Input to INPMOD 1. General Information The purpose of the INPMOD module is to administer reading/interpretation of system and environmental data. The following data groups are included: General Control Data - Data Group A Single Riser Data - Data Group B Component Data - Data Group C Environmental Data - Data Group D Support Vessel Data - Data Group E An INPMOD run may consist of a combination of the data groups, but a data group included must be complete. Data group A is mandatory, while data groups B-E normally will be given. All data groups except data group A can be given more than once. Note that running INPMOD always overwrites old information in the INPFIL. That means that all needed data on INPFIL must be generated in one INPMOD run. Within each group, the first two data groups (identification and control data) must be given first, while the order of the remaining data groups, to some extent, is arbitrary. Data groups in one section cannot be mixed with data groups in another section. This means that when the program finds a data group identifier it will only check the data within the current section. If one or more errors are found, an error message is written and an error flag is written to the INPFIL file. A run with STAMOD or DYNMOD using this file will then be terminated. INPMOD will continue to read data until the END input line is found (see Termination of input data) regardless of the number of errors detected. 2. Data Group A: General Control Data General inputs include the unit system. 2.1. INPMOD identification text An identification text describing the INPMOD run may be given. If given, this text is printed on the front page of the INPMOD print file. 2.1.1. Data group identifier, one input line Mandatory. INPMod IDENtification TEXT CHVERS CHVERS: character(8): RIFLEX input file version, e.g. 3.2 2.1.2. Identification text, three input lines Mandatory. Heading, line no 1 Heading, line no 2 Heading, line no 3 Always three input lines, which may all be blank. Each line may contain up to 60 characters. 2.2. Selection of unit system physical constant The program applies a set of consistent units. The user is free to select any combination of unit names for: time \([\mathrm T]\) length \([\mathrm L]\) mass \([\mathrm M]\) force \([\mathrm F]\) 2.2.1. Data group identifier, one input line Mandatory. UNIT NAME SPECification 2.2.2. Unit names and gravitational constant Mandatory. UT UL UM UF GRAV GCONS UT: character(6), default: "s": Unit name for time UL: character(6), default: "m": Unit name for length UM: character(6), default: "kg": Unit name for mass UF: character(6), default: "kN": Unit name for force GRAV: real > 0, default: 9.81: Numerical value of gravitational constant \([\mathrm {L/T^2}]\) GCONS: real > 0, default: 0.001: Consistency acceleration parameter. GCONS = ACC[UF/UM]/ACC where ACC` is the numerical value of acceleration with the force and mass units, and with the length and time units, respectively. With a consistent set of units, GCONS = 1.0. Example: For the default units, the acceleration of gravity is \(9.81\times 10^{-3}\,\mathrm {kN/kg}\) or \(9.81\,\mathrm {m/s}^2\) and GCONS may be calculated as \(\mathrm {9.81\times 10^{-3}/9.81=0.001}\). In the case of GCONS \(\mathrm {\neq 1}\), the calculation of drag force coefficients must be multiplied by GCONS, for example CDY = GCONS\(\mathrm {(\frac{1}{2}\rho C_DD)}\), see also Hydrodynamic force coefficients. The unit names are printed as an output heading as shown below. +--------------------------------------------------------+ ! CONSISTENT UNITS USED THROUGHOUT THE ANALYSES ! !--------------------------------------------------------! ! NAME FOR TIME : T = s ! ! NAME FOR LENGTH : L = m ! ! NAME FOR MASS : M = kg ! ! NAME FOR FORCE : F = kN ! ! ! ! GRAVITATIONAL CONSTANT : ! ! G = 9.810 L/T**2 ! ! CONSISTENCY ACCELERATION PARAMETER : ! ! GCONS = 0.1000E-02 (F/M)/(L/T**2) ! +--------------------------------------------------------+ 2.3. Termination of input data As mentioned an INPMOD run consist of some of the data groups A, B, C, D, E and F. No termination is to be provided between the data groups, but after the last data group is given, the following input line must be given to terminate the input stream: END 3. Data Group B: Single Riser Data The riser description consists of the data group Riser type specification followed by one of Standard system SA, Standard system SB, Standard system SC, Standard system SD or Arbitrary system AR with the topology and boundary conditions. The data group Line and segment specification is used for the specification of the line types that are used in topology specification. 4. 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` 4.1. 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 4.1.1. Data group identifier NEW COMPonent CRS0 4.1.2. 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] 4.1.3. 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. 4.1.4. 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 4.1_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. 4.1.5. 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. 4.1.6. 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. 4.1.7. Hydrodynamic load types Identical to input for cross-section type CRS1 except that the load type HNET is not available, see Hydrodynamic load type. 4.1.8. Aerodynamic force coefficients Identical to input for cross-section type CRS1, see Aerodynamic load type identification. 4.1.9. Capacity parameter Identical to input for cross-section type CRS1, see Capacity parameter. :table-caption: Table :icons: font 4.2. 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 4.2.1. Data group identifier NEW COMPonent CRS1 4.2.2. 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 4.2.3. 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. 4.2.4. 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. 4.2.5. 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. 4.2.6. Axial stiffness. Case 1, IEA=1 EA EA: real > 0: Axial stiffness \(\mathrm {[F]}\) 4.2.7. 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 4.2.8. 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. 4.2.9. 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 4.2.10. 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 4.2.11. 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. 4.2.12. 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 4.2.13. 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 4.2.14. 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. 4.2.15. 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) 4.2.16. 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 4.2.17. 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 4.2.18. 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 4.3. CRS2 - Double symmetric cross section 4.3.1. Data group identifier NEW COMPonent CRS2 4.3.2. 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 4.3.3. 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. 4.3.4. 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. 4.3.5. 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. 4.3.6. Axial stiffness. Case 1 IEA=1 EA EA: real > 0: Axial stiffness \(\mathrm {[F]}\) 4.3.7. 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. 4.3.8. 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: 4.3.9. 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. 4.3.10. 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. 4.3.11. 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. 4.3.12. 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. 4.3.13. 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. 4.3.14. Damping specification Identical to input for cross-section type CRS1, see data group Damping specification. 4.3.15. 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. 4.3.16. Aerodynamic load type identification, One optional input line CHLOAD CHLOAD: character: = WIND - Text to identify wind coefficients 4.3.17. 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. 4.3.18. 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 4.4. CRS7 - General cross section 4.4.1. Data group identifier NEW COMPonent CRS7 4.4.2. 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 4.4.3. 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 \(\mathrm {(Y_m,Z_m)}\) \(\mathrm {[L]}\) 4.4.4. 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 4.4.5. Stiffness properties Only constant stiffness properties are allowed. 4.4.6. 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. 4.4.7. 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 \(\mathrm {[L]}\) 4.4.8. Axial stiffness EA EA: real > 0: Axial stiffness \(\mathrm {[F]}\) 4.4.9. 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 \(\mathrm {[FL^2]}\) 4.4.10. 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. 4.4.11. 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. 4.4.12. 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. 4.4.13. 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. 4.4.14. 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 4.4.15. Aerodynamic load type identification, One optional input line CHLOAD CHLOAD: character: = WIND - Text to identify wind coefficients 4.4.16. 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. 4.4.17. 