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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