDY ⇐ FRICST
. Not used in static analysis. Dummy ifCHAXI = OFF
. 
CHAXI: character
: Control parameter for axial sliding friction
= ON

= OFF


CHROT: character
: Control parameter for friction caused by rotation
= ON
RequiresCHAXI=ON

= OFF


VELLIM: real
: Velocity limit for determining that sliding has stopped \(\mathrm {[L/T]}\). If the relative sliding velocity between the pipes falls belowVELLIM
, the spring stiffnessSTFFR
is applied. Should be small, but not zero. Not used in static analysis. Dummy ifCHAXI = OFF
.
Based on specified damping level the stiffness proportional damping coefficient is calculated by
\(\mathrm {a_2=RELDAM\times 2\times \sqrt\frac{(AMS\times L)_M+(AMS\times L)_S}{STIFF}}\)
where \(\mathrm {(AMS\times L)_M}\) and \(\mathrm {(AMS\times L)_S}\) are total structural element mass of the master pipe and the slave pipe respectively and \(\mathrm {STIFF}\) is contact spring sitffness.
1.15. Soil
Soils for use with the soil layer profile definition, intended for modelling of embedded piles.
The soil layer profile is defined in Soil layer profile specification.
1.15.2. Soil ID and type
SOILID SOILMET

SOILID: character(8)
: Soil ID. Must be unique. 
SOILMET: character(8)
: Soil methodology.
= PISACLAY
: lateral displacement and rotation according to PISA methodology for clay 
= PISASAND
: lateral displacement and rotation according to PISA methodology for sand 
= PISADUNK
: lateral displacement and rotation according to PISA methodology for general Dunkirk sand

The PISA*
soil methodologies require a PISA
soil layer profile
methodology, and can not be combined with other methodologies. The
lateral displacement and crosssection rotation are modelled with
forcedisplacement (pv) and momentrotation (mt) curves.
1.15.3. Soil PISA curves, sand and clay
The figure above shows how the shape of PISA curves is related to four
parameters k
, n
, Xu
and Yu
. The initial stiffness is given by
k
and ultimate values are Xu
and Yu
. The parameter n
ranges from
0 to 1, where 0 gives a bilinear curve and 1 gives a straight line from
(0,0)
to (Xu,Yu)
. The equation below is used to define the exact
shape of the curve.
The initial stiffness k
must satisfy the requirement k > Yu/Xu
.
The following seventeen (1+4x4) lines are given if SOILMET = PISACLAY
or PISASAND
. The resulting curve is a `normalized' nondimensional
curve, which is scaled with physical soil layer properties defined in
the soil layer profile.
CURVRES

CURVRES: integer, default: 50
: resolution for all soil reaction curves.
Coefficients used to define parameters for lateral forcedisplacement (pv) soil reaction curve.
PVKC1 PVKC2 PVKC3 PVNC1 PVNC2 PVNC3 PVXC1 PVXC2 PVXC3 PVYC1 PVYC2 PVYC3

PVKC1, PVKC2, PVKC3: real
: pv curve parameter k (initial stiffness). 
PVNC1, PVNC2, PVNC3: real
: pv curve parameter n (0 ⇐ n ⇐ 1
). 
PVXC1, PVXC2, PVXC3: real
: pv curve upper Xvalue. 
PVYC1, PVYC2, PVYC3: real
: pv curve upper Yvalue.
Coefficients used to define parameters for momentrotation (mt) soil reaction curve.
MTKC1 MTKC2 MTKC3 MTNC1 MTNC2 MTNC3 MTXC1 MTXC2 MTXC3 MTYC1 MTYC2 MTYC3

MTKC1, MTKC2, MTKC3: real
: mt curve parameter k (initial stiffness). 
MTNC1, MTNC2, MTNC3: real
: mt curve parameter n (0 ⇐ n ⇐ 1
). 
MTXC1, MTXC2, MTXC3: real
: mt curve upper Xvalue. 
MTYC1, MTYC2, MTYC3: real
: mt curve upper Yvalue.
Coefficients used to define parameters for base shear load soil reaction curve.
BSKC1 BSKC2 BSKC3 BSNC1 BSNC2 BSNC3 BSXC1 BSXC2 BSXC3 BSYC1 BSYC2 BSYC3

