Large Deformation Dynamic Analysis of a Cable System by a New Hamiltonian Finite Element Method

Abstract

This paper develops a new Hamiltonian nodal position finite element method for dynamic analysis of spatial flexible cable systems with large deformation. The dynamic governing equation is derived from finite elasticity theory. Logarithmic strain is applied to construct large deformation Hamiltonian canonical equations. An efficient second-order symplectic difference algorithm is built to solve the canonical equations numerically. A large strain conical pendulum system is analyzed numerically by the proposed method, and the numerical results are compared with those retracted from the existing Hamiltonian methods and Livermore Software Technology Corporation: dynamics (LS-DYNA). The proposed method is further verified by two tethered dynamic experiments involving large displacement motion and large deformation. The comparisons and verifications demonstrate that the proposed method is of symplectic conservation, has high accuracy and has stability for calculating flexible cable system dynamics with large deformation.