A high accurate hamiltonian nodal position finite element method for spatial cable structures undergoing long-term large overall motion

Abstract

This paper addresses the challenges faced by the error accumulation over long-term numerical calculation for dynamic modeling of spatial flexible cable structures undergoing large translational and rotational motion. A high accurate Hamiltonian nodal position finite element method is proposed to deal with the challenges. The new nodal position finite element discrete formulation is derived by Hamiltonian theory and Green strain theory with full expression of global stiffness matrices without additional simplifications. Symplectic difference algorithm is built for numerical solution to optimally preserve the energy, momenta and area (volume) of the phase space. Forth-order closed Newton-Cotes numerical integration is applied to calculate the aerodynamic drag force. The Symplectic conservation feature of the proposed method is validated by the dynamics of a long-period classical pendulum. The numerical accuracy and stability of the proposed method are validated by LS-DYNA simulations for a flexible polyethylene rubber conical pendulum, the experiments of a three-dimensional circularly towed cable and the experiments of a free swing cable. The present algorithm is compared with the conventional second-order Runge-Kutta algorithm. All validations and comparisons indicate that the proposed method is stable and highly accurate.