Dynamics calculation for variable-length underwater cable with geometrically nonlinear motion

A new finite element model of the variable-length underwater cable with geometrically nonlinear motion is presented in this paper. This model accounts for the effects of axial load, shear, bending, and torsion completely. First, a set of nonlinear, time-varying differential equations is derived from the theorem of linear and angular momentum, and its weak formulation is obtained by the principle of D'Alembert-Lagrange correspondingly. Through a series of consistent linearization with the Frechet derivative and discretization with the isoparametric interpolation, the governing finite element model for this variable-length cable is established. Second, the corresponding Newmark implicit time integration formulation is derived, and a scheme of adaptive step size is proposed to avoid convergence difficulty during the numerical calculation, and the way of mesh rediscretization is also illustrated to show the process of cable deployment. Third, after comparing with the results of two validation examples, the performance of the proposed approaches is further assessed with four numerical cases, which take consideration of the top alternating excitation, the terminal follower forces, and the sea current along the cable, since these terms are found to have a significant impact on the motion of variable-length underwater cable. Finally, some conclusions are drawn