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 4.5. CRS8 - Axisymmetric cross section with axial/torsion strain model and hysteresis effects in bending/cuvature relation 4.5.1. Data group identifier NEW COMPonent CRS8 4.5.2. Component type identifier Identical to input for cross-section type CRS1 , see Component type identifier for CRS1. 4.5.3. Mass and volume Identical to input for cross-section type CRS1 , see Mass and volume for CRS1. 4.5.4. 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 4.5.5. Axial stiffness. Case 1, IEAIGT=1 EA EA: real > 0: Axial stiffness \(\mathrm {[F]}\) 4.5.6. 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 4.5.7. Bending stiffness properties 4.5.8. 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 4.5.9. 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. 4.5.10. Damping specification Identical to input for cross-section type CRS1 , see Damping specification for CRS1. 4.5.11. Hydrodynamic load types Identical to input for cross-section type CRS1, see Hydrodynamic load type identification for CRS1. 4.5.12. Aerodynamic force coefficients Identical to input for cross-section type CRS1, see Aerodynamic load type identification for CRS1. 4.5.13. Capacity parameter Identical to input for cross-section type CRS1, see Capacity parameter for CRS1. 4.6. BODY - Description of attached bodies 4.6.1. Data group identifier NEW COMPonent BODY 4.6.2. 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. 4.6.3. Mass and volume AM AE AM: real: Mass \(\mathrm {[M]}\) AE: real: Displacement volume \(\mathrm {[L^3]}\) 4.6.4. 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 4.7. 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. 4.7.1. Data group identifier NEW COMPonent CONB 4.7.2. Component type identifier CMPTYP-ID CMPTYP-ID: character(8): Component type identifier 4.7.3. Mass and volume AM AE AM: real: Mass \(\mathrm {[M]}\) AE: real: Displacement volume \(\mathrm {[L^3]}\) 4.7.4. 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 4.7.5. 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 4.8. 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. 4.8.1. Data group identifier NEW COMPonent FLEX 4.8.2. Component type identifier CMPTYP-ID CMPTYP-ID: character(8): Component type identifier 4.8.3. 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 \(\mathrm {[FLT/deg]}\) 4.8.4. 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: \(\mathrm {FY=CDY\times \sqrt{VRELY^2+VRELZ^2}\times VRELY}\) \(\mathrm {FZ=CDY\times \sqrt{VRELY^2+VRELZ^2}\times VRELZ}\) 4.8.5. 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. 4.8.6. 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. 4.9. FLUID - Specification of internal fluid flow 4.9.1. Data group identifier NEW COMPonent FLUId 4.9.2. Component type number CMPTYP-ID CMPTYP-ID: character(8): Component type identifier 4.9.3. 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) 4.10. 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. 4.10.1. Data group identifier NEW COMPonent EXT1 4.10.2. Component type identifier CMPTYP-ID CMPTYP-ID: character(8): Component type identifier 4.10.3. 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 4.10.4. 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 4.11. 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. 4.11.1. Data group identifier NEW COMPonent CRS5 4.11.2. Component type identifier Identical to Component type identifier for CRS2. 4.11.3. Mass and volume Identical to Mass and volume. 4.11.4. Stiffness properties classification Identical to Stiffness properties classification for CRS2 4.11.5. Axial stiffness. Case 1, IEA=1 Identical to Axial stiffness. Case 1 4.11.6. Axial stiffness. Case 2, IEA=N Identical to Axial stiffness. Case 2 4.11.7. Bending stiffness. Case 1, IEJ=1 IPRESS=0 Identical to Bending stiffness. Case 1 4.11.8. Bending stiffness. Case 2, IEJ=1 IPRESS=1 (not implemented) Identical to Bending stiffness. Case 2 4.11.9. Bending stiffness description. Case 3 IEJ=N IPRESS=0 Identical to Bending stiffness description. Case 3 IEJ=N IPRESS=0 for CRS2 4.11.10. Bending stiffness. Case 4 IEJ=N1, IPRESS=N2 (not implemented) Identical to Bending stiffness. Case 4 IEJ=N1 4.11.11. Damping specification Identical to Damping specification for CRS2 4.11.12. 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 4.11.13. 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. 4.11.14. 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 4.11.15. Capacity parameter Identical to Capacity parameter for CRS2 4.12. 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. 4.12.1. Data group identifier NEW COMPonent CONTact 4.12.2. Component type identifier CMPTYP-ID CMPTYP-ID: character(8): Component type identifier 4.12.3. 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. 4.12.4. 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. 4.12.5. 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 \(\mathrm {[FT/L]}\) 4.12.6. 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 4.12.7. 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. 4.13. 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. 4.13.1. Data group identifier, one input line NEW COMPonent TENSioner 4.13.2. Component type identifier CMPTYP-ID CMPTYP-ID: character(8): Component type identifier 4.13.3. 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 4.14. Tubular contact component This component is available for elastic contact surface description only. 4.14.1. Data group identifier, one input line NEW COMponent TUBUlar contact 4.14.2. Component type number CMPTYP-ID CMPTYP-ID: character(8): Component type identifier 4.14.3. 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. 4.14.4. Contact spring stiffness; IKS = 1 STIFF STIFF: real: Spring compression stiffness \(\mathrm {[F/L]}\) 4.14.5. 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 4.15. 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. 4.15.1. Data group identifier, one input line NEW COMPonent SOIL 4.15.2. 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. 4.15.3. 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. 4.15.4. 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. 4.15.5. 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). 4.16. 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. 4.16.1. Data group identifier, one input line NEW COMPonent SEAFloor contact 4.16.2. 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 4.16.3. 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. 4.16.4. 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. 4.17. Drag chain element The drag chain element is a single node element that models a simplified contact between a drag chain and the seafloor. 4.17.1. Data group identifier, one input line NEW COMPonent DRAGchain 4.17.2. Component type identifier, one input line CMPTYP-ID CMPTYP-ID: character(8): Component type identifier 4.17.3. 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 \(\mathrm {[F/L]}\) 4.18. Fibre rope cross section 4.18.1. Data group identifier NEW COMPonent FIBRe_rope 4.18.2. 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. 4.18.3. 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. 4.18.4. 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. 4.18.5. 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. 4.18.6. 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 4.18.7. Damping specification Identical to Damping specification 4.18.8. Hydrodynamic force coefficients Similar to Hydrodynamic force coefficients, but only Morison type loading is available. 4.18.9. Capacity parameter Identical to Capacity parameter 4.19. Growth - Specification of marine growth profile 4.19.1. Data group identifier, one input line NEW COMPonent GROWth 4.19.2. Component type identifier, one input line CMPTYP-ID NGRLEV CMPTYP-ID: character(8): Component type identifier NGRLEV : integer: Number of growth levels 4.19.3. 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. 5. Data Group D: Environmental Data A complete environmental description consists of environmental constants, wave and current data. When an environment description has been completed, a new one may be given by repeating data groups Identification of the environment' to `Current parameters' with the appropriate data for the new environment. Up to 10 complete environmental descriptions may be given as input to `INPMOD in one run each identified by an unique identifier given in data group `Identification of the environment'. The minimum data required in one environmental condition is environmental constants (i.e. data groups `Water depth and wave indicator' and `Environment constants' are required). Note that this data group is dummy for coupled analysis. 5.1. Identification of the environment 5.1.1. Data group identifier, one input line ENVIronment IDENtification 5.1.2. Describing text. One input line < TEXT > character(60): Description of the environment by alphanumerical text. Note: May be empty, but must be present. 5.1.3. Data-set identifier. One input line IDENV IDENV: character(6): Data set identifier for this environment description. Each environment must have a unique identifier. 