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: CMPTYP-ID. 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: CRS0: Thin-walled pipe cross section CRS1: Axisymmetric cross section CRS2: Double symmetric cross section BODY: Body attached at one point. Mass point CONB: Connector. Ball-joint type FLEX: Flex joint (supressed translations) FLUID: Internal fluid flow EXT1: External wrapping, rotation symmetry CRS5: Partly submerged general shaped cross section CONT: Contact point specification of roller type TENS: Contact point specification of tensioner type TUBU: Tubular contact point specification 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 - Thin-walled pipe cross section This cross-section allows for simplified input of circular, homogenous cross-sections. The input format is convenient for metallic pipe cross sections. A thin-walled 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 1.1.1. Data group identifier NEW COMPonent CRS0 1.1.2. Component type identifier CMPTYP-ID TEMP ALPHA BETA CMPTYP-ID: 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 Thin-walled pipe cross section_cross (below) as: \(\mathrm {\frac{DIAST(1-2\nu)}{4THST\times EMOD}}\) where \(\mathrm {\nu=\frac{EMOD}{2GMOD}}-1\) Axis symmetric pipe cross section image::um_ii_fig56.svg [title="Axis symmetric pipe cross section",width=456] 1.1.3. Cross-section 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 * pipe-in-pipe 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: elastic-plastic MATKIND = 3: strain-stress 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 strain-stress curve for plastic region \(\mathrm {[F/L^2]}\). EMODY < EMOD MATKIND = 3: Number of user specified strain-stress 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: \(\mathrm {GMOD\frac{\pi (D_e^2-D_i^2)}{4}0.5}\) For MATKIND = 3: NPAIR input lines of the strain-stress curve must be given Section 1.1_strain. Strain-stress curve (NPAIR input lines to be specified for MATKIND=3) EPS(I) SIG(I) EPS(i): real: Strain for point i on strain-stress curve \(\mathrm {[1]}\) SIG(i): real: Stress for point i on strain-stress curve \(\mathrm {[F/L^2]}\) The first point in the stress-strain 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. Bending-torsion 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): bending-torsion 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 cross-section 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 cross-section 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 cross-section type CRS1, see Aerodynamic load type identification. 1.1.9. Capacity parameter Identical to input for cross-section type CRS1, see Capacity parameter. :table-caption: 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 'cmptyp-id 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/L0-1=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 230E-3 1.0 1.0 'tb ycurmx 1600 0.1 1.2.1. Data group identifier NEW COMPonent CRS1 1.2.2. Component type identifier CMPTYP-ID TEMP ALPHA BETA CMPTYP-ID: 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. Figure 1. Axis symmetric cross section 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 cross-sectional area \(\mathrm {[L^2]}\) AI: real: Internal cross-sectional area \(\mathrm {[L^2]}\) RGYR: real: Radius of gyration about local x-axis \(\mathrm {[L]}\). Dummy for bar elements, i.e. IEJ = 0: zero bending stiffness. AST: real: Cross-section area for stress calculations \(\mathrm {[L^2]}\) The default value is calculated as seen below WST: real: Cross-section 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 cross-section is assumed: AST \(\mathrm {=AE-AI}\) WST \(\mathrm {=\pi (D_e^4-D_i^4)/(32D_e)}\) DST \(\mathrm {=D_e}\) THST \(\mathrm {=(D_e-D_i)/2}\) 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 pipe-in-pipe contact Tubular contact point specification 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 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 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 and IMF = 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. Bending-torsion 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): bending-torsion coupling identifier. If the BTGC identifier is present, geometric coupling between torsion and bending is accounted for. 1.2.6. Axial stiffness. Case 1, IEA=1 EA EA: real > 0: Axial stiffness \(\mathrm {[F]}\) 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 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. Figure 2. Axial force corresponding to relative elongation 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 IMF-values: 0, Data required: None. Case: 1a, IEJ: 1, IPRESS: 0, Allowed IMF-values: 0, Data required: EI, GAs. Case: 1b, IEJ: 1, IPRESS: 0, Allowed IMF-values: 1, Data required: EI, MF. Case: 2, IEJ: 1, IPRESS: 1, Allowed IMF-values: 0, Data required: Not implemented. Case: 3, IEJ: N, IPRESS: 0, Allowed IMF-values: 0, 1, Data required: CURV(I): I=1,N. BMOM(I): I=1,N. Case: 4, IEJ: N1, IPRESS: N2, Allowed IMF-values: 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. Figure 3. Internal friction moment description 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 Figure 4. 