BSKC1, BSKC2, BSKC3: real
: base shear load curve parameter k (initial stiffness). 
BSNC1, BSNC2, BSNC3: real
: base shear load curve parameter n (0 ⇐ n ⇐ 1
). 
BSXC1, BSXC2, BSXC3: real
: base shear load curve upper Xvalue. 
BSYC1, BSYC2, BSYC3: real
: base shear load curve upper Yvalue.
Coefficients used to define parameters for base moment soil reaction curve.
BMKC1 BMKC2 BMKC3 BMNC1 BMNC2 BMNC3 BMXC1 BMXC2 BMXC3 BMYC1 BMYC2 BMYC3

BMKC1, BMKC2, BMKC3: real
: base moment curve parameter k (initial stiffness). 
BMNC1, BMNC2, BMNC3: real
: base moment curve parameter n (0 ⇐ n ⇐ 1
). 
BMXC1, BMXC2, BMXC3: real
: base moment curve upper Xvalue. 
BMYC1, BMYC2, BMYC3: real
: base moment curve upper Yvalue.
For each group of 3 coefficients the corresponding curve parameter is
given according to the following z/D
dependency: c = c1 + c2 * z/D
if c3 = 0
, otherwise it is c = c1 + c2 * exp(c3 * z/D)
. The
quantities z
and D
are the subsurface depth and pile diameter,
respectively.
1.15.4. Soil PISA curves, general Dunkirk sand
The following seventeen (1+4x4) lines are given if SOILMET = PISADUNK
,
to define the shape of soil reaction curves for general Dunkirk sand.
The coefficients given here are used together with a density ratio Dr
which is defined per layer in the soil layer profile. The resulting
curve is a `normalized' nondimensional curve, which is scaled with
physical soil layer properties also defined in the soil layer profile.
The parametrisation of PISA curves for general Dunirk sand is identical
to that for other PISA curves, except that four rather than three
coefficients are required.
CURVRES

CURVRES: integer, default: 50
: resolution for all soil reaction curves.
Coefficients used to define parameters for lateral forcedisplacement (pv) soil reaction curve.
PVKC1 PVKC2 PVKC3 PVKC4 PVNC1 PVNC2 PVNC3 PVNC4 PVXC1 PVXC2 PVXC3 PVXC4 PVYC1 PVYC2 PVYC3 PVYC4

PVKC1, PVKC2, PVKC3, PVKC4: real
: pv curve parameter k (initial stiffness). 
PVNC1, PVNC2, PVNC3, PVNC4: real
: pv curve parameter n (0 ⇐ n ⇐ 1
). 
PVXC1, PVXC2, PVXC3, PVXC4: real
: pv curve upper Xvalue. 
PVYC1, PVYC2, PVYC3, PVYC4: real
: pv curve upper Yvalue.
Coefficients used to define parameters for momentrotation (mt) soil reaction curve.
MTKC1 MTKC2 MTKC3 MTKC4 MTNC1 MTNC2 MTNC3 MTNC4 MTXC1 MTXC2 MTXC3 MTXC4 MTYC1 MTYC2 MTYC3 MTYC4

MTKC1, MTKC2, MTKC3, MTKC4: real
: mt curve parameter k (initial stiffness). 
MTNC1, MTNC2, MTNC3, MTNC4: real
: mt curve parameter n (0 ⇐ n ⇐ 1
). 
MTXC1, MTXC2, MTXC3, MTXC4: real
: mt curve upper Xvalue. 
MTYC1, MTYC2, MTYC3, MTYC4: real
: mt curve upper Yvalue.
Coefficients used to define parameters for base shear load soil reaction curve.
BSKC1 BSKC2 BSKC3 BSKC4 BSNC1 BSNC2 BSNC3 BSNC4 BSXC1 BSXC2 BSXC3 BSXC4 BSYC1 BSYC2 BSYC3 BSYC4

