Fibre Rope Model

The fibre rope model is capable of modelling the load-history dependent elongation and mean-tension dependent dynamic stiffness. Required input is

  • Tension-strain curve for the original curve (OC, dummy)

  • Tension-strain curve for the original working curve (OWC, see Figure 1)

  • Tension-strain curve for a single working curve (WC), shifted so the curve starts at the origin (see Figure 1)

  • Dynamic stiffness coefficients, \(A\) [N] and \(B\) [-]

  • Historic highest mean tension, (\(T_{max}\)) [N], given as input in Elongation Characteristics

SyropeProcedure input
Figure 1. Input stiffness curves

When modelled, the line length should correspond to the length of the unloaded line. Prior to the static analysis the line length will be adjusted to account for permanent elongation. This is done by shifting the WC along the strain axis until OWC and WC intercept at \(T_{max}\). The strain predicted by the moved WC at zero tension (\(\epsilon_{perm}\)) corresponds to the permanent elongation of the fibre rope (see Figure 2).

SyropeProcedure static
Figure 2. Permament elongation and static stiffness

In the static analysis the elongated fibre rope is loaded along the WC. Using the static tension in each segment as an estimate of the mean tension, \(\bar{T}\), the linear dynamic stiffness is calculated as

\[K_{dyn} = A+B*\bar{T}.\]

Prior to the dynamic analysis the line is again elongated by \(\epsilon_{dyn}\), such that the WC and the dynamic strain-tension curve intersects at \(\bar{T}\). Finally, the dynamic analysis is performed with a line length \(L=L_0*(1+\epsilon_{perm+dyn})\), where \(L_0\) is the modelled length of the unloaded line, \(\epsilon_{perm+dyn}\) is permanent and mean dynamic elongation. The rope linear dynamic stiffness, \(K_{dyn}\), is used in the dynamic calculations. See Figure 3.

SyropeProcedure dynamic
Figure 3. Dynamic elongation and stiffness

Further information can be found in Falkenberg et al. (2017).