1. CRS2 - Double symmetric cross section

1.1. Data group identifier

NEW COMPonent CRS2

1.2. Component type identifier

CMPTYP-ID TEMP
  • CMPTYP-ID: character(8): Component type identifier

  • TEMP: real: Temperature at which the specification applies

    • Dummy in present version

um ii fig89
Figure 1. Cross section with 2 symmetry planes

1.3. Mass and volume

AMS AE AI RGYR
  • AMS: real: Mass per unit length \(\mathrm {[M/L]}\)

  • AE: real: External cross-sectional area \(\mathrm {[L^2]}\)

  • AI: real: Internal cross-sectional area \(\mathrm {[L^2]}\)

  • RGYR: real: Radius of gyration about local x-axis \(\mathrm {[L]}\)

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 X-axis, i.e. at the origin of the local Y- and Z-axes.

1.4. Stiffness properties classification

IEA IEJ IGT IPRESS
  • IEA: integer, default: 0: Axial stiffness code

    • 1 - constant stiffness

    • N - table with N pairs of tension-elongation 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- non-symmetric ``constant'' stiffness

    • N - symmetric, N (positive) pairs specified

    • -N- general torsion/relation (non-symmetric) 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.

1.5. Bending-torsion geometric coupling specification

This data group is optional, and will only be applied for IEJ=1 and IGT=1.

BTGC
  • BTGC: character(4): bending-torsion coupling identifier.

If the BTGC identifier is present, geometric coupling between torsion and bending is accounted for.

1.6. Axial stiffness. Case 1 IEA=1

EA
  • EA: real > 0: Axial stiffness \(\mathrm {[F]}\)

1.7. Axial stiffness. Case 2 IEA=N

EAF(1) ELONG(1) . . . EAF(N) ELONG(N)
  • EAF(1): real: Axial force corresponding to relative elongation ELONG(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.

1.8. 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:

1.9. Bending stiffness. Case 1, IEJ=1 IPRESS=0

EJY EJZ GAsZ GAsY
  • EJY: real > 0: Bending stiffness around local y-axis \(\mathrm {[FL^2]}\)

  • EJZ: real > 0: Bending stiffness around z-axis \(\mathrm {[FL^2]}\)

  • GAsZ: real: Shear stiffness in Z-direction \(\mathrm {[F]}\)

  • GAsY: real: Shear stiffness in Y-direction \(\mathrm {[F]}\)

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 X-axis, i.e. at the origin of the local Y- and Z-axes.

1.10. 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 y-axis \(\mathrm {[FL^2]}\)

  • EJZ(1): real: Bending stiffness around local z-axis \(\mathrm {[FL^2]}\)

  • 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)

um ii fig93
Figure 2. Bending stiffness around y-axis as function of pressure.

Values at other pressure levels than PRESS(1) and PRESS(2) are obtained by linear interpolation/ extrapolation.

1.11. 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, y-axis
BMOMY(1) . . . BMOMY(N)
  • BMOMY(1): real: Bending moment around local y-axis \(\mathrm {[FL]}\)

  • .

  • .

  • .

  • BMOMY(N): real

Bending moment, z-axis
BMOMZ(1) . . . BMOMZ(N)
  • BMOMZ(1): real: Bending moment around local z-axis \(\mathrm {[FL]}\)

  • .

  • .

  • .

  • BMOMZ(N): real

CURV(1), BMOMY(1) and BMOMZ(1) have to be zero. See also the figure Bending moment around y-axis as function of curvature.

1.12. 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 y-axis 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:

Bending moment, y-axis
BMOMY(1,1) . . . BMOMY(N1,N2)
  • BMOMY(I,J): real: Bending moment about local y-axis at curvature I and pressure J \(\mathrm {[FL]}\).

  • .

  • .

  • .

  • BMOMY(N1,N2):real:

BMOMY(1,J), J=1, N2 have to be zero.

Bending moment, z-axis
BMOMZ(1,1) . . . BMOMZ(N1,N2)
  • BMOMZ(I,J): real: Bending moment about local Z-axis at curvature I and pressure J \(\mathrm {[FL]}\).