BSKC1, BSKC2, BSKC3, BSKC4: real
: base shear load curve parameter k (initial stiffness). 
BSNC1, BSNC2, BSNC3, BSNC4: real
: base shear load curve parameter n (0 ⇐ n ⇐ 1
). 
BSXC1, BSXC2, BSXC3, BSXC4: real
: base shear load curve upper Xvalue. 
BSYC1, BSYC2, BSYC3, BSYC4: real
: base shear load curve upper Yvalue.
Coefficients used to define parameters for base moment soil reaction curve.
BMKC1 BMKC2 BMKC3 BMKC4 BMNC1 BMNC2 BMNC3 BMNC4 BMXC1 BMXC2 BMXC3 BMXC4 BMYC1 BMYC2 BMYC3 BMYC4

BMKC1, BMKC2, BMKC3, BMKC4: real
: base moment curve parameter k (initial stiffness). 
BMNC1, BMNC2, BMNC3, BMNC4: real
: base moment curve parameter n (0 ⇐ n ⇐ 1
). 
BMXC1, BMXC2, BMXC3, BMXC4: real
: base moment curve upper Xvalue. 
BMYC1, BMYC2, BMYC3, BMYC4: real
: base moment curve upper Yvalue.
For each group of 4 coefficients the corresponding curve parameter is
given according to the following r
and Dr
dependency:
c = (c1*Dr + c2)*r + c3*Dr + c4
.
For the pv and mt curves the ratio r
is z/D
, except for the
Yvalues where it is z/L
. For the base shear and base moment curves
the ratio r
is L/D
. The quantities z
, D
and L
are the
subsurface depth, pile diameter and embedded depth of the pile,
respectively. The relative density Dr
is given in the soil layer
profile.
1.15.5. Soil damping factor, PISA
The following line is given if SOILMET = PISACLAY
, PISASAND
or
PISADUNK
.
DMPPV DMPMT DMPBS DMPBM

DMPPV: real, default: 0.0
: Damping factor for pv curve (DMPPV >= 0.0
). 
DMPMT: real, default: 0.0
: Damping factor for mt curve (DMPMT >= 0.0
). 
DMPBS: real, default: 0.0
: Damping factor for base shear load curve (DMPBS >= 0.0
). 
DMPBM: real, default: 0.0
: Damping factor for base moment curve (DMPBM >= 0.0
).
The damping factors must currently be zweo.
Stiffness proportional damping is applied with respect to displacements along the axis defined by the corresponding curve (either lateral deflection or crosssection rotation) with the provided factor used together with the initial stiffness of the curve to produce a constant stiffness proportional damping (Rayleigh damping with only stiffness term).
1.16. Seafloor contact
The seafloor contact properties are relevant for riser systems with
tubular cross sections, which are partly resting on the bottom. This may
be the case for SB
and AR
systems.
1.16.2. Component type identifier and type
CMPTYPID CHSFCT

CMPTYPID: character(8)
: Component identifier 
CHSFCT: character(4)
: Seafloor contact component type
= SPRI
: Original RIFLEX seafloor springs normal to the seafloor and separate axial and lateral springfriction contact in the seafloor plane. 
= SOIL
: Consolidated risersoil interaction model

1.16.3. Original RIFLEX seafloor spring contact
The following three lines of input must be given if CHSFCT = SPRI
Seafloor normal contact parameters
STFBOT DAMBOT

STFBOT: real > 0
: Seafloor stiffness normal to the seafloor \([\mathrm {F/L^2}]\) 
DAMBOT: real >= 0, default: 0
: seafloor damping coefficient normal to the seafloor \([\mathrm {F\times T/L^2}]\)
STFBOT
is used for computing the spring stiffness normal to the
seafloor, \(\mathrm {k_V}\) , for seafloor contact.
\(\mathrm {k_V}\) = STFBOT
\(\mathrm {\times L}\)
where \(\mathrm {L}\) is the element length.
Seafloor inplane contact parameters, two input lines
STFAXI FRIAXI DAMAXI

