A hamiltonian global nodal position finite element method for dynamics analysis of submarine cables

Abstract

The dynamics of submarine cables can be expressed in Hamiltonian formalism, which can reduce the error accumulation over long-term numerical calculation. This paper proposes a Hamiltonian global nodal position finite element method to study the dynamic responses of submarine cables undergoing bending deformation and long-term large overall motions. The new global nodal position finite element discrete formulation is derived by Hamiltonian theory and Euler-Bernoulli beam theory, which takes the bending deformation of submarine cables into consideration. To verify the proposed method, the second-order Symplectic difference algorithm is built for numerical solution. Five-point Gauss-Legendre quadrature formulate is applied to calculate the hydrodynamic force. The calculation accuracy and efficiency of the proposed method are validated by the freefall cantilever test of submarine cable, the towing test of submarine cable with lumped mass, the motion simulation of submarine cable connected to the remotely operated vehicle (ROV) and the towing test of a submerged body. Compared with the existing Hamiltonian nodal position finite element method, all validations and results indicate that the proposed method can solve the motion of various submarine cables under different working conditions with higher accuracy and efficiency.