  • .

  • .

  • .

  • BMOMZ(N1,N2):real:

BMOMZ(1,J), J=1, N2 have to be zero.

1.13. Torsion stiffness

Constant torsion stiffness. Case 1 |IGT|=1
GT- GT+
  • GT-: real > 0: Torsion stiffness (negative twist) \(\mathrm {[FL^2/Radian]}\)

  • GT+: real: D.o. for positive twist. Dummy for IGT=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 \(\mathrm {[Radian/L]}\)

If IGT is positive TMOM(1) and TROT(1) have to be zero. TROT must be given in increasing order.

1.14. Damping specification

Identical to input for cross-section type CRS1, see data group Damping specification.

1.15. Hydrodynamic load type identification, One input line

CHLOAD
  • CHLOAD: character: = HYDR - Text to identify hydrodynamic load type

Note: Required if non-Morison 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: As MORI, but improved by taking into account partially submerged cross-section

    • = MACF: Load based on MacCamy-Fuchs 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 cross-section is reduced in proportional with the instantaneous wet portion of the cross-section.

  • the Froude-Krylov 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 x-direction \(\mathrm {[F/((L/T)^2\times L)]}\)

  • CDY: real: Drag force coefficient for local y-direction \(\mathrm {[F/((L/T)^2\times L)]}\)

  • CDZ: real: Drag force coefficient for local z-direction \(\mathrm {[F/((L/T)^2\times L)]}\)

  • CDTMOM: real: Drag force coefficient for local x-rotation. Not used in present version.

  • AMX: real: Added mass per length in x-direction \(\mathrm {[M/L]}\)

  • AMY: real: Added mass per length in y-direction \(\mathrm {[M/L]}\)

  • AMZ: real: Added mass per length in z-direction \(\mathrm {[M/L]}\)

  • AMTOR: real: Added mass for local x-rotation \(\mathrm {[ML^2/L]}\) Not used in present version.

  • CDLX: real, default: 0: Linear drag force coefficients in local x-direction \(\mathrm {[F/((L/T)\times L)]}\)

  • CDLY: real, default: 0: Linear drag force coefficients in local y-direction \(\mathrm {[F/((L/T)\times L)]}\)

  • CDLZ: real, default: 0: Linear drag force coefficients in local z-direction \(\mathrm {[F/((L/T)\times L)]}\)

  • SCFKN: real, default: 1: Scaling factor for the Froude-Krylov term in Morison’s equation in normal direction

  • SCFKT: real, default: 1: Scaling factor for the Froude-Krylov 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 z-directions

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

  • \(\mathrm {VRELX,VRELY,VRELZ}\): are relative water velocities in local x, y and z-directions

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 z-direction, respectively

  • \(\mathrm {C_{dx},C_{dy},C_{dz}}\): nondimensional drag coefficients in local x, y and z-directions, 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 z-directions, respectively

Hydrodynamic force coefficients if CHTYPE=MACF

MacCamy-Fuchs frequency-dependent hydrodynamic loads on a stationary vertical circular cylinder will be applied for CHTYPE=MACF. MacCamy-Fuchs forces are pre-computed based on the element position after static calculation. MacCamy-Fuchs forces are only available for irregular time domain analysis.

Quadratic drag may also be applied on elements with MacCamy-Fuchs loading. McCamy Fuchs assumes that the cross-section 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 cross-sectional area given as input in data section Mass and volume

Hydrodynamic force coefficients if CHTYPE=POTN

Frequency-dependent 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 cross-sections with potential flow loading.

CQX CQY CQZ ICODE D SCFKT
  • CQX: real: Quadratic drag coefficient in local x-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 local y-direction

    • 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 z-direction

    • 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 cross-sectional area given as input in data section Mass and volume

  • SCFKT: real, default: 1: Scaling factor for the Froude-Krylov term in Morison’s equation in tangential direction. Only the values 0.0 and 1.0 are permitted.

