﻿ Line theory: Overview

# Line theory: Overview

OrcaFlex uses a finite element model for a line as shown in the figure below.

 Figure: OrcaFlex line model

The line is divided into a series of line segments which are then modelled by straight massless model segments with a node at each end.

The model segments only model the axial and torsional properties of the line. The other properties (mass, weight, buoyancy etc.) are all lumped to the nodes, as indicated by the arrows in the figure above.

Nodes and segments are numbered 1, 2, 3, … sequentially from end A of the line to end B. So segment $n$ joins nodes $n$ and $n{+}1$.

### Nodes

Each node is effectively a short straight rod that represents the two half-segments either side of the node. The exception to this is end nodes, which have only one half-segment next to them, and so represent just one half-segment.

Each line segment is divided into two halves and the properties (mass, weight, buoyancy, drag etc.) of each half-segment are lumped and assigned to the node at that end of the segment.

Forces and moments are applied at the nodes – with the exception that weight can be applied at an offset. Where a segment pierces the sea surface, all the fluid related forces (e.g. buoyancy, added mass, drag) are calculated allowing for the varying wetted length up to the instantaneous water surface level.

### Segments

Each model segment is a straight massless element that models just the axial and torsional properties of the line. A segment can be thought of as being made up of two co-axial telescoping rods that are connected by axial and torsional spring-dampers.

The bending properties of the line are represented by rotational spring-dampers at each end of the segment, between the segment and the node. The line does not have to have axial symmetry, since different bend stiffness values can be specified for two orthogonal planes of bending.