5.2. Water depth and wave indicator 5.2.1. Data group identifier, one input line WATErdepth AND WAVEtype 5.2.2. Water depth and control parameters. One input line WDEPTH NOIRW NORW NCUSTA NWISTA WDEPTH: real: Water depth \(\mathrm {[L]}\) NOIRW: integer: Number of irregular wave cases, maximum 10 NORW: integer: Number of regular wave cases, maximum 10 NCUSTA: integer: Number of current states, maximum 10 NWISTA: integer, default: 0: Number of wind states, maximum 10 WDEPTH>0. This water depth is defined as a scalar. This parameter is used in calculation of water particle motions. An environment description can contain up to 10 irregular wave cases and 10 regular wave cases. A uniquely defined environment used in STAMOD or DYNMOD must refer to the actual environment by the identifier IDENV and wave case number. If a numerically defined spectrum is used, IWASP1=5 in Irregular wave control, the number of irregular wave cases is limited to NOIRW=1. If a current line (Spatially varying current) is specified, then NCUSTA must be set to the total number of current profiles given. 5.3. Environment constants 5.3.1. Data group identifier, one input line ENVIronment CONStants 5.3.2. Constants. One input line AIRDEN WATDEN WAKIVI AIRKIVI AIRDEN: real > 0: Air density \(\mathrm {[M/L^3]}\) WATDEN: real > 0: Water density \(\mathrm {[M/L^3]}\) WAKIVI: real, default: \(\mathrm {1.188\times 10^{-6}}\): Kinematic viscosity of water \(\mathrm {[L^2/T]}\) AIRKIVI: real, default: \(\mathrm {1.516\times 10^{-5}}\): Kinematic viscosity of air \(\mathrm {[L^2/T]}\) Typical values of AIRDEN and WATDEN are \(\mathrm {[AIRDEN=1.3kg/m^3]}\) and if the units m and kg are used. 5.4. Irregular waves This data group is given only if NOIRW > 0, and is then repeated NOIRW times. 5.4.1. Data group identifier, one input line NEW IRREgular SEAState 5.4.2. Irregular wave control data Irregular wave control NIRWC IWASP1 IWADR1 IWASP2 IWADR2 NIRWC: integer: Irregular wave case number IWASP1: integer: Wave-spectrum type (wind sea) IWASP1=1: Two-parameter Pierson-Moscowitz type spectrum IWASP1=2: One-parameter Pierson-Moscowitz type spectrum IWASP1=3: Jonswap spectrum IWASP1=4: Derbyshire-Scott spectrum IWASP1=5: Numerically defined spectrum IWASP1=6: Ochi spectrum To be used only for SI and modified SI units IWASP1=7: Bretschneider I spectrum To be used only for SI and modified SI units IWASP1=8: Bretschneider II spectrum To be used only for SI and modified SI units IWASP1=9: Three parameter Jonswap spectrum To be used only for SI and modified SI units IWASP1=10: Double peaked spectrum (Torsethaugen) To be used only for SI and modified SI units IWADR1: integer: Wave-direction code (wind sea) IWADR1=0: Unidirectional IWADR1>1: Cosine-spreading function, IWADR1 directions are used. IWADR1=1: Cosine-spreading function, 11 directions are used. IWADR1=1 is thus equivaent to specifying IWADR1=11. IWASP2: integer: Wave-spectrum type (swell) IWASP2=0: No swell spectrum For interpretation of other values, see IWASP1 above IWADR2: integer: Wave-direction code (swell) (dummy if IWASP2=0) IWADR2=0: Unidirectional IWADR2>1: Cosine-spreading function, IWADR2 directions are used. IWADR2=1: Cosine-spreading function, 11 directions are used. IWADR2=1 is thus equivaent to specifying IWADR2=11. Bretschneider I is based on fetch and wind speed. Bretschneider II is based on wave height and wave period. For IWADR1 > 0, the directions will be evenly spaced around the average wave propagation direction WADIR1 at intervals of 180/(IWADR1+1) degrees. Specifying an even numbers of directions should be avoided as the average wave propagation direction will not be included in this case. The same applies to IWADR2. 5.4.3. Wave spectrum parameters (wind sea) Data group identifier, one input line WAVE SPECtrum WIND Spectrum parameters One of (i), (ii), …., (x) is given, depending on the value of the IWASP1 parameter in the data group Irregular wave control data above. (i) Two-parameter Pierson-Moscowitz (IWASP1=1), one input line. SIWAHE AVWAPE SIWAHE: real: Significant wave-height, \(\mathrm {H_S}\) \(\mathrm {[L]}\) AVWAPE: real > 0: Zero-crossing wave-period, \(\mathrm {T_Z}\) \(\mathrm {[T]}\) - \(\mathrm {S_{\eta }(\omega )=A\omega ^{-5}exp[-^B/\omega ^4];0<\omega <\infty}\) \(\mathrm {A=124.2H_S^2/T_Z^4}\) - \(\mathrm {B=496/T_Z^4}\) The relation between peak period, \(\mathrm {T_p}\) and zero-crossing period is \(\mathrm {T_Z\approx T_p/1.408}\) (ii) One-parameter Pierson-Moscowitz (IWASP1=2), one input line SIWAHE SIWAHE: real > 0: Significant wave-height, \(\mathrm {H_S}\) \(\mathrm {[L]}\) \(\mathrm {S_{\eta }(\omega )=A\omega ^{-5}exp[-^B/\omega ^4];0<\omega <\infty}\) \(\mathrm {A=0.0081g^2}\) \(\mathrm {B=3.11/H_S^2}\) (iii) Jonswap spectrum (IWASP1=3), one input line PEAKFR ALPHA BETA GAMMA SIGMAA SIGMAB PEAKFR: real > 0: Peak frequency (wp) \(\mathrm {[radians/T]}\) ALPHA: real, default: 0.008: Phillip’s constant BETA: real, default: 1.25: Form parameter GAMMA: real, default: 3.3: Peakedness parameter giving the ratio of the maximum spectral energy to that of the corresponding Pierson- Moscowitz spectrum 0 < GAMMA ⇐ 20 SIGMAA: real > 0, default: 0.07: Spectrum width parameter SIGMAB: real > 0, default: 0.09: Spectrum width parameter \(\mathrm {S_{\eta }(\omega )=\alpha g^2\omega ^{-5}exp(-\beta (\frac{\omega _p}{\omega })^4)\times \gamma ^{exp(-\frac{(\omega -\omega _p)^2}{2\sigma ^2\omega ^2_p})}}\) \(\mathrm {\alpha =1.2905H_S^2/T_Z^4}\) \(\mathrm {\beta =1.25}\) for North Sea conditions \(\mathrm {\gamma =}\) \(\begin{cases}\mathrm {1.0;}\quad \mathrm {T_p>=5\sqrt{H_S}}\\\mathrm {exp(5.75-1.15T_p/\sqrt{H_S})}\\\mathrm {5.0;}\quad \mathrm {T_p<3.6\sqrt{H_S}}\end{cases}\) \(\mathrm {\sigma =}\) \(\begin{cases}\mathrm {\sigma _a=0.07}\quad \mathrm {for}\quad \omega <=\omega _p\\\mathrm {\sigma _b=0.09}\quad \mathrm {for}\quad \omega <=\omega _p\end{cases}\) \(\mathrm {\omega _p=\frac{2\pi }{T_p}}\) - \(\mathrm {\frac{T_p}{T_Z}=1.407(1-0.287ln\gamma )^{1/4}}\) (iv) Derbyshire-Scott spectrum (IWASP1=4), one input line SPEC1 SPEC2 SPEC3 SIWAHE AVWAPE TRUNCL TRUNCU SPEC1: real, default: 0.214: Spectrum parameter, a \(\mathrm {[T/rad]}\) SPEC2: real > 2, default: 0.065: Spectrum parameter, b \(\mathrm {[rad/T]}\) SPEC3: real, default: 0.26: Spectrum parameter, d \(\mathrm {[rad/T]}\) SIWAHE: real: Significant wave height, \(\mathrm {H_S}\) \(\mathrm {[L]}\) AVWAPE: real > 0: Average wave period, \(\mathrm {T}\) \(\mathrm {[T]}\) TRUNCL: real, default: 0.0414: Lower truncation parameter \(\mathrm {[radians/T]}\) TRUNCU: real, default: 10.367: Upper truncation parameter \(\mathrm {[radians/T]}\) \(\mathrm {S_{\eta }(\omega )=\alpha H_S^2exp\sqrt{\frac{(\omega -\omega _p)^2}{b(\omega -\omega _p+d)}}}\) for \(\mathrm {TRUNCL<\omega <TRUNCU}\) (v) Numerically defined spectrum (IWASP1=5) Both (v.1) and (v.2) must be given. (v.1) Number of discrete frequencies, one input line. NDFRQ1 NDFRQ1: integer >= 4: Number of discrete frequencies (v.2) Spectrum values, NDFRQ input lines. Either: FRQ DSPDEN FRQ: real: Frequency \(\mathrm {[radians/T]}\) DSPDEN: real: Associated discrete spectral density value \(\mathrm {[L^2T]}\) The input lines must be given in sequence of increasing frequency values. (vi) Ochi spectrum (IWASP1=6), one input line. SIWAHE SIWAHE: real: Significant wave height \(\mathrm {[L]}\) (vii) Bretschneider spectrum I (IWASP1=7), one input line FETCH WISPD FETCH: real: Fetch \(\mathrm {[L]}\) WISPD: real: Wind speed \(\mathrm {[L/T]}\) (viii) Bretschneider spectrum II (IWASP1=8), one input line SIWAHE SIWAPE SIWAHE: real: Significant wave height \(\mathrm {[L]}\) SIWAPE: real > 0: Significant wave period \(\mathrm {[T]}\) (ix) Three parameter JONSWAP spectrum (IWASP1=9), one input line. SIWAHE PEAKPE GAMMA SIWAHE: real: Significant wave height \(\mathrm {[L]}\) PEAKPE: real > 0: Peak period \(\mathrm {[T]}\) GAMMA: real, default: see below: Peakedness parameter giving the ratio of the maximum spectral energy to that of the corresponding Pierson-Moscowitz spectrum 0< GAMMA ⇐ 20 Default value of GAMMA is calculated from SIWAHE and PEAKPE, see (iii) Jonswap spectrum (IWASP1=3): \(\mathrm {GAMMA=exp[5.75-1.15\times \frac{PEAKPE}{\sqrt{SIWAHE}}]}\) \(\mathrm {1<=GAMMA<=5}\) Note that use of the three parameter JONSWAP spectrum requires that the SI units m and s be used. (x) Double peaked JONSWAP spectrum (IWASP1=10) (described by Torsethaugen) , one input line. SIWAHE PEAKPE SIWAHE: real: Significant wave height \(\mathrm {[L]}\) PEAKPE: real > 0: Peak period \(\mathrm {[T]}\) Note that use of the double peaked JONSWAP spectrum requires that the SI units m and s be used. 5.4.4. Wave spectrum parameters (swell) This data group is omitted for IWASP2=0, see Irregular wave control data (no swell present). Data group identifier, one input line WAVE SPECtrum SWELl Spectrum parameters One of (i), (ii), …, (x) is given, depending on the value of the IWASP2 parameter given in data group Irregular wave control data. The input is identical to input of wind sea spectrum and is therefore not repeated, see Wave spectrum parameters (wind sea). 