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To accurately simulate the motion of slack marine cables, it is necessary to capture the effects of the cable’s bending and torsional stiffness. In this paper, a computationally efficient and novel third-order finite element is presented that provides a representation of both the bending and torsional effects and accelerates the convergence of the model at relatively large element sizes. Using a weighted residual approach, the discretized motion equations for the new cubic element are developed. Applying inter-element constraint equations, we demonstrate how an assembly of these novel elemental equations can be significantly reduced to prevent the growth of the system equations normallly associated with such higher order elements and allow for faster evaluation of the cable dynamics in either taut or low-tension situations.

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Accurate computer modelling is critical in achieving cost-effective floating offshore wind turbine designs. Although a range of modelling fidelities are available for all parts of the simulation, a lower-fidelity quasi-static approach that neglects inertia and hydrodynamics is often used for the mooring line model. The loss of accuracy from using this approach has not been thoroughly studied across different support structure designs. To test the adequacy of this widely used simplified mooring line modelling approach, the floating wind turbine simulator FAST (National Renewable Energy Laboratory, Golden, Colorado) was modified to allow the use of a high-fidelity dynamic mooring line model, ProteusDS (Dynamic Systems Analysis Inc. of Victoria, BC, Canada). Three standard floating wind turbine designs were implemented in this new simulator arrangement and tested using a set of steady and stochastic wind and wave conditions. The static equivalence between the built-in quasi-static mooring model and the dynamic mooring model is within 0.6% in terms of fairlead tension. Tests of the systems' responses in still water indicate that the hydrodynamic damping of the mooring lines can constitute anywhere from 1% to 35% of the overall system damping in pitch, depending on the design. Tests in steady and stochastic operating conditions show that for very stable designs with slack moorings, or designs with taut moorings, a quasi-static mooring model can in many conditions predict the platform motions and turbine loads with reasonable accuracy. For slackmoored designs with larger platform motions, however, a quasi-static model can lead to inaccuracies of as much as 30% in the damage-equivalent and extreme loads on the turbine. An important observation is that even in situations where the platform response is predicted reasonably well by a quasi-static model, larger inaccuracies can arise in the response of the rotor blades. These inaccuracies are more severe in the time series (with instantaneous discrepancies as high as 50% of the mean load) than in the corresponding damage-equivalent and extreme loads calculated over multiple stochastic simulations. Consequently, differences in damage-equivalent and extreme load metrics should be considered a floor to the measure of inaccuracy caused by a quasi-static mooring model.

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