An improved Hamiltonian finite element method for three-dimensional nonlinear dynamics of towed system

Abstract

An improved Hamiltonian nodal position finite element method without any coordinate transformation is developed to numerically analyse the three-dimensional nonlinear dynamics of towed system, in which the dynamic equation of towed system is derived and built in global system. The medium resistance effect is taken into consideration, the deformation of towing cable is modelled using logarithmic strain theory, the coupling force between towed system and the surrounding medium is modelled by Morison formulation. The dynamic canonical equations of towed system would be updated for each time step due to the strong nonlinearity of the flexible towing cable. A first-order Symplectic difference scheme is formulated and applied to solve the canonical equations. The Symplectic conservation and high efficiency features of the proposed method are firstly validated by the solution of a U-turn towed system dynamics, the results are compared with the ones retraced by LS-DYNA. A linear towed system experiment in air environment is reconstructed and calculated to further validate the robustness of the proposed method, in which the air resistance influence is of the essence.