5.4.5. Direction parameters of waves Data group identifier, one input line DIRECTION PARAMETERS The two input lines below (`Wave direction parameters (wind sea)' and `Wave direction parameters (swell)') must be given in sequence if both are present. Wave direction parameters (wind sea), one input line WADR1 EXPO1 WADR1: real: Average propagation direction of waves, measured in degrees from the global X-axis. Confer the figure Location of support vessel coordinate system EXPO1: real: Exponent of cosine distribution dummy if IWADR1=0, see Irregular wave control data. If IWADR1 > 0, a cosine directional spreading function is used: \(\mathrm {f(\alpha _i)=\frac{[cos(\alpha _i-WADR1)]^{EXPO1}}{\sum[f(\alpha _j)]}}\) where \(\mathrm {\alpha _i}\) is one of the IWADR1 short-crested wave directions. The sum in the denominator is taken over all IWADR1 directions. The total wind sea energy is thus kept. Wave direction parameters (swell), one input line This data group is omitted for IWASP2=0, see Irregular wave control data (no swell present). WADR2 EXPO2 WADR2: real: Average propagation direction of waves, measured in degrees from the global X-axis. Confer the figure Location of support vessel coordinate system EXPO2: real: Exponent of cosine distribution dummy if IWADR2=0, see Irregular wave control data. If IWADR2 > 0, a cosine directional spreading function is used: \(\mathrm {f(\alpha _i)=\frac{[cos(\alpha _i-WADR2)]^{EXPO2}}{\sum[f(\alpha _j)]}}\) where \(\mathrm {\alpha _i}\) is one of the IWADR2 short-crested wave directions. The sum in the denominator is taken over all IWADR2 directions. The total swekk energy is thus kept. 5.5. Regular waves This data group is given only if NORW > 0. 5.5.1. Data group identifier, one input line REGULAR WAVE DATA 5.5.2. Regular wave data, NORW input lines INRWC AMPLIT PERIOD WAVDIR INRWC: integer: Regular wave case number AMPLIT: real: Wave amplitude \(\mathrm {[L]}\) PERIOD: real > 0: Wave period \(\mathrm {[T]}\) WAVDIR: real: Wave propagation direction from the global X-axis \(\mathrm {[deg]}\) Confer the figure Location of support vessel coordinate system 5.6. Current parameters This data group is given only if NCUSTA > 0, and is then repeated NCUSTA times. 5.6.1. Data group identifier, one input line May be omitted if no current is present for actual environment. NEW CURRENT STATE 5.6.2. Current dimension parameter, one input line ICUSTA NCULEV L_EXT ICUSTA: integer: Current state number NCULEV: integer: Number of current levels L_EXT: integer, default: 0: Flag to indicate if current data is given in this input file, or if it shall be read from an external file. For details on the format of the external file, confer CURMOD User’s Documentation. 0: Data specified on this file 1: Data specified on external file 1 ⇐ NCULEV ⇐ 30. Current states must be given in increasing order, i. e. 1,2, …, NCUSTA 5.6.3. Current profile, one input line per current level, i.e. NCULEV input lines This data group is given only if L_EXT = 0 CURLEV CURDIR CURVEL CURLEV: real: Z coordinate of level given in global coordinate system \(\mathrm {[L]}\) CURDIR: real: Current velocity direction at this level. The angle is measured in degrees from the global X-axis counter-clockwise around the global Z-axis. (seen from above) CURVEL: real: Current velocity at this level \(\mathrm {[L/T]}\) The input lines must be given in sequence of decreasing Z coordinates. Linear interpolation is applied between the levels. Outside the specified range of levels a flat extrapolation is used, i.e. for Z > CURLEV(1) the velocity is set to CURVEL(1) and for Z < CURLEV(NCULEV) the velocity is set to CURVEL(NCULEV) This current profile may be scaled when applied in static or dynamic analysis. Z coordinate is zero at mean water level and negative below sea surface. This data group is given only if L_EXT = 1 CURRFILE CURRFILE: character(120): Name of external file with specified current data 5.7. Spatially varying current 5.7.1. Data group identifier, one input line NEW CURRENT LINE 5.7.2. Current line control parameters, one input line ICUSTA NPT ICUSTA: integer: Current state number NPT: integer: Number of current profiles given The number of current states NCUSTA (see Water depth and control parameters) must be increased by NPT for each current line specified. Current states must be given in ascending order 5.7.3. Current dimension parameters, one input line IPT NCULEV XPT YPT IPT: integer: Current profile number. Must be given from 1 to NPT consecutively NCULEV: integer: Number of current levels 1 < NCULEV ⇐ 30 XPT: real: Global X- and Y- coordinates YPT: real: For which this current profile is specified 5.7.4. Current profile, one input line per current level, i.e. NCULEV input lines CURLEV CURDIR CURVEL CURLEV: real: Z coordinate of level given in global coordinate system \(\mathrm {[L]}\) CURDIR: real: Current velocity direction at this level. The angle is measured in degrees from the global X-axis counter-clockwise around the global Z-axis. (seen from above) CURVEL: real: Current velocity at this level \(\mathrm {[L/T]}\) The input lines must be given in sequence of decreasing Z coordinates. Linear interpolation is applied between the levels. Outside the specified range of levels a flat extrapolation is used, i.e. for Z > CURLEV(1) the velocity is set to CURVEL(1) and for Z < CURLEV(NCULEV) the velocity is set to CURVEL(NCULEV) This current profile may be scaled when applied in static or dynamic analysis. Z coordinate is zero at mean water level and negative below sea surface. 5.8. Wind parameters This data group is given only if NWISTA > 0, and is then repeated NWISTA times. 5.8.1. Data group identifier, one input line May be omitted if no wind is present for actual environment. NEW WIND SPECification 5.8.2. Wind case number, one input line IWISTA IWISTA: integer: Wind case number 5.8.3. Wind type, one input line IWITYP IWITYP: integer: Wind type IWITYP=10: Stationary uniform wind with shear, values interpolated at grid points IWITYP=11: Fluctuating uniform 2-component wind IWITYP=12: Fluctuating 3-comp. wind read from files (IECWind format) IWITYP=13: Fluctuating 3-comp. wind read from files (TurbSim Bladed style format) IWITYP=14: Stationary uniform wind with shear The wind types 10 - 14 are intended for wind turbine analyses. However, they may also be applied for other type of analysis. For the IECWind fluctuating 3-component wind (IWITYP=12), only the fluctuating part of the wind is given in the wind input files. The mean wind speed UMEAN given above is added to the yield the total wind velocity in the longitudinal direction. The input files must conform to the 3-dimensional 3-component wind time series from the rectangular IEC format (See Thomsen, K., 2006. Mann turbulence for the IEC Code Comparison Collaborative (OC3). Risø National Laboratory). More specifically they must include time series of wind velocity in binary format, with a 3-dimensional array having indices in vertical direction running fastest, then indices in lateral direction and indices in longitudinal direction running slowest. For wind files from NREL’s TurbSim (IWITYP=13), the mean wind speed and shear are included in the binary files. The input files must be generated by TurbSim with WrBLFF=True. Both the .wnd file and .sum file are needed. 5.8.4. Wind type specifications Stationary uniform wind with shear, values interpolated at grid points (IWITYP=10) Wind direction, one input line WIDIR WIDIR: real: Wind propagation direction in global XY-plane \(\mathrm {[deg]}\) Wind velocity, one input line UMVEL VMVEL WMVEL UMVEL: real: Longitudinal wind velocity component \(\mathrm {[L/T]}\) VMVEL: real: Lateral wind velocity component \(\mathrm {[L/T]}\) WMVEL: real: Vertical (global Z-axis) wind velocity component \(\mathrm {[L/T]}\) The parameters UMVEL and VMVEL refer to the direction given by the WIDIR parameter Number of levels in shear profile, one input line NZPROF NZPROF: integer: Number of vertical levels for defining the shear profile Wind velocity profile definition, NZPROF input lines ZLEV UFACT VFACT WFACT ZLEV: real: Vertical coordinate of profile level \(\mathrm {[L]}\) UFACT: real: Wind speed scaling factor for longitudinal wind velocity VFACT: real: Wind speed scaling factor for the lateral wind velocity WFACT: real: Wind speed scaling factor for the vertical wind velocity Wind field domain location, one input line Z0 Z0: real: Z coordinate of the lower edge of the wind field domain \(\mathrm {[L]}\) Domain size, one input line NS NZ: integer: Number of grid points in Z- (vertical) direction Domain resolution, one input line DLWFZ DLWFZ: real: Domain resolution in the vertical direction \(\mathrm {[L]}\) Fluctuation uniform 2-component wind read from file (IWITYP=11) Wind direction, one input line WIDIR WIDIR: real: Wind propagation direction in global XY-plane \(\mathrm {[deg]}\) Wind data file name, one input lines CHWIFI CHWIFI: character(256): Path and filename for import of wind velocity time series. See the SIMO User Manual (`Reading wind time series from file' in `Initialization of time domain simulation' in `Use of DYNMOD') for explanation on file format. Fluctuating 3-component wind field read from IECWind format file (IWITYP=12) Mean wind direction, one input line WIDIR WIDIR: real: Wind propagation direction in global XY-plane \(\mathrm {[deg]}\) Mean wind velocity, one input line UMVEL UMVEL: real: Mean wind velocity along WIDIR \(\mathrm {[L/T]}\) Number of levels in shear profile, one input line NZPROF NZPROF: integer: Number of vertical levels for defining the shear profile Wind velocity profile definition, NZPROF input lines ZLEV UMFACT UFACT VFACT ZFACT ZLEV: real: Vertical coordinate of profile level \(\mathrm {[L]}\) UMFACT: real: Scaling