STFAXI: real >= 0, default: 0
: Inplane seafloor stiffness for friction in axial direction \([\mathrm {F/L^2}]\) 
FRIAXI: real >= 0, default: 0
: Inplane seafloor friction coefficient in axial direction [1] 
DAMAXI: real >= 0, default: 0
: Inplane seafloor damping coefficient in axial direction \([\mathrm {F\times T/L^2}]\)
STFLAT FRILAT DAMLAT ILTOR

STFLAT: real >= 0, default: 0
: Inplane seafloor stiffness for friction in lateral direction \([\mathrm {F/L^2}]\) 
FRILAT: real >= 0, default: 0
: Inplane seafloor friction coefficient in lateral direction [1] 
DAMLAT: real >= 0, default: 0
: Inplane seafloor damping coefficient in lateral direction \([\mathrm {F\times T/L^2}]\) 
ILTOR: integer, default: 0
: Option for applying lateral contact forces at the external contact radius, giving a torsional moment
= 0
: Lateral loads are applied at the node 
= 1
: Lateral loads are applied at the external contact radius if it is specified for the associated beam crosssection.

Contact in the seafloor plane is modelled independently in the axial and lateral directions. Contact is initially modelled with linear springs. Sliding will occur when an axial or lateral spring force reaches the friction force value. Springs will be reinstated if the line starts sliding in the opposite direction, or if the friction force increases and is greater than the spring force. The spring stiffness is calculated as \(k_h=\mathrm {Stalks}\times L_h\), where \(\mathrm {L_h}\) is the length of the element’s horizontal projection. The seafloor friction forces are calculated as \(F=\mathrm {FRIxxx}\times F_{vert}\) and are directed against the axial or lateral displacements, where \(\mathrm {F_{vert}}\) is the vertical contact force between the pipe and the bottom.
1.16.4. Consolidated risersoil seafloor contact
The following four lines of input must be given if CHSFCT = SOIL
The external contact radius R_EXTCNT
must be positive for the segments
that have consolidated risersoil seafloor contact.
Seafloor soil properties
W A1 A2 V G

W: real > 0
: Soil submerged weight \(\mathrm {[F/L^3]}\) 
A1: real > 0
: Soil shear strength at seabed \(\mathrm {[F/L^2]}\) 
A2: real
: Soil shear strength vertical gradient \(\mathrm {[F/L^3]}\) 
V: real > 0
: Soil Poisson ratio \(\mathrm {[1]}\) 
G: real
: Soil Gmodulus/compressive strength \(\mathrm {[F/L^2]}\)
Consolidated risersoil seafloor contact options
F ALPHA BETA KBC KT

F: real, default: 0.88
: Relationship between dynamic stiffness and Gmodulus \(\mathrm {[1]}\) 
ALPHA: real, default: 1.0
: Control parameter for suction release displacement \(\mathrm {[1]}\) 
BETA: real, default: 1.0
: Scaling factor for peak soil suction relative to peak soil compression \(\mathrm {[1]}\) 
KBC: real, default: 0.05
: Mobilization displacement for soil bearing capacity as fraction of pipe soil contact width \(\mathrm {[1]}\) 
KT: real, default: 0.08
: Mobilization displacement for max soil suction as fraction of pipe soil contact width \(\mathrm {[1]}\)
Inplane contact parameters, two input lines
STFAXI FRIAXI DAMAXI

STFAXI: real >= 0, default: 0
: Inplane seafloor stiffness for friction in axial direction \([\mathrm {F/L^2}]\) 
FRIAXI: real >= 0, default: 0
: Inplane seafloor friction coefficient in axial direction [1] 
DAMAXI: real >= 0, default: 0
: Inplane seafloor damping coefficient in axial direction \([\mathrm {F\times T/L^2}]\)
STFLAT FRILAT DAMLAT