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. 1.2.12. 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, y-axis BMOMY(1) BMOMY(N) BMOMY(1): real: Bending moment around y-axis \(\mathrm {[FL]}\) 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). Figure 5. Bending moment around y-axis as function of curvature 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, y-axis 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). Figure 6. Bending moment around y-axis as function of curvature and pressure 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 if 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 \(\mathrm {[Radian/L]}\) . . . 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 text DAMP) 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 elongation ELONG(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 elongation ELONG(1) ELONG(1): real: Relative elongation ( ) FRCAXI(2): real, default: FRCAXI(1): Dynamic friction force corresponding to elongation ELONG(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 non-Morison 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: 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: 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 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. 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 cross-sectional 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 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. Definition of hydrodynamic force coefficients The tangential force which is a friction force per unit length acting in local x-axis, \(\mathrm {Ft}\) is computed by: \(\mathrm {Ft=CDX\times VRELX\times |VRELX|+CDLX\times VRELX}\) The drag force per unit length acting normal to the local x-axis, \(\mathrm {F_n}\), 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 y-directions (i.e. tangential and normal directions) \(\mathrm {CDLX,CDLY}\): are the dimensional linear drag force coefficients in local x- and y-directions \(\mathrm {VRELX,VRELY,VRELZ}\): are relative water velocities in local x,y and z-directions 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 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 cross-sections with MacCamy-Fuchs 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 cross-sectional 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 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 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 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. 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: Cross-flow VIV loads only = CFIL: Cross-flow and in-line VIV loads calculated independently. Restricted option = IL: In-line 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 Cross-flow 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) cross-flow load term (nondimensional) FNULL: real > 0: Natural cross-flow vortex shedding frequency (nondimensional) FMIN: real > 0: Minimum cross-flow vortex shedding frequency (nondimensional) FMAX: real > FMIN: Maximum cross-flow vortex shedding frequency (nondimensional) Independently calculated in-line 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) in-line load term (nondimensional) FNULIL: real > 0: Natural in-line vortex shedding frequency (nondimensional) FMINIL: real > 0: Minimum in-line vortex shedding frequency (nondimensional) FMAXIL: real > FMINIL: Maximum in-line vortex shedding frequency (nondimensional) The VIV parameters are nondimensional and independent of ICODE. VIV parameters for pure CF are shown in Table 1. Table 1. Suggested VIV empirical parameters used for CHTVIV=CF, i.e. Cross flow only. CQY and CAY are nondimensional drag force and added mass coefficients in normal direction. Flow conditions Structure type Parameters CV CQY CAY FNULL FMIN FMAX Constant current Bare riser section 1.3 1.0 1.0 0.13 0.10 0.26 Buoyancy section (Lb/Lr=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 (Lb /Lr=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 Lb/Lr is the ratio between the length of the buoyancy element and the bare riser section, see Figure 7. Figure 7. Ratio between the length of the buoyancy element and the bare riser section 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 X-axis 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: \(\mathrm {C_{D1}=\frac{1}{2}\rho \times (-0.04+SN-1.24SN^2+13.7SN^3)cos(\alpha)}\) Direction dependent lift force coefficient: \(\mathrm {C_l=\frac{1}{2}\rho \times (0.57SN-3.54SN^2+10.1SN^3)sin(2\alpha})\) 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 cross-sectional 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: Morison-like 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: non-dimensional 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: non-dimensional 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 cross-sectional 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 x-axis, \(\mathrm {F_t}\) is computed by: \(\mathrm {F_t=CDXa\times VRELX\times |VRELX|}\) The drag force per unit length acting normal to the local x-axis, \(\mathrm {F_n}\), 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 y-directions (i.e. tangential and normal directions) \(\mathrm {VRELX,VRELY,VRELZ}\): are relative wind velocities in local x,y and z-directions 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 1.2.18. Capacity parameter TB YCURMX TB: real: Tension capacity \(\mathrm {[F]}\) YCURMX: real: Maximum curvature \(\mathrm {[1/L]}\) These parameters are dummy in the present version 1.3. CRS2 - Double symmetric cross section 1.3.1. Data group identifier NEW COMPonent CRS2 1.3.2. 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 Figure 8. Cross section with 2 symmetry planes 1.3.3. 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. 1.3.4. Stiffness properties classification IEA IEJ IGT IPRESS IEA: integer, default: 0: Axial stiffness code 1 - constant stiffness N - table with N pairs of 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. 1.3.5. 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. 1.3.6. Axial stiffness. Case 1 IEA=1 EA EA: real > 0: Axial stiffness \(\mathrm {[F]}\) 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 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. 1.3.8. 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 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. 1.3.10. 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 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) Figure 9. 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. 1.3.11. 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, 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. 1.3.12. 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 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. 1.3.13. 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. 1.3.14. Damping specification Identical to input for cross-section 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 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. 1.3.16. 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: 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. Figure 10. 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. 1.3.18. 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 1.4. CRS7 - General cross section 1.4.1. Data group identifier NEW COMPonent CRS7 1.4.2. 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 Figure 11. General cross-section 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 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 1.4.5. Stiffness properties Only constant stiffness properties are allowed. 1.4.6. 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. 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 \(\mathrm {[L]}\) 1.4.8. Axial stiffness EA EA: real > 0: Axial stiffness \(\mathrm {[F]}\) 1.4.9. 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 \(\mathrm {[FL^2]}\) 1.4.10. 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. 1.4.11. 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. 1.4.12. 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. 1.4.13. 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. 1.4.14. 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 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: 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. 1.4.17. 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 1.5. CRS8 - Axisymmetric cross section with axial/torsion strain model and hysteresis effects in bending/cuvature relation 1.5.1. Data group identifier NEW COMPonent CRS8 1.5.2. Component type identifier Identical to input for cross-section type CRS1 , see Component type identifier for CRS1. 1.5.3. Mass and volume Identical to input for cross-section 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 tension-elongation and moment-rotation to be specified 1.5.5. Axial stiffness. Case 1, IEAIGT=1 EA EA: real > 0: Axial stiffness \(\mathrm {[F]}\) 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 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. Figure 12. Axial force corresponding to relative elongation 1.5.7. Bending stiffness properties 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. Figure 13. Internal friction moment description 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(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. 