factor for the mean wind velocity UFACT: real: Scaling factor for fluctuating part of the longitudinal wind velocity VFACT: real: Scaling factor for fluctuating part of the lateral wind velocity ZFACT: real: Scaling factor for fluctuating part of the vertical wind velocity Name of file containing the fluctuating longitudinal wind time series, one input line CHWFU CHWFU: character(256): Path and filename for the fluctuating U-component wind time series Name of file containing the fluctuating lateral wind time series, one input line CHWFV CHWFV: character(256): Path and filename for the fluctuating V-component wind time series Name of file containing the fluctuating vertical wind time series, one input line CHWFW CHWFW: character(256): Path and filename for the fluctuating Z-component wind time series Wind field domain location, one input line X0LL Y0LL Z0LL X0LL: real: X-coordinate of the lower left corner of the upstream border of the wind field domain \(\mathrm {[L]}\) Y0LL: real: Y-coordinate of the lower left corner of the wind field domain \(\mathrm {[L]}\) Z0LL: real: Z-coordinate of the lower left corner of the wind field domain\(\mathrm {[L]}\) These three coordinates defines the lower left corner of the wind field domain, which is defined as a rectangular cuboid. The coordinates refers to a coordinate system centred at the global origin, with the x-axis (longitudinal direction) pointing in the down-stream mean wind speed direction and the z-axis coincident with the global z-axis. Domain size, one input line NX NY NZ NX: integer: Number of grid points in X- (longitudinal) direction \(\mathrm {[L]}\) NY: integer: Number of grid points in Y- (lateral) direction \(\mathrm {[L]}\) NZ: integer: Number of grid points in Z- (vertical) direction\(\mathrm {[L]}\) Field size, one input line LWFX LWFY LWFZ LWFX: real: Field size in X- (longitudinal) direction LWFY: real: Field size in Y- (lateral) direction LWFZ: real: Field size in Z- (vertical) direction Buffer size, one input line NSLICE NSLICE: integer, default: 800: Buffer size: Number of wind crossectional planes (Slices) in memory Figure 23. The turbulence wind box. The lower left corner is shown with a red dot, and the center of the wind box is located at the green point. Fluctuating 3-component wind field read from TurbSim file (IWITYP=13) The wind field domain- and field size are extracted from the TurbSim .sum file. The wind field domain location in the global coordinate system is not given explicitly by the user. The vertical position of the wind field center is the same as in TurbSim; i.e. taken as the hub height given on the turbsim .sum file. Horizontally, the wind field is positioned around the global origin, but with a half grid width downwind of the origin. Since the TurbSim wind is non-periodic, this is necessary to ensure that the entire turbine lies in the same part of the wind field at the start of the simulation. The wind at the global origin will thus not start at the first slice The wind field must be large enough to ensure that the whole structure is within the wind field during the entire simulation. As the TurbSim wind field is nonperiodic, the beginning and end of the wind field will not fit together. Mean wind direction, one input line WIDIR WIDIR: real: Wind propagation direction in global XY-plane \(\mathrm {[deg]}\) Name of binary (.wnd) file containing the TurbSim fluctuating wind time series, one input line CHWFTW ..... * `CHWFTW: character(256)`: Path and filename for the binary TurbSim (.wnd) file Name of the summary (.sum) file from TurbSim, one input line ... CHWFTS CHWFTS: character(256): Path and filename for the summary TurbSim (.sum) file Buffer size, one input line NSLICE NSLICE: integer, default: 800: Buffer size: Number of wind crossectional planes (Slices) in memory Note: Since TurbSim files are not periodic, time series are shifted by 1/2 Grid Width. The number of slices in memory must be greater than (Grid Width/MeanWindSpeed/WindFileTimeStep). Figure 24. Example of grid and rotor placements in Turbsim: the circles pictured here are the rotor diameters assumed by TurbSim. The actual rotor diameter(s) will be smaller than in the figures Stationary uniform wind with shear (IWITYP=14) Wind direction, velocity and shear profile type, one input line WIDIR UMVEL WMVEL CH_SHEAR WIDIR: real: Wind propagation direction in global XY-plane \(\mathrm {[deg]}\) UMVEL: real: Longitudinal wind velocity component \(\mathrm {[L/T]}\) WMVEL: real: Vertical (global Z-axis) wind velocity component \(\mathrm {[L/T]}\) CH_SHEAR: character(4): Shear profile type NONE - No shear profile POWR - Power shear profile LOGA - Logarithmic shear profile UMVEL is the wind velocity in the direction WIDIR. Poser shear profile input, one input line, only given if CH_SHEAR = POWR ZREF ALPHA ZREF: real: Reference height \(\mathrm {[L]}\) ALPHA: real: Wind shear exponent \(\mathrm {[-]}\) Logarithmic shear profile input, one input line, only given if CH_SHEAR = LOGA ZREF Z0 ZREF: real: Reference height \(\mathrm {[L]}\) Z0: real: Roughness length \(\mathrm {[L]}\) 6. Data Group E: Support Vessel Data Observe that the motion transfer function definition is related to the wave field definition. See Motion Transfer Functions in the Theory Manual for the definition of wave field and motion transfer functions. Transfer functions based on other definitions must be converted by appropriate phase shift operations before they are used as input to this program. This data group needs not be given for systems with no vessel attachment points. Note that either Support vessel data on file or Identification through Transfer function input is to be given. 6.1. Support vessel data on file 6.1.1. Data group identifier, one line TRANsfer FUNCtion FILE 6.1.2. File name CHFTRA CHFTRA: character(80): File name with transfer functions data File with transfer function data given in RIFLEX format terminated with an END statement. This group replaces the rest of group E if given. Either Support vessel data on file or Identification through Transfer function input should be given. If Support vessel data on file is given, the content on the file should be Identification to Transfer function input with an END termination. 6.2. Identification 6.2.1. Data group identifier, one input line SUPPort VESSel IDENtification 6.2.2. Heading, one input line Heading Text describing the transfer functions. Always one input line, which may be blank. The line may contain up to 60 characters. 6.2.3. Identifier, one input line IDWFTR IDWFTR: character(6): Identifier for transfer functions. The value NONE is not allowed. 6.3. Transfer function reference position This data group is used as control parameter and compared with vessel position specified in INPMOD: Data Group B: Single Riser Data. 6.3.1. Data group identifier, one input line HFTRan REFErence POSItion 6.3.2. Reference position, one input line ZG ZG: real: Vertical position of the support vessel coordinate system. \(\mathrm {[L]}\) (The global Z coordinate for which the vessel motion transfer function is calculated.) Confer the figure Location of support vessel coordinate system (below). This parameter is used as control parameter and compared with ZG in data groups. Figure 25. Location of support vessel coordinate system 6.4. Dimension parameter and input type code 6.4.1. Data group identifier, one input line HFTRansfer CONTrol DATA 6.4.2. Dimension parameters, one input line NDHFTR NWHFTR ISYMHF ITYPIN NDHFTR: integer: No. of directions for which transfer functions are given NDHFTR=1 or NDHFTR>=4 NWHFTR: integer: No of frequencies for which transfer functions are given NWHFTR>=4 ISYMHF: integer: Symmetry code related to transfer functions ISYMHF=0: No symmetry ISYMHF=1: Symmetry about XV-ZV plane ISYMHF=2: Symmetry about XV-ZV and YV-ZV planes ITYPIN: integer: Code for which format the HF-transfer function are given ITYPIN=1: Non-dimensional complex form ITYPIN=2: Non-dimensional amplitude ratio and phase, where phase is given in degrees ITYPIN=3: Non-dimensional amplitude ratio and phase, where phase is given in radians The complex form and the amplitude ratio are to be given as non-dimensional. This means: L/L for freedoms surge, sway and heave radian/radians or degrees/degrees for freedoms roll, pitch and yaw, giving motion angle/surface wave slope amplitude. The wave slope amplitude is defined by \(\mathrm {\gamma _a=k\zeta_a}\) where \(\mathrm {k}\) is the wave number and \(\mathrm {\zeta_a}\) is the wave amplitude. If NDHFTR=1, ISYMHF is dummy (set to zero by the program). In this case the specified transfer function is used, regardless of the wave direction. Note that the specified motions are applied in the local vessel coordinate system regardless of the wave direction; e.g. surge motions are applied in the local vessel x-direction. In practice, the wave direction will not have any effect on the vessel motions in this case. To rotate the motions with the wave direction, update the vessel heading when the wave direction is changed. This method must however be used with care, if the model is not symmetric and connected to the vessel in the local vessel origo, it may not give the desired effect. 6.5. Specifications of wave directions Wave directions given in vessel coordinate system for input of motion transfer functions. 