Line theory: Structural model details

The following figure gives greater detail of the line model, showing a single mid-line node and the segments either side of it. The figure includes the various spring-dampers that model the structural properties of the line, and also shows the xyz-frames of reference and the angles referred to in the theory which follows.

As shown in the diagram, there are 3 types of spring-dampers in the model:

• The axial stiffness and damping of the line are modelled by the axial spring-damper at the centre of each segment, which applies an equal and opposite effective tension force to the nodes at each end of the segment.
• The bending properties are represented by rotational spring-dampers either side of the node, spanning between the node's axial direction $\vec{n}_\mathrm{z}$ and the segment's axial direction $\vec{s}_\mathrm{z}$.
• If torsion is included (this is optional) then the line's torsional stiffness and damping are modelled by the torsional spring-damper at the centre of each segment, which applies equal and opposite torque moments to the nodes at each end of the segment. If torsion is not included then this torsional spring-damper is missing and the two halves of the segment are then free to twist relative to each other.

OrcaFlex uses five stages to calculate the forces and moments on the mid-node shown in the diagram:

1. Tension forces
2. Bend moments
3. Shear forces
4. Torsion moments
5. Total load.