Model Structure
MoorDyn v2 models the dynamics of mooring structures in an object-oriented approach. There are four main object types: Lines, Points, Rods, and Bodies. MoorDyn v1 only contained Lines and Points. Lines are the fundamental discretized lumped-mass modeling component. Points and Rods provide a means of connecting lines with additional 3- and 6-DOF properties (respectively), and Bodies provide a way to create more complex 6-DOF rigid-body assemblies. These objects have predefined ways or interacting. Kinematics are passed from the top down in and are used to calculate the forces which are passed up back to the outside program or to output channels. This hierarchy is shown below:
Each object type and its key parameters are detailed in the following sections.
Note: The variables described below are for MoorDyn-C. MoorDyn-F has the same general structure as MoorDyn-C, with similar variables. The biggest difference between the codes underlying modeling is that in MoorDyn-C quaternions are used to describe the position and orientation of 6DOF objects, while in MoorDyn-F traditional Euler angles are used. To read more about quaternions and their implementation, refer to the theory section.
Lines
MoorDyn uses a lumped-mass approach to discretize the dynamics over the length of the mooring line. A line is broken up into N evenly sized line segments connecting N+1 node points. The indexing starts at the anchor (or lower end), with the anchor node given a value of zero, and the cable segment between nodes 0 and 1 given an index of 1/2.
The model uses a right-handed inertial reference frame with the z axis being measured positive up from the water plane, consistent with NREL’s FAST simulator. Each node’s position is defined by a vector r. Each segment of the cable has identical properties of unstretched length, diameter, density, and Young’s modulus. Different cables can have different sets of properties, and cables can be connected together at the ends, enabling mooring systems with interconnected lines.
Hydrodynamic loads are calculated directly at the node points rather than at the segment centers. This ensures damping of transverse cable vibrations having a wavelength of twice the cable segment length. To approximate the cable direction at the node points, the cable tangent at each node is assumed to be the average of the tangent directions of the two adjacent cable elements. Aside from this detail, the formulation of the mooring model is fairly standard. Further technical details and validation results are available in the theory section.
Bending stiffness is a recent capability addition in MoorDyn-C (it is not yet implemented in MoorDyn-F). The word cable is used to refer to a Line object with nonzero bending stiffness.
MoorDyn reads a user defined table of line types from the input file to describe the cross-sectional (or per-meter) properties of the mooring lines. Each line type has an alphanumeric name to identify it and contains all the properties aside from length and discretization that are needed to describe a mooring line in MoorDyn.
Line objects have the following variables:
General:
env: a pointer to the global environment object
waves: a pointer to the global object storing information about waves/currents
t: the simulation time, as a real
seafloor: a pointer to the global object storing the 3d seafloor information
Specific to each Line:
N: int indicating the number of line segments in N
UnstrLen: real indicating the unstretched length of the line
d: real describing the line diameter
rho: real describing the linear density of the line
E: Young’s modulus of the line (Pa)
EI: real Bending stiffness (Nm^2)
c: real damping coefficient (Ns). This can be the literal damping coefficient, or a negative value representing fraction of critical damping
Can: real normal added mass coefficient
Cat: real axial added mass coefficient
Cdn: real normal drag coefficient w/r/t frontal area
Cdt: real axial drag coefficient w/r/t surface area
BAin: real axial-internal damping
A: real cross sectional area
nEApoints: number of values in stress-strain lookup table
stiffXs: x-array for stress-strain lookup table
stiffYs: y-array of reals for stress-strain lookup table
nEIpoints: number of values in bent-stiffness lookup table
bstiffXs: x-array for bent-stiffness lookup table
bstiffYs: y-array of reals for bent-stiffness lookup table
nCpoints: number of values in stress-strain rate lookup table (0 for constant c)
dampXs: x array for stress-strain rate lookup table
dampYs: y array for stress-strain rate lookup table
State:
r: a vector of 3D node positions for the nodes representing the line.
rd: a vector of 3D velocities for each of the nodes representing the line
Dynamics:
q: a vector of 3D tangent vectors for each node
qs: a vector of 3D tangent vectors for each segment
l: a vector of unstretched line segment lengths (as reals)
lstr: a vector of stretched segment lengths (as reals)
ldstr: a vector of reals describing the rate of stretch for each segment
Kurv: a vector of reals describing the curvature at node points
M: a vector of 3x3 matrices describing the mass+added mass of each node in the line
V: a vector of line-segment volumes as reals
F: a vector of reals indicating volume of each segment submerged (1 = fully submerged, 0 = out of water)
Forces are computed at every node in the line. Hence, all line forces are represented as vectors of 3D force vectors:
T: a vector of 3D vectors describing segment tensions
Td: a vector of 3D vectors describing segment Damping forces
Bs: a vector of 3D vectors describing bending stiffness forces
W: a vector of 3D vectors describing weight (gravity) forces
Dp: a vector of 3D vectors describing node drag (transversal)
Dq: a vector of 3D vectors describing node drag (axial)
Ap: a vector of 3D vectors describing added-mass forcing (Transversal)
Aq: a vector of 3D vectors describing mass-forcing (axial)
B: a vector of 3D vectors describing node bottom contact force
Fnet: a vector of 3D vectors describing total force on each node in the line
Misc:
endTypeA, endTypeB: indicates whether ends are pinned or cantilevered to rod
endMomentA, endMomentB: 3D moment vectors at ends, to be applied to attached Rod/Body
outfile: pointer to outfile to write to
channels: which channels to write to the outfile
Points
Point objects attach to the ends of Lines and can be used to connect Lines to other things or to each other. (In MAP and older versions of MoorDyn, these objects were called Connections or Nodes). A Point has three degrees of freedom and can have any number of Lines attached to it. There are three types of Points:
Fixed/Anchor/Body: their location is fixed to an XYZ coordinate (stationary) or a XYZ coordinate in the Body reference frame. They can be used as anchor points or to attach mooring lines to a Body.