1.5.10. Damping specification Identical to input for cross-section type CRS1 , see Damping specification for CRS1. 1.5.11. Hydrodynamic load types Identical to input for cross-section type CRS1, see Hydrodynamic load type identification for CRS1. 1.5.12. Aerodynamic force coefficients Identical to input for cross-section type CRS1, see Aerodynamic load type identification for CRS1. 1.5.13. Capacity parameter Identical to input for cross-section type CRS1, see Capacity parameter for CRS1. 1.6. BODY - Description of attached bodies 1.6.1. Data group identifier NEW COMPonent BODY 1.6.2. 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. 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 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 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. 1.7.1. Data group identifier NEW COMPonent CONB 1.7.2. Component type identifier CMPTYP-ID CMPTYP-ID: character(8): Component type identifier 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 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 1.7.5. 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. Figure 14. Rotation freedom for a ball joint component 1.8. 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. 1.8.1. Data group identifier NEW COMPonent FLEX 1.8.2. Component type identifier CMPTYP-ID CMPTYP-ID: character(8): Component type identifier 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 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 \(\mathrm {[FLT/deg]}\) 1.8.4. 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: \(\mathrm {FY=CDY\times \sqrt{VRELY^2+VRELZ^2}\times VRELY}\) \(\mathrm {FZ=CDY\times \sqrt{VRELY^2+VRELZ^2}\times VRELZ}\) 1.8.5. 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. 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 1.9.1. Data group identifier NEW COMPonent FLUId 1.9.2. Component type number CMPTYP-ID CMPTYP-ID: character(8): Component type identifier 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. 1.10.1. Data group identifier NEW COMPonent EXT1 1.10.2. Component type identifier CMPTYP-ID CMPTYP-ID: character(8): Component type identifier 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 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 Figure 15. Description of external wrapping 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 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 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 z-axis approximately parallel the global z-axis 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. 1.11.1. Data group identifier NEW COMPonent CRS5 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 1.11.9. Bending stiffness description. Case 3 IEJ=N IPRESS=0 Identical to Bending stiffness description. Case 3 IEJ=N IPRESS=0 for CRS2 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 y-axis \(\mathrm {[F/((L/T)^2\times L)]}\) CDZ: real: Drag force coefficient per length, local z-axis \(\mathrm {[F/((L/T)^2\times L)]}\) CDTMOM: real: Drag coefficient around local x-axis 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 x-direction 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 x-direction - \(\mathrm {V_{y,rel}}\): is relative water velocity in local y-direction - \(\mathrm {V_{z,rel}}\): is relative water velocity in local z-direction 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 z-axis. 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 two-dimensional 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 y-coordinate for offset point INB ZB: real: Local z-coordinate for offset point INB Only one half of the cross section shape is modelled due to the assumed symmetry about local z-axis. The offset points must be given in increasing order with decreasing value of the z-coordinate. 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. Figure 16. Example of modelling cross sectional shapes of frame elements 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. Figure 17. Example of a pipe support consisting of four rollers. 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. 1.12.1. Data group identifier NEW COMPonent CONTact 1.12.2. Component type identifier CMPTYP-ID CMPTYP-ID: character(8): Component type identifier 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: Y-coordinate of roller origin \(\mathrm {[L]}\) ZR: real, default: 0: Z-coordinate 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. Figure 18. Spring stiffness, IKS = 1 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 compression ZS(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. Figure 19. Spring stiffness, IKS > 2 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. 