STFLAT: real >= 0, default: 0
: Inplane seafloor stiffness for friction in lateral direction \([\mathrm {F/L^2}]\) 
FRILAT: real >= 0, default: 0
: Inplane seafloor friction coefficient in lateral direction [1] 
DAMLAT: real >= 0, default: 0
: Inplane seafloor damping coefficient in lateral direction \([\mathrm {F\times T/L^2}]\)
Contact in the seafloor plane is modelled independently in the axial and lateral directions. Contact is initially modelled with linear springs. Sliding will occur when an axial or lateral spring force reaches the friction force value. Springs will be reinstated if the line starts sliding in the opposite direction, or if the friction force increases and is greater than the spring force. The spring stiffness is calculated as \(k_h=\mathrm {Stalks}\times L_h\), where \(\mathrm {L_h}\) is the length of the element’s horizontal projection. The seafloor friction forces are calculated as \(F=\mathrm {FRIxxx}\times F_{vert}\) and are directed against the axial or lateral displacements, where \(\mathrm {F_{vert}}\) is the vertical contact force between the pipe and the bottom.
1.17. Drag chain element
The drag chain element is a single node element that models a simplified contact between a drag chain and the seafloor.
1.17.2. Component type identifier, one input line
CMPTYPID

CMPTYPID: character(8)
: Component type identifier
1.17.3. Drag chain element properties, one input line
LDC WDC FRDC LCAB WCAB

LDC: real
: Drag chain length \(\mathrm {[L]}\) 
WDC: real
: Drag chain weight \(\mathrm {[F/L]}\) 
FRDC: real
: Chain / seafloor friction coefficient \(\mathrm {[1]}\) 
LCAB: real, default: 0
: Cable length \(\mathrm {[L]}\) 
WCAB: real, default: 0
: Cable weight \(\mathrm {[F/L]}\)
1.18. Fibre rope cross section
1.18.2. Component type identifier
CMPTYPID TEMP ALPHA BETA

CMPTYPID: character(8)
: Component type identifier 
TEMP: real, default: 0
: Temperature at which the specification applies \(\mathrm {[Temp]}\) 
ALPHA: real, default: 0
: Thermal expansion coefficient \(\mathrm {[Temp^{1}]}\) 
BETA: real, default: 0
: Pressure expansion coefficient \(\mathrm {[1/(F/L^2)]}\)
BETA
gives the expansion of an element with zero effective tension from the difference between the internal and the external pressure.

1.18.3. Mass and volume
AMS AE R_EXTCNT

AMS: real
: Mass/unit length \(\mathrm {[M/L]}\) 
AE: real
: External crosssectional area \(\mathrm {[L^2]}\) 
R_EXTCNT: real, default: 0
: External contact radius \(\mathrm {[L]}\)
The outer contact radius of the cross section, R_EXTCNT
, is used for
seafloor contact. The default value of R_EXTCNT
is zero.
1.18.4. Stiffness properties classification
NOC NOWC NWC TMAX

NOC: integer, default: 0
: Original curve, number of point pairs 
NOWC: integer, default: 0
: Original working curve, number of point pairs 
NWC: integer, default: 0
: Working curve, number of point pairs 
TMAX: real, default: 0
: Maximum mean tension \(\mathrm {[F]}\)
The nonlinear material curve used in static analysis is given by
shifting the working curve by redefining the initial stressfree length
so that the working and original working curves intersect at tension
TMAX
. See figure Tension strain curves.
1.18.5. Axial stiffness curves
EAF(1) ELONG(1) . . . EAF(N) ELONG(N)