Coupled/Vessel: they move under the control of the driver program/script. They can be used as fairlead points when the platform is modeled externally. See the coupling documentation.
Free/Point: they are free to move according to the forces acting on them, which includes the tensions of attached lines as well as their own self weight and buoyancy, if applicable.
Free Points facilitate more advanced mooring systems. They can be used to connect two or more mooring lines together, to create multi-segmented lines or junctions such as in a bridle mooring configuration. If a free Point is given nonzero volume or mass properties, it can also represent a clump weight or float.
In MoorDyn-C, “Points” are represented as Point objects. Currently, every line must have 2 points at each endpoint (Rod ends serve as points). Point objects expose a public member, Point::attachment, that contains 1) a pointer to the Line object attached to the point and 2) a field indicating which “end” (A or B) of the line is attached to the point.
Points Objects have the following variables:
General:
env: a pointer to a global struct holding environmental settings
waves: a pointer to a global object representing Waves in the system
t: the simulation time, as a real
seafloor: a pointer to the global object storing the 3d seafloor information
Specific to each Point:
attached: a vector of attachments, describing all lines attached to the point
pointM: the mass of the point as a real
pointV: the volume of the point as a real
pointF: a 3D vector of forces on the point
pointCdA: prag coefficient of the point
pointCa: pdded mass coefficient of the point
State:
r: 3D node position
rd: 3D node velocity
Dynamics:
r_ves: 3D fairlead position for coupled points
rd_ves: 3D fairlead velocity for coupled points
FNet: 3D force vector on node
M: 3x3 mass + added mass matrix
Acc: 3D node acceleration vector
Misc:
number: point ID (unique int)
type: point type, one of moordyn::Point::types
Rods
Rod objects provide an option for rigid cylindrical elements within a mooring system. They have similar modeling details as Lines except for their rigidity, which gives them six degrees of freedom. Like Lines, they are divided into nodes at which weight, buoyancy, seabed contact, and Morison-based hydrodynamic forces are calculated. Unlike Lines, their internal forces are not calculated. Generally, more nodes in a rod increase the accuracy of rod dynamics calculations. The end nodes of a rod are available for attachment of lines (specified as “R2A” for end A of Rod 2) and can be set up in the input file.
Rods can have 6, 3, or 0 DOF.
Fixed: Rods are full constrained, and their movement is defined by that of a body, the ground, or a coupling point (0 DOF).
Coupled: They move under the control of the calling program/script (constrained in all 6 DOF). See the coupling documentation.
Free: Rods are unconstrained to move in all 6 DOF.
Pinned: The rod end A translational movement is fixed while the rotational movement about end A is free.
Coupled pinned: The rod end A translational movement is coupled while the rotational movement about end A is free.
Pinned or Fixed Rods attached to a body (e.g. body 1) are labelled “Body1Pinned” or “Body1”. Rods attached to bodies have their coordinates defined in the body reference frame Pinned or fixed rods that serve as a coupling point are labelled “CoupledPinned” or “Coupled”.
A special case exists if a Rod is specified with zero elements: in that case it is given zero length, and its end B coordinates in the input file are instead interpreted as vector components to describe its direction vector. This case is meant for making cantilever points of a line with bending stiffness. A fixed zero-length rod can be used to make a cantilever point of a power cable to the ground, a body, or a coupling point. A free zero-length rod can be used to join two different types of power cable segments, and it will pass moments between the cable segments without adding any mass or other characteristics.
Rod objects have the following variables:
General:
env: a pointer to a global struct holding environmental settings
waves: a pointer to a global object representing Waves in the system
t: the simulation time, as a real
seafloor: a pointer to the global object storing the 3d seafloor information
Attachments:
attachedA: A vectors of lines attached to the end point A of the rod
attachedB: A vector of lines attached to the end point B of the rod
Specific to each rod:
N: The number of rod segments
UnstrLen: The constrained length of the rod
q0: The original rod orientation vector
d: Rod diameter
rho: Rod linear density
Can: Normal added mass coefficient
Cat: Axial added mass coefficient
Cdn: Normal drag coefficient (unused)
Cdt: Axial drag coefficient (unused)
CdEnd: Rod end drag coefficient
CaEnd: Rod end added mass coefficient
State:
r7: A quaternion describing the rods position
v6: Rod 6dof velocity[vx,vy,vz,wx,wy,wz] (end A velocity and rotational velocities about unrotated axes)
vel7: A quaternion describing the rods velocity that when integrated gives r7. It is equivalent to v6.