1.16. Aerodynamic load type identification, One optional input line

CHLOAD
  • CHLOAD: character: = WIND - Text to identify wind coefficients

1.17. Load type identification, One optional input line

CHTYPE
  • CHTYPE: character: Type of wind load coefficients

    • = MORI: Morison-like 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: Morison-like aerodynamic drag, One input line
CDXAERO CDYAERO CDZAERO
  • CDXAERO: real: Dimensional quadratic drag coefficient for local x-direction \(\mathrm {[F/((L/T)^2\times L)]}\)

  • CDYAERO: real: Dimensional quadratic drag coefficient for local y-direction \(\mathrm {[F/((L/T)^2\times L)]}\)

  • CDZAERO: real: Dimensional quadratic drag coefficient for local z-direction \(\mathrm {[F/((L/T)^2\times L)]}\)

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 z-directions

  • \(\mathrm {VRELX,VRELY,VRELZ}\): are relative wind velocities in local x, y and z-directions

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 z-direction, respectively

  • \(\mathrm {C_{dx},C_{dy},C_{dz}}\): nondimensional drag coefficients in local x, y and z-directions, 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: Y-coordinate of foil origin \(\mathrm {[L]}\)

  • ZFC: real, default: 0: Z-coordinate 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.

riflex um foil
Figure 3. 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.

1.18. Capacity parameter

TB YCURMX ZCURMX
  • TB: real: Tension capacity \(\mathrm {[F]}\)

  • YCYRMX: real: Maximum curvature around local y-axis \(\mathrm {[1/L]}\)

  • ZCURMX: real: Maximum curvature around local z-axis \(\mathrm {[1/L]}\)

These parameters are dummy in the present version

2. CRS7 - General cross section

2.1. Data group identifier

NEW COMPonent CRS7

2.2. Component type identifier

CMPTYP-ID TEMP ALFA
  • CMPTYP-ID: 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

CRS7 allecc
Figure 4. General cross-section

2.3. 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 \(\mathrm {(Y_m,Z_m)}\) \(\mathrm {[L]}\)

2.4. Buoyancy

YECC_BUOY ZECC_BUOY
  • YECC_BUOY: real: Buoyancy center Y-coordinate in beam element system \(\mathrm {[L]}\)

    • Dummy in present version. Bouyancy center set equal to mass center.

  • ZECC_BUOY: real: Buoyancy center Z-coordinate in beam element system \(\mathrm {[L]}\)

    • Dummy in present version. Bouyancy center set equal to mass center.

AE AI
  • AE: real: External cross-sectional area \(\mathrm {[L^2]}\)

    • Basis for calculation of buoyancy

  • AI: real: Internal cross-sectional area \(\mathrm {[L^2]}\)

    • Dummy in present version

2.5. Stiffness properties

Only constant stiffness properties are allowed.

2.6. Area center and principal axes

The area center is the cross-section 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 cross-section area. The orientation of the principal axes is defined in terms of a positive X-rotation \(\mathrm {\theta }\) relative to the beam element YZ-coordinate system as shown in the figure General cross-section

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 cross-section.

2.7. 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 \(\mathrm {[L]}\)

2.8. Axial stiffness

EA
  • EA: real > 0: Axial stiffness \(\mathrm {[F]}\)

2.9. Bending stiffness

The bending stiffness refers to the principal axes V and W, see figure General cross-section.

EJV EJW
  • EJV: real > 0: Bending stiffness about principal V-axis \(\mathrm {[FL^2]}\)

  • EJW: real > 0: Bending stiffness about principal W-axis \(\mathrm {[FL^2]}\)

2.10. Shear stiffness

The shear stiffness refers to the principal axes V and W, see figure General cross-section.

GAsW GAsV
  • GAsW: real: Shear stiffness in principal W-direction \(\mathrm {[F]}\)

  • GAsV: real: Shear stiffness in principal V-direction \(\mathrm {[F]}\)

The shear stiffness, GAsW and GAsV, are optional input parameters.

Specified GAsW>0 and GAsV>0 will include shear deformation.

2.11. Torsion stiffness

GT
  • GT: real > 0: Torsion stiffness \(\mathrm {[FL^2/Radian]}\)

For a circular cross-section the torsion stiffness is given by the polar moment of inertia. Note that this is not the case for non-circular cross-sections.