6.5.1. Data group identifier, one input line WAVE DIREctions 6.5.2. Directions, NDHFTR input lines IHEAD HEAD IHEAD: integer: Direction number HEAD: real: Direction. The angle HEAD is measured in degrees from the XV axis counter clockwise to the wave propagation vector IHEAD and HEAD must be given in ascending order If NDHFTR=1, HEAD is dummy. If the directions do not cover a full circle, the transfer functions for the first direction will be repeated for the direction HEAD(1) + 360. For ISYMHF> 0, the last direction after mirroring is 360 - HEAD(1). 6.6. Specification of wave frequencies 6.6.1. Data group identifier, one input line WAVE FREQuencies 6.6.2. Frequencies, NWHFTR input lines IFREQ WHFTR IFREQ: integer: Frequency number WHFTR: real: Frequency \(\mathrm {[rad/T]}\) Frequencies must be given in increasing order. 6.7. Transfer function input 6.7.1. Data group identifier, one input line HFTRansfer FUNCtion "DOF" dof is either SURGE, SWAY, HEAVE, ROLL, PITCH or YAW 6.7.2. Transfer function for HF dof motion, NDHFTR x NWHFTR input lines IDIR IFREQ A B IDIR: integer: Direction number IFREQ: integer: Frequency number A: real: Interpretation according to value of ITYPIN (given in the data group Data Group E: Support Vessel Data_transfer_reference_reference) ITYPIN=1: A - Real part ITYPIN=2: A - Amplitude ratio ITYPIN=3: A - Amplitude ratio B: real: Interpretation according to value of ITYPIN (given in the data group Data Group E: Support Vessel Data_transfer_reference_reference) ITYPIN=1: B - Imaginary part ITYPIN=2: B - Phase (degrees) ITYPIN=3: B - Phase (radians) Data Group E: Support Vessel Data_transfer_input_data is repeated for each degree of freedom included in motion description. If one (or more) degrees of freedom are omitted, they are set equal to zero. For phase and sign convention, see Motion Transfer Functions in the Theory Manual. If only one direction is specified (NDHFTR=1), the transfer function is used independent of incoming wave direction. Amplitudes and phase angles at required frequencies are calculated by linear interpolation/extrapolation in the dynamic analysis. Transfer functions will therefore be extrapolated for spectral components outside the frequency range defined for the transfer function. Ensure that the amplitude values given for the two highest/lowest frequencies give physical realistic values when extrapolated. Add two zero amplitude components at both ends of the frequency range if no extrapolation is wanted. Linear interpolation is also used for wave direction. 6.8. Termination of input data Do not forget the END input line if this is the last data group given in this INPMOD run. See also Termination of input data. END 7. Data Group F: Floater Force Model Data This option enables the user to make a coupled model, i.e. a FEM model that contains SIMO bodies in addition to beam and / or bar elements. Vessel motions and mooring line / riser dynamics may this be simulated simultaneously. A SIMO body node is added for each SIMO body in the system. This node may have a rigid connection to an existing node or may be a free or fixed node not automatically connection to the rest of the system. The vessel load model may account for wind, wave and current forces, which are applied as nodal loads. For a further description of the vessel load models, see the SIMO User Manual. this option requires a SIMO license. 7.1. Data group identifier, one input line FLOAter FORCe MODEl 7.2. Number of SIMO bodies, one input line NSBODY NSBODY: integer: The number of SIMO bodies NSBODY>0 7.2.1. SIMO Body identification, location and optional artificial stiffness The input lines SIMO Body identification through SIMO Body artificial stiffness and must be given in one block for each of the NSBODY SIMO bodes. SIMO Body identification, SIMO body node identification and location option CHBODY CHBODY_NOD_ID CHLOCA_OPT CHBODY: character(8): SIMO Body identification CHBODY_NOD_ID: character(8), default: SBDY<body_nr>: SIMO body node identifier, where <body_nr> is the order in which the SIMO bodies are specified here. Thus the first SIMO body specified will have a default SIMO body node identifier of SBDY1. CHLOCA_OPT: character(4), default: ELEM: SIMO body location option CHLOCA_OPT='ELEM': The SIMO body node is a slave of a node specified by line, segment, element and end node CHLOCA_OPT='NODE': The SIMO body node is a slave of a node specified by line, segment and node CHLOCA_OPT='POSI': The SIMO body node is a free or fixed node that is not attached to the rest of the system. The position of the node is specified below. A connection may be made by making a supernode a slave of the body node or by using a boundary change in static or dynamic analysis. CHBODY_NOD_ID is the SIMO body node identifier which is set automatically if not specified by the user. The automatic naming convention is based on concatenating the character string SBDY and the RIFLEX internal number of the SIMO body starting at 1 for the first SIMO body. SIMO Body location, orientation and artificial stiffness option for CHLOCA_OPT=ELEM The input line below must be specified for the option CHLOCA_OPT=ELEM or if CHBODY_NOD_ID and CHLOCA_OPT are omitted. LINE-ID ISEG IEL IEND ROTX ROTY ROTZ IST LINE-ID: character(8): Reference to line identifier ISEG: integer: Local segment number within line IEL: integer: Local element number within segment IEND: integer: Element end (1 or 2) ROTX0: real, default: 0: Rotation around X-axis \(\mathrm {[deg]}\) ROTY0: real, default: 0: Rotation around Y-axis \(\mathrm {[deg]}\) ROTZ0: real, default: 0: Rotation around global Z-axis \(\mathrm {[deg]}\) IST: integer, default:0: Artificial stiffness option IST=0: No artificial stiffness IST=1: Artificial stiffness is specified The SIMO body node will be a slave of the node at LINE-ID ISEG IEL IEND. ROTX0, ROTY0 and ROTZ0 are the Euler angles taken in the order ROTZ0 → ROTY0 → ROTX0. SIMO Body location, orientation and artificial stiffness option for CHLOCA_OPT=NODE The input line below is specified for the option CHLOCA_OPT=NODE only. LINE-ID ISEG ISEGNOD ROTX ROTY ROTZ IST LINE-ID: character(8): Reference to line identifier ISEG: integer: Local segment number within line ISEGNOD: integer: Local node within segment ROTX0: real, default: 0: Rotation around X-axis \(\mathrm {[deg]}\) ROTY0: real, default: 0: Rotation around Y-axis \(\mathrm {[deg]}\) ROTZ0: real, default: 0: Rotation around global Z-axis \(\mathrm {[deg]}\) IST: integer, default:0: Artificial stiffness option IST=0: No artificial stiffness IST=1: Artificial stiffness is specified The SIMO body node will be a slave of the node at LINE-ID ISEG ISEGNODD. ROTX0, ROTY0 and ROTZ0 are the Euler angles taken in the order ROTZ0 → ROTY0 → ROTX0. SIMO Body position, orientation, boundary conditions and artificial stiffness option for CHLOCA_OPT=POSI The input lines in this section are specified for the option CHLOCA_OPT=POSI only. The first input line reads: CHBOUND IST CHBOUND: character(4), default: FREE: Boundary condition for all nodal DOFs CHBOUND=FREE: All DOFs for the SIMO body node are free CHBOUND=FIXEd: All DOFs for the SIMO body node are initially fixed IST: integer, default:0: Artificial stiffness option IST=0: No artificial stiffness IST=1: Artificial stiffness is specified The next input line defines the initial position and orientation of the SIMO body: XG0 YG0 ZG0 ROTX0 ROTY0 ROTZ0 XG0: real, default: 0: Initial global X-coordinate of the SIMO body node \(\mathrm {[L]}\) YG0: real, default: 0: Initial global Y-coordinate of the SIMO body node \(\mathrm {[L]}\) ZG0: real, default: 0: Initial global Z-coordinate of the SIMO body node \(\mathrm {[L]}\) ROTX0: real, default: 0: Initial rotation around X-axis \(\mathrm {[deg]}\) ROTY0: real, default: 0: Initial rotation around Y-axis \(\mathrm {[deg]}\) ROTZ0: real, default: 0: Initial rotation around global Z-axis \(\mathrm {[deg]}\) ROTX0, ROTY0 and ROTZ0 are the Euler angles taken in the order ROTZ0 → ROTY0 → ROTX0. If CHBOUND=FIXEd, an additional input line defining the initial and orientation of the SIMO body: at the final static equilibrium must be included. However, the values must at present be identical to the values specified for the initial configuration: XG YG ZG ROTX ROTY ROTZ XG: real, default: XG0: Global X-coordinate of the SIMO body node at final static equilibrium \(\mathrm {[L]}\) YG: real, default: YG0: Global Y-coordinate of the SIMO body node at final static equilibrium \(\mathrm {[L]}\) ZG: real, default: ZG0: Global Z-coordinate of the SIMO body node at final static equilibrium \(\mathrm {[L]}\) ROTX: real, default: ROTX0: Rotation around X-axis at the final static equilibrium \(\mathrm {[deg]}\) ROTY: real, default: ROTY0: Rotation around Y-axis at the final static equilibrium \(\mathrm {[deg]}\) ROTZ: real, default: ROTZ0: Rotation around global Z-axis at the final static equilibrium \(\mathrm {[deg]}\) The SIMO body node is a free or fixed node at the specified position that is not attached to the system. A connection may be made by making a supernode a slave of the SIMO body node or by using a boundary change in static or dynamic analysis. ROTX, ROTY and ROTZ are the Euler angles taken in the order ROTZ → ROTY → ROTX. SIMO Body artificial stiffness This input line is given if IST=1 only. STX STY STZ SRX SRY SRZ STX: real, default: 0: Stiffness in global X-direction \(\mathrm {[F/L]}\) STY: real, default: 0: Stiffness in global Y-direction \(\mathrm {[F/L]}\) STZ: real, default: 0: Stiffness in global Z-direction \(\mathrm {[F/L]}\) SRX: real, default: 0: Stiffness around global X-direction \(\mathrm {[FL/deg]}\) SRY: real, default: 0: Stiffness around global Y-direction \(\mathrm {[FL/deg]}\) SRZ: real, default: 0: Stiffness around global Z-direction \(\mathrm {[FL/deg]}\) The artificial stiffness is applied in static analysis only for improving the convergence properties. It does not affect the final static solution. Boundary change in static or dynamic analysis is often a better alternative than using artificial stiffness. 