Dynamics:
acc6: Final 6 DOF rod acceleration used for outputs. When integrated gives v6.
r: 3D vector of node positions
rd: 3D vector of node velocities
q: Unit tangent vector for the rod
l: Rod segment lengths
M: 3x3 node mass and added mass matrix
V: Segment volumes
r_ves: 6D vector of fairlead position for coupled rods
rd_ves: 6D vector of fairlead velocity for coupled rods
Forces:
FextA: A vector of external forces from attached lines on/about end A
FextB: A vector of external forces from attached lines on/about end B
Mext: A vector of external moments (from attached cables or waterplane hydrostatic moment)
F6net: Total force and moment about end A (excluding inertial loads) that Rod may exert on whatever it’s attached to
M6net: total 6x6 mass matrix about end A of Rod and any attached Points
W: A vector of node dry weights
Bo: A vector of node buoyancy
Pd: A vector of the Froud-Krylov force
Dp: A vector of node drag forces (axial)
Dq: A vector of node drag forces (transversal)
Ap: A vector of node added mass (transversal)
Aq: A vector of the long wave diffraction force
B: A vector of node bottom contact force
Fnet: A vector of total force on node (depreciated)
Wave stuff:
VOF: VOF submergence scalar for each node (1 = fully submerged, 0 = out of water)
h0: instantaneous axial submerged length
Misc:
outfile: pointer to the main outfile for the rod
channels: which channels to write to the outfile
Bodies
Body objects provide a generic 6 DOF rigid-body representation based on a lumped-parameter model of translational and rotational properties (e.g. hydrodynamic drag and added mass coefficients). Rod elements can be added to bodies and mooring lines can be attached at any location, allowing a wide variety of submerged structures to be integrated into the mooring system. The body itself does not have a defined geometry (the volume is only used in buoyancy calculations), rather its geometry is defined by the rods attached to it. Therefore, for simplicity, any hydrodynamic loads associated with a body on its own (with no attached objects) are always calculated as though the body is fully submerged. Partial submergence is handled in any attached objects. Aside from contributions which might come from incorporated Rod objects or attached Point and Line objects, the core Body object properties are as follows:
mass, and center of mass
volumetric displacement (assumed to be at reference point)
mass moment of inertia about each axis
hydrodynamic drag coefficient in each direction
rotational hydrodynamic drag coefficient about each axis
added mass coefficient in each direction
added mass moment of inertia coefficient about each axis
There are three possible types for bodies:
Free: the body kinematics are computed by MoorDyn based on the applied loads and inertia
Fixed: the body is fixed, either to a particular location or to a connected, moving entity.
Coupled: the body kinematics are controlled by the calling program.
Coupled pinned: The body’s translational movement is coupled while the rotational movement is free.
Body objects have the following variables:
General:
env: a pointer to a global struct holding environmental settings
waves: a pointer to a global object representing Waves in the system
Attachments:
attachedP: a vector of pointers to point objects, indicating all the points attached to the body
attachedR: a vector of pointers to Rod objects attached to the body.
rPointRel: a vector of 3d vectors describing the attachment points locations for Points
r6RodRel: a vector<vec6> of 6D vectors describing the attachment points and orientation of each rod.
Body Properties. Note that these are all set to zero for all Body types other than FREE, as they are not relevant to COUPLED or FIXED scenarios:
body_r6: 6D reference point for the body.
body_rCG: 3D location of body center-of-gravity
bodyM: real number describing the body’s mass
bodyV: real number describing the body’s displaced volume
bodyI: 3d Vector describing the inertia diagonal components of the body
bodyCdA: 6D vector describing the body’s drag coefficients
bodyCa: 6D vector describing added-mass coefficients
State:
r7: quaternion describing body’s position
v6: 6D vector describing body’s velocity
dPos: quaternion describing the body’s velocity that when integrated gives r7. It is equivalent to v6.
Dynamics and Forces:
a6: 6D vector of body acceleration that when integrated gives v6.
r_ves: 6D vector describing fairlead position if a coupled body (may be different than overall r6)
rd_ves: 6D vector describing fairlead velocity if a coupled body (may be different than overall v6)
F6net: 6D vector describing total force/moment vector on node
M: 6x6 matrix representing total body mass + added mass
M0: 6x6 matrix representing ‘starting mass’ matrix of body, not taking into account rod elements.
OrMat: 3x3 matrix representing orientation of the body
Misc:
number: a unique int id identifying the body
type: FREE, COUPLED, or FIXED, describing the “type” of body to be modeled
outfile: pointer to the main output file for the body