Mooring Lines¶

OASIS models mooring lines as dynamic finite elements using a Spectral Element Method (SEM). Lines connect pairs of Boundary Condition Points (BCPs) and can interact with the seabed.

Modelling Approach¶

Each mooring line is discretised into finite elements with high-order Lagrange polynomials (spectral elements). The governing equations solve for:

Position of each node in 3D
Tension along the line
Contact forces with the seabed
Friction forces (if enabled)

Initial line configuration is computed by either:

Catenary solution (flagStatic = 0) — analytical, fast
Newton's method (flagStatic = 1) — numerical, handles complex geometry

Line Properties¶

Each line is defined by its physical and numerical parameters:

Parameter	Symbol	Units	Description
`lineType`	—	—	1 = dynamic, 2 = quasi-static
`nNodes`	\(N\)	—	Number of finite element nodes
`p`	\(p\)	—	Polynomial order per element
`L`	\(L\)	m	Unstretched line length
`rho0`	\(\rho_0\)	kg/m	Mass per unit length
`d`	\(d\)	m	Line diameter
`Cmn`	\(C_{mn}\)	—	Normal added mass coefficient
`Cdn`	\(C_{dn}\)	—	Normal drag coefficient
`Cdt`	\(C_{dt}\)	—	Tangential drag coefficient
`CB`	\(C_B\)	—	Seabed friction coefficient
`GK`	\(G_K\)	N/m³	Ground spring stiffness
`GC`	\(G_C\)	—	Ground damping coefficient

Stiffness Models¶

Selected via flag_stiffness:

Value	Model	Description
0	Linear	Constant axial stiffness \(EA\)
1	Viscoelastic	Spring-dashpot model (\(EA\), \(EA_d\), \(\alpha\))
> 1	Tabulated	Force-strain lookup table with \(N\) points

Linear (`flag_stiffness = 0`)¶

0               // flag_stiffness
1.0e8           // EA [N]

Viscoelastic (`flag_stiffness = 1`)¶

1               // flag_stiffness
1.0e8           // EA [N]
5.0e7           // EA_d [N] (dashpot stiffness)
0.01            // alpha [-] (relaxation parameter)

Tabulated (`flag_stiffness = N`)¶

5               // flag_stiffness (N = number of points)
0.0   0.0       // strain [-], force [N]
0.01  1.0e5
0.02  2.5e5
0.05  8.0e5
0.10  2.0e6

Tension Model¶

Selected via flag_tension:

Value	Behaviour
0	Tension-only — line goes slack when compressed
1	Symmetric — supports both tension and compression

Seabed Contact¶

Lines interact with the seabed via a spring-damper ground contact model:

\[F_{\text{ground}} = G_K \cdot \delta + G_C \cdot \dot{\delta}\]

where \(\delta\) is the penetration depth below the seabed surface.

The seabed surface is defined via indexSeaFloor:

Value	Seabed type
0	Flat at `waterDepth`
> 0	Custom surface from `dataSeaFloor.dat`

Custom seabed surfaces can be flat, inclined planes, or bathymetric meshes (STL).

Friction Models¶

Selected via frictionModel:

Value	Model	Description
0	None	No seabed friction
1	Isotropic	Same friction in all directions
2	Anisotropic	Different tangential and normal friction

Friction uses a stick-slip model:

Parameter	Symbol	Description
`vth`	\(v_{th}\)	Threshold velocity for stick-slip transition [m/s]
`ust` / `usn`	\(\mu_s\)	Static friction coefficient (tangential/normal)
`ud`	\(\mu_d\)	Dynamic friction coefficient
`deltamax`	\(\delta_{\max}\)	Maximum displacement for stick phase [m]

BCP Connections¶

Each line connects two BCPs (start and end nodes). The BCP types determine how the endpoints behave:

BCP type	Class	Behaviour
Anchor	`AnchorBCP`	Fixed point in space
Fairlead (Body)	`BodyBCP`	Moves with a floating body
Joint	`JointBCP`	Multi-line junction with mass and volume
Elastic Anchor	`ElasticAnchorBCP`	Anchor with elastic spring
Actuator	`FairleadBCP`	Prescribed motion from file

BCP Index Order

BCP indices are assigned globally in order: actuators, anchors, joints, body fairleads, elastic anchors. Lines reference BCPs by these 1-based global indices.

Input Example¶

ASCIIYAML

In dataLines.dat:

//////////////////
////////////////// New line [1]
//////////////////
1               // lineType (dynamic)
0               // flag_tension (tension-only)
21              // nNodes
4               // p (polynomial order)
200.0           // L [m]
100.0           // rho0 [kg/m]
0.1             // d [m]
0               // flag_stiffness (linear)
1.0e8           // EA [N]
0.5             // CB
1.0             // Cmn
1.0             // Cdn
0.1             // Cdt
1.0e5           // GK [N/m³]
100.0           // GC
0               // indexSeaFloor (flat)
1               // BCP_N (end node)
4               // BCP_1 (start node)
0               // frictionModel (none)
0.001           // vth
0.3             // ust
0.2             // ud
0.01            // deltamax

In dataProblem.yaml:

lines:
  - line_type: 1
    tension_flag: 0
    nodes: 21
    polynomial_order: 4
    length: 200.0
    mass_per_length: 100.0
    diameter: 0.1
    stiffness:
      type: 0
      EA: 1.0e8
    friction_coef: 0.5
    Cmn: 1.0
    Cdn: 1.0
    Cdt: 0.1
    ground_stiffness: 1.0e5
    ground_damping: 100.0
    seafloor_index: 0
    BCP_end: 1
    BCP_start: 4
    friction_model: 0
    vth: 0.001
    ust: 0.3
    ud: 0.2
    deltamax: 0.01

Output Files¶

File	Content
`NodePosX_<ID>.txt`	Time + N node X positions
`NodePosY_<ID>.txt`	Time + N node Y positions
`NodePosZ_<ID>.txt`	Time + N node Z positions
`EndsTen_<ID>.txt`	Time + tension at both ends (6 components)
`LineTen_<ID>.txt`	Time + N node tensions
`LineIni_<ID>.txt`	Initial configuration (s, x, y, z, tension)

Example	Feature
`lines/single_line`	Single catenary mooring
`lines/multi_line`	Multi-line spread mooring
`lines/joint_connection`	Lines connected via JointBCP
`lines/elastic_anchor`	Elastic anchor point
`lines/prescribed_motion`	Actuator-driven fairlead
`lines/viscoelastic`	Viscoelastic material
`lines/tabulated_stiffness`	Tabulated force-strain curve
`lines/tension_symmetric`	Symmetric tension/compression
`lines/seabed_contact`	Ground contact model
`lines/friction_isotropic`	Isotropic seabed friction
`lines/friction_anisotropic`	Anisotropic seabed friction