7.3. Termination of input data Do not forget the END input line if this is the last data group given in this INPMOD run. See also Termination of input data. END 8. Additional Features This group gives a description of special features that normally are not used in analysis of flexible riser system. 8.1. Local element axis definition Additional to Arbitrary system AR. This data group may be used to specify a reference vector that is used to determine the initial orientation of the local y- and z-axes of beam elements. If a local element axis is not specified for an element, the default procedure described in Line, line type and supernode connectivity is used. This data group must be given for all cross sections with hydrodynamic loads model: Net properties and hydrodynamic added mass coefficients for net (HNET) as the reference vector and the element’s x-axis define the net plane during static and dynamic analysis. 8.1.1. Data group identifier, one input line LOCAl ELEMent AXIS 8.1.2. Number of input lines for special axis definition, one input line NAXDEF NAXDEF: integer: Number of input lines for special axis definition 8.1.3. Specification of reference vector for definition of the local axes in the initial configuration, NAXDEF input lines LINE-ID ISEG IEL RNX RNY RNZ LINE-ID: character(8): Line identifier. ISEG: character/integer: Local segment number within line LINE-ID = ``0’ or `ALL' means all segments in specified line IEL: character/integer: Local element number within segment ISEG = `0’ or `ALL' means all elements in specified segment `ISEG RNX: real: X-component of the reference vector RNY: real: Y-component of the reference vector RNZ: real: Z-component of the reference vector The reference vector is to be given in global system. The element’s local x-axis goes from end 1 to end 2 of the element. The element’s local z-axis is given by the cross product between the element’s local x-axis and the reference vector. The element’s local y-axis is given by the cross product of the local z-axis and the local x-axis. The reference vector must not be parallel with the element’s initial x-axis. For cross sections with hydrodynamic load type: Net properties and hydrodynamic added mass coefficients for net cross sections, the reference vector must be chosen so that it is not parallel to the element’s x-axis during the static and dynamic analyses. For beam elements, the element axes are found at the stress-free configuration and will subsequently follow the element. 9. Additional Input Files 9.1. Specification of internal control system for blade pitch and electrical power 9.1.1. Description of internal control system The implemented control system is based on the choice of a conventional variable-speed, variable blade-pitch-to-feather configuration wind turbine and consists of two basic control systems: a generator torque controller and a full span rotor-collective blade-pitch controller. The two control systems are designed to work independently. The objective of generator-torque controller is to maximize power capture below the rated operation point. The goal of the blade-pitch controller is to regulate generator speed above the rated operation point. Control measurement filter Both the generator torque and blade pitch controllers use the generator speed as the sole feedback input. A recursive, single-pole low-pass filter exponential smoothing to reduce the high frequency excitation of the control systems is provided. The discrete time recursion equation for this filter is \(\mathrm {\omega _{f.k}=\alpha \omega _{f.k-1}+(1-\alpha )\omega _K}\) where \(\mathrm {\alpha =exp((-\Delta t)/(TC))}\) where \(\mathrm {\Delta t}\) is the discrete time step, \(\mathrm {TC}\) is the filter time constant, \(\mathrm {\alpha }\) is the low-pass filter coefficient \(\mathrm {\omega _f}\) is low pass filtered generator speed and \(\mathrm {k}\) indicates the time step. The relation between the filter time constant and the cut off (corner) frequency \(\mathrm {f_C}\) is given by: \(\mathrm {TC=\frac{1}{2\pi f_C}}\) Generator torque controller The generator torque is computed as a tabulated function of the filtered generator speed, incorporating five control regions: 1, 1 1/2, 2, 2 1/2 and 3 as illustrated in the figure `Illustration of the variable speed controller - Generator torque versus generator speed' below. Region 1 is a control region before cut-in wind speed, where the generator torque is zero and no power is extracted. Instead, the wind is used to accelerate the rotor for start-up. Region 2 is a control region for optimizing power capture. Here, the generator torque is proportional to the quare of the filtered generator speed to maintain a constant (optimal) tip-speed ratio. In region 3, the generator torque or the generator power is held constant. In case of constant power the generator torque is inversely proportional to the filtered generator speed. Blade pitch controller In region 3, the collective blade pitch angle commands are computed using a gain-scheduled proportional-integral (PI) control on the speed error between the filtered generator speed and the rated generator speed. The PI regulator is represented by the Laplace transform: \(\mathrm {(K(s+a))/s}\) where \(\mathrm {K}\) and \(\mathrm {a}\) are the proportional gain and the integrator gain. The corresponding and simple regulator algorithm is given by \(\mathrm {R(t+\Delta t)=R(t)+\Delta \omega \Delta t}\) \(\mathrm {\theta =K_P\Delta \omega aK_PR(t\Delta t)=K_P\Delta \omega K_IR(t\Delta t)}\) where \(\mathrm {\Delta t}\) is the regulator time step, \(\mathrm {\Delta \omega }\) is the rotor speed error, i.e. the difference between filtered rotor speed and rated rotor speed. \(\mathrm {R}\) is accumulated time integrated speed error which is set to zero for filtered generator speed less than rated generator speed. \(\mathrm {\theta }\) is the instructed/required collective blade pitch angle. Gain scheduling Gain scheduling is introduced because the optimal proportional and integrator gains are dependent of the blade pitch angle. At each step the gain will be corrected based on the pitch angle applied in the previous step. The user may specify a gain scheduling law or choose to apply the default law presented in the table `The defaults gain scheduling law'. For intervening generator speeds, linear interpolation is used. Illustration of the variable speed controller - Generator torque versus generator speed. The defaults gain scheduling law Collective Blade Pitch Angle Correction Factor \(\mathrm {[deg]}\) \(\mathrm {[1]}\) 0.0 1.00 5.0 0.56 10.0 0.39 15.0 0.30 20.0 0.24 90.0 0.05 9.1.2. Input description Engine Data, Generator, One input line GBRATIO GNS_RATE TRQ_RATE RGN3MP GBRATIO: real >= 1: Gear box ratio. Number of rotations of the high speed shaft for one rotation of the low speed shaft, i.e. generator versus rotor GNS_RATE: real > 0: Rated generator speed \(\mathrm {[rad/T]}\) TRQ_RATE: real > 0: Rated generator torque \(\mathrm {[FL]}\) RGN3MP: real: Minimum pitch angle for which electrical torque versus generator speed will stay in region 3 \(\mathrm {[deg]}\) Engine Data, Generator One input line RGN15SP RGN20SP RGN25SP RGN30SP TRQRGN2 RGN15SP: real > 0: Transitional generator speed between region 1 and 1 1⁄2. Start speed for extracting power. \(\mathrm {[rad/T]}\) RGN20SP: real > RGN15SP: Transitional generator speed between region 1 1⁄2 and 2. \(\mathrm {[rad/T]}\) RGN25SP: real > RGN20SP: Transitional generator speed between region 2 and 2 1⁄2 \(\mathrm {[rad/T]}\) RGN30SP: real > RGN25SP: Transitional generator speed between region 2 1⁄2 and 3 \(\mathrm {[rad/T]}\) TRQRGN2: real > 0: Generator torque constant in region 2\(\mathrm {[FL/(rad/T)^2]}\) Engine Data, Generator One input line METRGN3 METRGN3: character(6): Method for power extraction in region 3 POWER: Constant Power TORQUE: Constant Torque Engine Data, Generator actuator One input line TRQ_MAXRAT TRQ_MAX TRQ_MAXRAT: real > 0: Maximum torque rate \(\mathrm {[FL/T]}\) TRQ_MAX: real > 0: Maximum electrical torque \(\mathrm {[FL]}\) Blade pitch Controller/actuator One input line PC_MINPIT PC_MAXPIT PC_MAXRAT PC_MINPIT: real: Minimum pitch setting in pitch controller \(\mathrm {[deg]}\) PC_MAXPIT: real: Maximum pitch setting in pitch controller \(\mathrm {[deg]}\) PC_MAXRAT: real: Maximum pitch rate \(\mathrm {[deg/T]}\) Controller Data (PI regulator : K(s+a)/s One input line KP KI G_SHEDULE TC KP: real: Proportional gain at zero pitch angle KI: real: Integral gain G_SHEDULE: character: Gain scheduling; Default or Tabulated = D: Default = T: Tabulated TC: real: Time constant for first order low pass filter, \(\mathrm {TC=1/\omega }\) \(\mathrm {[s/rad]}\) Input refer to low-speed shaft Gain scheduling (G_SHEDULE=T) One input line GSNumber NOP_GST: integer > 0 : Number of points in gain scheduling table. The maximum is currently 30. Gain Scheduling; Gain correction factors. NOP_SGST input lines BPITCH GCF BPITCH: real: Blade pitch angle \(\mathrm {[deg]}\) GCF: real: Gain correction factor Controller sample interval DTSAMP DTSAMP: real > 0: Controller sample interval \(\mathrm {[T]}\) Example input for control system ‘ 'gbratio gnsrate trq_rate rgn3mp 97 122.911 43.09355 1.0 'rgn15sp rgn20sp rgn25sp rgn30sp trqrgn2 70.16 91.208 119.0137 121.6805 0.002332288 'metrgn3 TORQUE 'trq_maxrat trq_max 15.0 43.09355 'pc-minpit pc-maxpit pc-maxrat 1. 