1.13.1. Data group identifier, one input line NEW COMPonent TENSioner 1.13.2. Component type identifier CMPTYP-ID CMPTYP-ID: character(8): Component type identifier 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: TMAX-TMIN \(\mathrm {[L]}\) SIGNX: real, default: 1: Direction of applied load referring to local x-axis of the element going through the tensioner \(\mathrm {[]}\) SIGNX = 1.0: The load will act in local x-axis direction SIGNX = -1.0: The load will act opposite local x-axis The stiffness characteristics of the tensioner will be derived from DELTA as: STIFF = (TMAX-TMIN)/DELTA 1.14. Tubular contact component This component is available for elastic contact surface description only. 1.14.1. Data group identifier, one input line NEW COMponent TUBUlar contact 1.14.2. Component type number CMPTYP-ID CMPTYP-ID: character(8): Component type identifier 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 or OUTWARDS 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 coefficient FRICST, \(\mathrm {[F/L]}\). 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 if CHAXI = OFF. FRICST: real: Static friction coefficient \(\mathrm {[1]}\). Not used in static analysis. Dummy if CHAXI = OFF. FRICDY: real: Dynamic sliding friction coefficient \(\mathrm {[1]}\). FRICDY ⇐ FRICST. Not used in static analysis. Dummy if CHAXI = OFF. CHAXI: character: Control parameter for axial sliding friction = ON = OFF CHROT: character: Control parameter for friction caused by rotation = ON Requires CHAXI=ON = OFF VELLIM: real: Velocity limit for determining that sliding has stopped \(\mathrm {[L/T]}\). If the relative sliding velocity between the pipes falls below VELLIM, the spring stiffness STFFR is applied. Should be small, but not zero. Not used in static analysis. Dummy if CHAXI = 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. 1.14.4. Contact spring stiffness; IKS = 1 STIFF STIFF: real: Spring compression stiffness \(\mathrm {[F/L]}\) 1.14.5. Contact spring stiffness; IKS > 1 FS(1) ZS(1) ........ FS(N) ZS(N) FS(1): real < 0: Pressure force corresponding to compression ZS(1) \(\mathrm {[F]}\) ZS(1): Spring compression \(\mathrm {[L]}\) ZS(i) must be given in increasing order 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. 1.15.1. Data group identifier, one input line NEW COMPonent SOIL 1.15.2. Soil ID and type SOIL-ID SOILMET SOIL-ID: 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 cross-section rotation are modelled with force-displacement (p-v) and moment-rotation (m-t) curves. 1.15.3. Soil PISA curves, sand and clay Figure 20. Parametrized PISA curves 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. Figure 21. Parametrized PISA curve equation 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' non-dimensional 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 force-displacement (p-v) soil reaction curve. PVKC1 PVKC2 PVKC3 PVNC1 PVNC2 PVNC3 PVXC1 PVXC2 PVXC3 PVYC1 PVYC2 PVYC3 PVKC1, PVKC2, PVKC3: real: p-v curve parameter k (initial stiffness). PVNC1, PVNC2, PVNC3: real: p-v curve parameter n (0 ⇐ n ⇐ 1). PVXC1, PVXC2, PVXC3: real: p-v curve upper X-value. PVYC1, PVYC2, PVYC3: real: p-v curve upper Y-value. Coefficients used to define parameters for moment-rotation (m-t) soil reaction curve. MTKC1 MTKC2 MTKC3 MTNC1 MTNC2 MTNC3 MTXC1 MTXC2 MTXC3 MTYC1 MTYC2 MTYC3 MTKC1, MTKC2, MTKC3: real: m-t curve parameter k (initial stiffness). MTNC1, MTNC2, MTNC3: real: m-t curve parameter n (0 ⇐ n ⇐ 1). MTXC1, MTXC2, MTXC3: real: m-t curve upper X-value. MTYC1, MTYC2, MTYC3: real: m-t curve upper Y-value. 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 X-value. BSYC1, BSYC2, BSYC3: real: base shear load curve upper Y-value. 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 X-value. BMYC1, BMYC2, BMYC3: real: base moment curve upper Y-value. 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' non-dimensional 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 force-displacement (p-v) soil reaction curve. PVKC1 PVKC2 PVKC3 PVKC4 PVNC1 PVNC2 PVNC3 PVNC4 PVXC1 PVXC2 PVXC3 PVXC4 PVYC1 PVYC2 PVYC3 PVYC4 PVKC1, PVKC2, PVKC3, PVKC4: real: p-v curve parameter k (initial stiffness). PVNC1, PVNC2, PVNC3, PVNC4: real: p-v curve parameter n (0 ⇐ n ⇐ 1). PVXC1, PVXC2, PVXC3, PVXC4: real: p-v curve upper X-value. PVYC1, PVYC2, PVYC3, PVYC4: real: p-v curve upper Y-value. Coefficients used to define parameters for moment-rotation (m-t) soil reaction curve. MTKC1 MTKC2 MTKC3 MTKC4 MTNC1 MTNC2 MTNC3 MTNC4 MTXC1 MTXC2 MTXC3 MTXC4 MTYC1 MTYC2 MTYC3 MTYC4 MTKC1, MTKC2, MTKC3, MTKC4: real: m-t curve parameter k (initial stiffness). MTNC1, MTNC2, MTNC3, MTNC4: real: m-t curve parameter n (0 ⇐ n ⇐ 1). MTXC1, MTXC2, MTXC3, MTXC4: real: m-t curve upper X-value. MTYC1, MTYC2, MTYC3, MTYC4: real: m-t curve upper Y-value. 