EAF(1): real
: Tension corresponding to strainELONG(1)
\(\mathrm {[F]}\) 
ELONG(1): real
: Strain (relative elongation) \(\mathrm {[]}\)
The pairs of EAF
and ELONG
must be given in increasing order on a
single input line. Three sets of pairs must be given, for the working
curve, original working curve and original curve, respectively. Each
curve must begin with the point pair (0.0, 0.0). For the three curves,
N
= NOC
, N
= NOWC
and N
= NWC
, respectively.
1.18.6. Dynamic stiffness coefficients
DSCA DSCB

DSCA: real, default: 1.0
: Dynamic stiffness coefficient a 
DSCB: real, default: 0.0
: Dynamic stiffness coefficient b
The linear material curve used in dynamic analysis is given by
\(\mathrm {DSCA+DSCB\cdot TMEAN}\), where TMEAN
is the mean
tension of the segment, and by redefining the initial stressfree length
such that the tension is identical between static and dynamic analysis
given the elongation of static analysis. See figure
Tension strain curves.
1.18.7. Damping specification
Identical to Damping specification
1.18.8. Hydrodynamic force coefficients
Similar to Hydrodynamic force coefficients, but only Morison type loading is available.
1.18.9. Capacity parameter
Identical to Capacity parameter
1.19. Growth  Specification of marine growth profile
1.19.2. Component type identifier, one input line
CMPTYPID NGRLEV

CMPTYPID: character(8)
: Component type identifier 
NGRLEV : integer
: Number of growth levels
1.19.3. Growth profile, one input line per growth level, i.e. NGRLEV input lines
GRLEV GRTH GRDENS

GRLEV: real
: Z coordinate of level given in global coordinate system \(\mathrm {[L]}\) 
GRTH: real
: Growth thickness \(\mathrm {[L]}\) 
GRDENS: real
: Growth density at this level \([\mathrm {M/L^3}]\)
The input lines must be given for decreasing values of GRLEV
;
i.e. with increasing depth. Linear interpolation will be used to find
values at intermediate levels. Outside the specified range, the growth
thickness is set to zero, i.e. for Z > GRLEV(1)
and
Z < GRLEV(NGRLEV)
the thickness is zero.
Marine growth will be applied to elements with CRS0
, CRS1
, CRS2
and CRS7
crosssections.
The volume loads will be modified if the external area is nonzero. A circular crosssection is assumed and the thickness of the marine growth is added to the radius corresponding to the initial external area.
The Morison quadratic drag and added mass coefficients will be modified
if the hydrodynamic diameter is nonzero. For CRS2
and CRS7
crosssections, the diameter of a circular crosssections with the same
external area is used as the hydrodynamic diameter.
The added mass coefficients will be scaled by the square of this ratio.
The quadratic drag coefficients will be scaled by the ratio of the updated to the initial hydrodynamic diameter. Linear drag coefficients will not be modified.
The correction of mass, hydrodynamic diameter, added mass and drag coefficients:

Mass per length
AMS
including marine growth
\(\mathrm {AMS_{growth}=AMS(AE_{growth}AE){\cdot}GRDENS}\)


Hydrodynamic diameter including marine growth

\(\mathrm {DH_{growth}=DH+2\cdot GRTH}\)


Added mass coefficients

\(\mathrm {CAX\cdot(\frac{DH_{growth}}{DH})^2}\)

\(\mathrm {CAY\cdot(\frac{DH_{growth}}{DH})^2}\)

\(\mathrm {CAZ\cdot(\frac{DH_{growth}}{DH})^2}\)


Quadratic drag coefficients
CDX
,CDY
andCDZ

\(\mathrm {CDX\cdot(\frac{DH_{growth}}{DH})}\)

\(\mathrm {CDY\cdot(\frac{DH_{growth}}{DH})}\)

\(\mathrm {CDZ\cdot(\frac{DH_{growth}}{DH})}\)

Marine growth will be applied if it is specified as a load group in
STAMOD
. The load incrementation procedure is specified as input to the
STAMOD
module.
Currently, only one growth profile may be given. 
Specification of marine growth profile cannot be used in combination with drag amplification. 