Research On Hamiltonian Nodal Position Finite Element Method For Spatial Flexible Cable System Dynamics

As a means of construction with minimum use of material,spatial flexible cable systems have plenty of advantages such as convenient to transfer power and electronical signs,and have been employed extensively in marine areas,aerospace fields and other areas,undergoing long-term and large scale motions,the dynamics of the spatial flexible cables are high nonlinear ragularly coupled with large deformation.For better prediction of dynamic responses of the cable systems,the incremental finite element methods based on conventional nodal displacements are applied to analyse the large deformation cable dynamics,the newly proposed nodal position finite element can simplify the complex solution process of the incremental finite element method.However,the existing nodal position finite element method was derived numerically based.on small strain theory and some theorical simplifications,the dynamic governing differential equations were solved by traditional integral schemes(Runge-Kutta,Newmark-? et al.).However,the calculation error caused by traditional integral schemes would be accumulated when abundant time steps are needed for long-term dynamic simulations of cable systems,resulting in the failure prediction of cable dynamics.The nodal position finite element method is expressed in total formate which is simple in expression and high in accuracy,at present,there is a lack of research on eliminating the accumulation of computational errors in this method.This paper deals with the spatial flexible cable systems undergong large-scale motion in fluid media.The Hamiltonian node coordinate finite element method with symplectic property is studied to eliminate the influence of computational error accumulation.The main research contents are summarized as the followings:(1)The widely used methods for the dynamics of flexible cable systems are summarized,including finite element method,lumped mass method,direct integration method,finite difference method and experimental method.When using the traditional finite element method based on nodal displacement,the numerical solution distortion of the long-term dynamic response caused by the cumulative calculation error is analyzed.(2)The Hamiltonian nodal position finite element method is proposed,preserving the traditional assumption of elastic potential energy.Both the undamped and damped dynamic governing equations are derived and the corresponding first-order,second-order Symplectic difference schemes are given.The Symplectic conservation feature and efficiency of the proposed method is validated numerical by a two-dimensional free fall pendulum and a free swing experiment of a steel cable without a lumped mass.(3)A high accurate Hamiltonian nodal position finite element method in total form is proposed.The process of analyzing the for long-term cable systems motion under large-scale displacements doesn't take the traditional assumption of elastic potential energy.Two numerical cases including a simple pendulum and a conical pendulum and two experiments including three-dimensional circularly towed cable experiment in air and a free swing steel cable experiment without a lumped mass are employed to validate the superiority,stability and applicability of the proposed method.(4)A direct solution to the drag effect of cable yielded by the fluid media in the Cartesian coordinate system is presented.Based on Morrison's equation,the drag force of cable drag with circular section is derived theoretically,and the fourth-order Newton-Cotes numerical integration method is used to calculate the drag.The jumbled process of solving drag resistance in local coordinates is avoided effectively,the calculation manner also tackles the problem that the medium drag is difficult to be modelled in commercial software such as LS-DYNA.(5)For the strain accumulation in the large-scale spatial motion of flexible cable systems,a new Hamiltonian nodal position finite element method in total form is proposed.The proposed method are validated by two numerical simulations,a conical pendulum system experiencing large-scale motion and a 1800 U-turn cable-towed system under large strain,and validated by the experiments of two rubber tethered systems with and without a lumped weight which are under large deformation motions.