90. 8. 'kp ki g_shedule TC 0.006275604 0.000896514 D 0.6366 ‘ ‘dtsamp 0.0125 9.2. Interface for external wind turbine blade pitch, electrical power and optionally nacelle yaw control system 9.2.1. Control system files needed for RIFLEX simulation The input to RIFLEX for the external wind turbine control system requires the (path and) name of the executable .jar file, the class to be used within that .jar file, and the (path and) name of a file which may contain input data for the external control. See Wind turbine specification. For example, the input may be: 'jarName MyController.jar 'className no.marintek.wind.control.WindTurbineController 'config ControlInput.txt Bladed style DLL controller: A Bladed style external controller may alternatively be used. See Bladed style controller. Note that currently only the measurements and feedback specified in the interface description will be available in the DLL. A DLL (or Linux .so file) may be specified by giving ";" as the .jar file and "no.marintek.wind.control.bladed.BladedController" as the class name. The third line is used to specify a file containing additional inputs to the wrapper; e.g. DLL (or .so) name, gear box ratio. For example, the input may be: 'jarname ; 'classname no.marintek.wind.control.bladed.BladedController 'config file controller.properties An example configuration file: #Properties configFilePath=DISCON.IN controllerDllPath=DISCON.dll gearBoxRatio=50.0 elementNum=1 elementEnd=2 This configuration file will be generated by Sima. If running without SIMA, the configuration file must be created by the user. To pass the "Yaw bearing My" signal to the controller, specify the tower top element as the only additional element measurement and specify at which end the bending moment is taken; i.e. elementEnd=1 or elementEnd=2. Currently the tower top must be the only additional element measurement and elementNum, the index to the measured element, is not used. 9.2.2. Description of control system interface See Java Based Controller Interface. 9.3. Specification of internal control system for nacelle yaw 9.3.1. Description of internal control system Only internal yaw control is currently available. See Wind turbine specification for a description of how to set up the model to use yaw control. The yaw error is found as the relative angle between the instantaneous wind at the hub and the orientation of the shaft. The controller starts aligning the rotor- nacelle assembly when a user defined threshold of the integral of the squared yaw error is reached. This gives more active response to fast changes in the yaw misalignment. The controller uses a constant, user defined yaw rate to get back to zero misalignment, or to a user defined yaw error. The input yaw error and the output yaw angle are low pass filtered with a fast and a slow corner frequency, respectively. The yaw controller logics follow the yaw rate controller described by Mulders and van Wingerden (2018). Yaw controller configuration input version number yawconfinput_ver yawconfinput_ver: integer > 0: Yaw controller configuration input version number. Current version is 1. Yaw controller time step DT_yawcontrol DT_yawcontrol: real > 0: Yaw controller sample interval \(\mathrm {[T]}\) Yaw set point YawErrSetPoint YawErrSetPoint: real [-180, 180]: Specified nacelle yaw misalignment \(\mathrm {[deg]}\) Yaw rate YawRate YawRate: real > 0: Rotational velocity for yaw engine \(\mathrm {[deg/T]}\) Yaw misalignment threshold YawErrThresh YawErrThresh: real > 0: Integral threshold for activation of yaw engine \(\mathrm {[deg^2T]}\) Fast filter corner period for low pass filtering T_LPfiltFast T_LPfiltFast: real > 0: Fast filter corner period for input signal \(\mathrm {[T]}\) Slow filter corner period for low pass filtering T_LPfiltSlow T_LPfiltSlow: real > 0: Slow filter corner period for output signal \(\mathrm {[T]}\) Figure 26. Definition of (positive) yaw misalignment between wind direction and shaft orientation Example input for internal yawcontrol system 'yawconfinput_ver 1 'DT_yawcontrol Yaw controller time step (s) 0.005 'YawErrSetPoint Yaw set point (deg) 0. 'YawRate Controller yaw rate, (deg) 0.5 'YawErrThresh Yaw misalignment threshold, (deg^2 s) 1.0 'T_LPfiltFast Fast filter corner period for low pass filtering (s) 1.0 'T_LPfiltSlow Slow filter corner period for low pass filtering (s) 60.0 9.4. Airfoil library file The airfoil library file contains the coefficient data required for aerodynamic calculations. All of the airfoils which are referred to must be included in a single file; i.e. whether or not they are part of a wind turbine. The airfoils may be listed in any order. Airfoils which are not referred to will be ignored. Comment lines may be included on any line, as in other input files. Blank lines between airfoils will at present be ignored, but it is recommended to use comment lines instead. Blank lines at other locations in the file will be interpreted as input lines and the default values will be used. For each airfoil, the following data groups must be given. 9.4.1. Airfoil identifier CHAIRF CHAIRF: character(32): Airfoil identifier 9.4.2. Airfoil table extension parameters IATEXT ATAIL1 ATAIL2 ANOSE1 ANOSE2 RNOSEC IATEXT: integer: Flag for extending the table to deep stall regime = 1: Extend the table = 0: Do not extend the table ATAIL1: real: tail angle between a line perpendicular to the flow and the line from the tip of the wedge, low (negative) angles of attack \(\mathrm {[deg]}\) ATAIL2: real: as ATAIL1, but for high (positive) angles of attack \(\mathrm {[deg]}\) ANOSE1: real: nose angle between a line perpendicular to the flow and the line from the tip of the wedge, low (negative) angles of attack \(\mathrm {[deg]}\) ANOSE2: real: as ANOSE1, but for high (positive) angles of attack \(\mathrm {[deg]}\) RNOSEC: real: ratio of the nose radius to the chord of the airfoil \(\mathrm {[1]}\) 9.4.3. Airfoil table size parameters NRE NGEO DSIN NRE: integer: Number of Reynolds numbers with coefficient data NGEO: integer, default: 0: number of points describing the airfoil geometry DSIN: integer, default: 0: flag for user-defined dynamic stall initialization parameters = 1: User-defined dynamic stall initialization parameters will be given below = 0: No user-defined dynamic stall initialization parameters will be given 9.4.4. Airfoil data One block per Reynolds number, i.e. NRE data blocks If only one block is given, the data will be used for all Reynolds numbers. For Reynolds numbers outside the range of Reynolds numbers given, the data for the closest Reynolds number will be used; i.e. flat extrapolation. Reynolds number RE NAOA RE: real: Reynolds number for this block \(\mathrm {[1]}\) NAOA: integer: number of angle-of-attack points for this data block Dynamic stall initialization parameters To be given only if DSIN=1 AOA0 DCLDA1 DCLDA2 AOAFS1 AOAFS2 AOA0: real: the angle of attack where there is zero lift, upcrossing \(\mathrm {[deg]}\) DCLDA1: real: maximum slope of the lift curve in the linear region above AOA0 \(\mathrm {[1/deg]}\) DCLDA2: real: maximum slope of the lift curve in the linear region below AOA0 \(\mathrm {[1/deg]}\) AOAFS1: real: angle of attack corresponding to full separation above AOA0 \(\mathrm {[deg]}\) AOAFS2: real: angle of attack corresponding to full separation below AOA0 \(\mathrm {[deg]}\) The dynamic stall initialization parameters are shown in the figure `Illustration of dynamic stall initialization parameters' below. Figure 27. Illustration of dynamic stall initialization parameters. Aerodynamic coefficients NAOA input lines AOA CL CD CM AOA: real: angle of attack \(\mathrm {[deg]}\) CL: real: non-dimensional lift coefficient \(\mathrm {[1]}\) CD: real: non-dimensional drag coefficient \(\mathrm {[1]}\) CM: real: non-dimensional moment coefficient \(\mathrm {[1]}\) 9.4.5. Normalized airfoil geometry NGEO input lines, to be given only if NGEO > 0. Airfoil coordinates are normalized by the chord length, with the origin at the aerodynamic reference point. Points around the full airfoil should be given, i.e. several lines may have the same XGEO and different values for YGEO. XGEO YGEO XGEO: real: x coordinate of geometry point, normalized by chord length. YGEO: real: y coordinate of geometry point, normalized by chord length. 10. References Mulders, S. P., and J. W. van Wingerden (2018): Delft Research Controller: an open-source and community-driven wind turbine baseline controller. Journal of Physics, Conference Series. Vol. 1037. No. 3.