2.12. Bending-torsion geometric coupling

This data group is optional.

BTGC
  • BTGC: character(4): bending-torsion coupling identifier.

If the BTGC identifier is present, geometric coupling between torsion and bending is accounted for.

2.13. Damping specification

Identical to input for cross-section 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.

2.14. Hydrodynamic load type identification, One input line

CHLOAD
  • CHLOAD: character: = HYDR - Text to identify hydrodynamic coefficients

Note: Required if non-Morison 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 x-direction \(\mathrm {[F/((L/T)^2\times L)]}\)

  • CDY: real: Drag force coefficient for local y-direction \(\mathrm {[F/((L/T)^2\times L)]}\)

  • CDZ: real: Drag force coefficient for local z-direction \(\mathrm {[F/((L/T)^2\times L)]}\)

  • CDTMOM: real: Drag force coefficient for local x-rotation. Not used in present version.

  • AMX: real: Added mass per length in x-direction \(\mathrm {[M/L]}\)

  • AMY: real: Added mass per length in y-direction \(\mathrm {[M/L]}\)

  • AMZ: real: Added mass per length in z-direction \(\mathrm {[M/L]}\)

  • AMTOR: real: Added mass for local x-rotation \(\mathrm {[ML^2/L]}\)

  • CDLX: real, default: 0: Linear drag force coefficients in local x-direction \(\mathrm {[F/((L/T)\times L)]}\)

  • CDLY: real, default: 0: Linear drag force coefficients in local y-direction \(\mathrm {[F/((L/T)\times L)]}\)

  • CDLZ: real, default: 0: Linear drag force coefficients in local z-direction \(\mathrm {[F/((L/T)\times L)]}\)

  • SCFKN: real, default: 1: Scaling factor for the Froude-Krylov term in Morison’s equation in normal direction

  • SCFKT: real, default: 1: Scaling factor for the Froude-Krylov 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 z-directions

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

  • \(\mathrm {VRELX,VRELY,VRELZ}\): are relative water velocities in local x, y and z-directions

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 z-direction, respectively

  • \(\mathrm {C_{dx},C_{dy},C_{dz}}\): nondimensional drag coefficients in local x, y and z-directions, 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 z-directions, respectively

2.15. Aerodynamic load type identification, One optional input line

CHLOAD
  • CHLOAD: character: = WIND - Text to identify wind coefficients

2.16. Load type identification, One optional input line

CHTYPE
  • CHTYPE: character: Type of wind load coefficients

    • = MORI: Morison-like 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: Morison-like aerodynamic drag, One input line
CDXAERO CDYAERO CDZAERO
  • CDXAERO: real: Dimensional quadratic drag coefficient for local x-direction \(\mathrm {[F/((L/T)^2\times L)]}\)

  • CDYAERO: real: Dimensional quadratic drag coefficient for local y-direction \(\mathrm {[F/((L/T)^2\times L)]}\)

  • CDZAERO: real: Dimensional quadratic drag coefficient for local z-direction \(\mathrm {[F/((L/T)^2\times L)]}\)

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 z-directions

  • \(\mathrm {VRELX,VRELY,VRELZ}\): are relative wind velocities in local x, y and z-directions

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 z-direction, respectively

  • \(\mathrm {C_{dx},C_{dy},C_{dz}}\): nondimensional drag coefficients in local x, y and z-directions, 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: Y-coordinate of foil origin \(\mathrm {[L]}\)

  • ZFC: real, default: 0: Z-coordinate 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.

2.17. Capacity parameter

TB YCURMX ZCURMX
  • TB: real: Tension capacity \(\mathrm {[F]}\)

  • YCYRMX: real: Maximum curvature around local y-axis \(\mathrm {[1/L]}\)

  • ZCURMX: real: Maximum curvature around local z-axis \(\mathrm {[1/L]}\)

These parameters are dummy in the present version

3. CRS8 - Axisymmetric cross section with axial/torsion strain model and hysteresis effects in bending/cuvature relation

3.1. Data group identifier

NEW COMPonent CRS8

3.2. Component type identifier

Identical to input for cross-section type CRS1 , see Component type identifier for CRS1.