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 X-value. BSYC1, BSYC2, BSYC3, BSYC4: real: base shear load curve upper Y-value. 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 X-value. BMYC1, BMYC2, BMYC3, BMYC4: real: base moment curve upper Y-value. 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 p-v and m-t curves the ratio r is z/D, except for the Y-values 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 p-v curve (DMPPV >= 0.0). DMPMT: real, default: 0.0: Damping factor for m-t 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 cross-section 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. 1.16.1. Data group identifier, one input line NEW COMPonent SEAFloor contact 1.16.2. Component type identifier and type CMPTYP-ID CHSFCT CMPTYP-ID: 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 spring-friction contact in the seafloor plane. = SOIL: Consolidated riser-soil 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 in-plane contact parameters, two input lines STFAXI FRIAXI DAMAXI STFAXI: real >= 0, default: 0: In-plane seafloor stiffness for friction in axial direction \([\mathrm {F/L^2}]\) FRIAXI: real >= 0, default: 0: In-plane seafloor friction coefficient in axial direction [1] DAMAXI: real >= 0, default: 0: In-plane seafloor damping coefficient in axial direction \([\mathrm {F\times T/L^2}]\) STFLAT FRILAT DAMLAT ILTOR STFLAT: real >= 0, default: 0: In-plane seafloor stiffness for friction in lateral direction \([\mathrm {F/L^2}]\) FRILAT: real >= 0, default: 0: In-plane seafloor friction coefficient in lateral direction [1] DAMLAT: real >= 0, default: 0: In-plane 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 cross-section. 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 riser-soil 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 riser-soil 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 G-modulus/compressive strength \(\mathrm {[F/L^2]}\) Consolidated riser-soil seafloor contact options F ALPHA BETA KBC KT F: real, default: 0.88: Relationship between dynamic stiffness and G-modulus \(\mathrm {[1]}\) 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 \(\mathrm {[1]}\) In-plane contact parameters, two input lines STFAXI FRIAXI DAMAXI STFAXI: real >= 0, default: 0: In-plane seafloor stiffness for friction in axial direction \([\mathrm {F/L^2}]\) FRIAXI: real >= 0, default: 0: In-plane seafloor friction coefficient in axial direction [1] DAMAXI: real >= 0, default: 0: In-plane seafloor damping coefficient in axial direction \([\mathrm {F\times T/L^2}]\) STFLAT FRILAT DAMLAT STFLAT: real >= 0, default: 0: In-plane seafloor stiffness for friction in lateral direction \([\mathrm {F/L^2}]\) FRILAT: real >= 0, default: 0: In-plane seafloor friction coefficient in lateral direction [1] DAMLAT: real >= 0, default: 0: In-plane 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. 1.17.1. Data group identifier, one input line NEW COMPonent DRAGchain 1.17.2. Component type identifier, one input line CMPTYP-ID CMPTYP-ID: 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 1.18.1. Data group identifier NEW COMPonent FIBRe_rope 1.18.2. Component type identifier CMPTYP-ID TEMP ALPHA BETA CMPTYP-ID: 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 cross-sectional 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 non-linear material curve used in static analysis is given by shifting the working curve by redefining the initial stress-free 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 strain ELONG(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 stress-free length such that the tension is identical between static and dynamic analysis given the elongation of static analysis. See figure Tension strain curves. Figure 22. 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 1.19.1. Data group identifier, one input line NEW COMPonent GROWth 1.19.2. Component type identifier, one input line CMPTYP-ID NGRLEV CMPTYP-ID: 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 cross-sections. The volume loads will be modified if the external area is non-zero. A circular cross-section 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 non-zero. For CRS2 and CRS7 cross-sections, the diameter of a circular cross-sections 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 and CDZ \(\mathrm {CDX\cdot(\frac{DH_{growth}}{DH})}\) \(\mathrm {CDY\cdot(\frac{DH_{growth}}{DH})}\) \(\mathrm {CDZ\cdot(\frac{DH_{growth}}{DH})}\) 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.