3.3. Mass and volume

Identical to input for cross-section type CRS1 , see Mass and volume for CRS1.

3.4. Stiffness properties classification

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

    • 1 - constant stiffness

    • N - table with N >= 3 pairs of tension-elongation and moment-rotation to be specified

3.5. Axial stiffness. Case 1, IEAIGT=1

EA
  • EA: real > 0: Axial stiffness \(\mathrm {[F]}\)

3.6. Axial stiffness. Case 2, IEAIGT=N

EAF(1) ELONG(1) . . . EAF(N) ELONG(N)
  • EAF(1): real: Axial force corresponding to relative elongation ELONG(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.

um ii fig70
Figure 5. Axial force corresponding to relative elongation

3.7. Bending stiffness properties

3.8. 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.

um ii fig71
Figure 6. Internal friction moment description

3.9. 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(N-1) TROT(N-1) BETA(N-1) 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(N-1): real

  • TROT(N-1): real:

  • BETA(N-1): 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.

3.10. Damping specification

Identical to input for cross-section type CRS1 , see Damping specification for CRS1.

3.11. Hydrodynamic load types

Identical to input for cross-section type CRS1, see Hydrodynamic load type identification for CRS1.

3.12. Aerodynamic force coefficients

Identical to input for cross-section type CRS1, see Aerodynamic load type identification for CRS1.

3.13. Capacity parameter

Identical to input for cross-section type CRS1, see Capacity parameter for CRS1.

4. BODY - Description of attached bodies

4.1. Data group identifier

NEW COMPonent BODY

4.2. Component type identifier

CMPTYP-ID
  • CMPTYP-ID: 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.

4.3. Mass and volume

AM AE
  • AM: real: Mass \(\mathrm {[M]}\)

  • AE: real: Displacement volume \(\mathrm {[L^3]}\)

4.4. 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 X-direction \(\mathrm {[F/(L/T)^2)]}\)

  • CDY: real: Drag force coefficient in Y-direction \(\mathrm {[F/(L/T)^2)]}\)

  • CDZ: real: Drag force coefficient in Z-direction \(\mathrm {[F/(L/T)^2)]}\)

  • AMX: real: Added mass in X-direction \(\mathrm {[M]}\)

  • AMY: real: Added mass in Y-direction \(\mathrm {[M]}\)

  • AMZ: real: Added mass in Z-direction \(\mathrm {[M]}\)

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 z-directions, respectively

  • \(\mathrm {VRELX,VRELY,VRELZ}\): are relative water velocities in global/local x, y and z-directions 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 z-direction

  • \(\mathrm {C_{dx},C_{dy},C_{dz}}\): nondimensional drag coefficients in global/local x, y and z-directions

5. 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.

5.1. Data group identifier

NEW COMPonent CONB

5.2. Component type identifier

CMPTYP-ID
  • CMPTYP-ID: character(8): Component type identifier

5.3. Mass and volume

AM AE
  • AM: real: Mass \(\mathrm {[M]}\)

  • AE: real: Displacement volume \(\mathrm {[L^3]}\)

5.4. 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 X-direction \(\mathrm {[F/(L/T)^2)]}\)

  • CDY: real: Drag force coefficient in Y-direction \(\mathrm {[F/(L/T)^2)]}\)

  • CDZ: real: Drag force coefficient in Z-direction \(\mathrm {[F/(L/T)^2)]}\)

  • AMX: real: Added mass in X-direction \(\mathrm {[M]}\)

  • AMY: real: Added mass in Y-direction \(\mathrm {[M]}\)

  • AMZ: real: Added mass in Z-direction \(\mathrm {[M]}\)

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 z-directions, respectively

  • \(\mathrm {VRELX,VRELY,VRELZ}\): are relative water velocities in global/local x, y and z-directions 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 z-directions, respectively

  • \(\mathrm {C_{dx},C_{dy},C_{dz}}\): nondimensional drag coefficients in global/local x, y and z-directions, respectively

5.5. Degrees of freedom

IRX IRY IRZ
  • IRX: integer, default: 0: Rotation freedom code, x-axis

  • IRY: integer, default: 0: Rotation freedom code, y-axis

  • IRZ: integer, default: 0: Rotation freedom code, z-axis

    • 1 - Fixed (no deformation)

    • 0 - Free (zero moment)

x-, y- and z-axes refer to local coordinate system of the neighbour element in the line where the ball joint is specified.

um ii fig114
Figure 7. Rotation freedom for a ball joint component

6. FLEX - Description of flex-joint 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, flex-joint connectors may only be used for nonlinear static and dynamic analysis.

6.1. Data group identifier

NEW COMPonent FLEX

6.2. Component type identifier

CMPTYP-ID
  • CMPTYP-ID: character(8): Component type identifier

6.3. 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 x-axis \(\mathrm {[L]}\)

  • RGY: real, default: 0: Radius of gyration around local y-axis \(\mathrm {[L]}\)

  • RGZ: real, default: 0: Radius of gyration around local z-axis \(\mathrm {[L]}\)

  • CRX: real, default: 0: Damping coeff. Rotational velocity around local x-axis \(\mathrm {[FLT/deg]}\)

  • CRY: real, default: 0: Damping coeff. Rotational velocity around local y-axis \(\mathrm {[FLT/deg]}\)

  • CRZ: real, default: 0: Damping coeff. Rotational velocity around local z-axis \(\mathrm {[FLT/deg]}\)

6.4. Hydrodynamic coefficients

CDX CDY CDZ AMX AMY AMZ AMXROT AMYROT AMZROT
  • CDX: real, default: 0: Drag coeff. in local x-direction \(\mathrm {[F/(L/T)^2)]}\)

  • CDY: real, default: 0: Drag coeff. in local y-direction \(\mathrm {[F/(L/T)^2)]}\)

  • CDZ: real, default: 0: Drag coeff. in local z-direction \(\mathrm {[F/(L/T)^2)]}\)

  • AMX: real, default: 0: Added mass in local x-direction \(\mathrm {[M]}\)

  • AMY: real, default: 0: Added mass in local y-direction \(\mathrm {[M]}\)

  • AMZ: real, default: 0: Added mass in local z-direction \(\mathrm {[M]}\)

  • AMXROT: real, default: 0: Added mass rotation around local x-direction \(\mathrm {[FL\times T^2]}\)

  • AMYROT: real, default: 0: Added mass rotation around local y-direction \(\mathrm {[FL\times T^2]}\)

  • AMZROT: real, default: 0: Added mass rotation around local z-direction \(\mathrm {[FL\times T^2]}\)

The tangential drag force, the force acting in local x-axis, is computed by:

\(\mathrm {FX=CDX\times VRELX\times |VRELX|}\)

The drag force acting normal to the local x-direction, is assumed to act in the same direction as the relative velocity transverse component and are computed according to:

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

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

6.5. Stiffness properties classification

IDOF IBOUND RAYDMP
  • IDOF: character(4): Degree of freedom

    • IDOF = IRX: Rotation around local x-axis

    • IDOF = IRY: Rotation around local y-axis

    • IDOF = IRZ: Rotation around local z-axis

    • 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 with IDOF = IRYZ

    • IBOUND = 1: Constant stiffness

    • IBOUND > 1: Table with IBOUND 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 z-axes 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.

6.6. 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.

7. FLUID - Specification of internal fluid flow

7.1. Data group identifier

NEW COMPonent FLUId

7.2. Component type number

CMPTYP-ID
  • CMPTYP-ID: character(8): Component type identifier

7.3. 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)

8. 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.

8.1. Data group identifier

NEW COMPonent EXT1

8.2. Component type identifier

CMPTYP-ID
  • CMPTYP-ID: character(8): Component type identifier

8.3. 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 x-axis \(\mathrm {[L]}\)

  • 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

um ii fig121
Figure 8. Description of external wrapping

8.4. 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 x-direction 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 x-axis 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 z-directions

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

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

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

  • \(\mathrm {VRELX,VRELY,VRELZ}\): are relative water velocities in local x, y and z-directions

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