Research On Dynamic Modeling And Adaptive Computation Of Flexible Cable Based On ANCF

As a kind of a widely used space structure,the flexible cable is featured in light weight and small damping,but is sensitive to the disturbance of external environment,which leads to vibration.Its dynamic characteristics have a vital influence on the effective implementation of space missions.Therefore,it is greatly required to develop the dynamic modeling and computation method with high precision and efficiency.Compared with traditional discrete modeling methods such as the lumped mass method and the finite segment method,the absolute nodal coordinate formulation(ANCF)has a series of advantages in dealing with the large deformation problem of flexible cable.However,there exists the strain coupling problems in general ANCF cable elements,and the internal nonlinear mechanical properties are not fully considered.In addition,the accuracy of flexible cable model is not only related to the element precision,but also affected by the distribution of elements.Unreasonable element division will cause the loss of computation efficiency.In view of the above problems,the dynamic modeling and adaptive computation of flexible cable are studied based on the ANCF method to improve the accuracy and efficiency of flexible cable dynamics.Based on the theory of continuum mechanics,the three dimentional ANCF cable element with two nodes is deduced,of which the specific expressions of cable element including the mass matrix,stiffness matrix,damping matrix,generalized force and its jacobian matrix are presented.On this basis,the dynamic equation of flexible cable system is established and the corresponding numerical algorithm is given,then the simulation verification of the model is carried out,which lays the theoretical foundation for both static and dynamic analysis of flexible cable.Carrying out the strain analysis of ANCF cable element,it is found that due to the shared dependency of axial and bending strains,there exists coupling problem between different element strains.This makes the calculated element stiffness larger than the theoretical value and affects the model accuracy.Therefore,an equivalent one-dimensional rod element is constructed to redefine the axial strain,thus the axial bending strains are able to be decoupled.Then the generalized viscoelastic force and its jacobian matrix are derived and a strain decoupled ANCF cable model is obtained.Compared with the original coupled model,the decoupled model has the advantages of fast convergence,good continuity and high accuracy,and it can avoid high-frequency vibration caused by element stiffening.The traditional ANCF cable model considers the flexible cable as a homogeneous and isotropic continuum without taking the complex inertal nonlinear mechanical properties into account.After analyzing the mechanical properties of fiber ropes,it is known that the fiber rope has the properties of incompressibility and relaxation,and the stress-strain relationship is nonlinear.Therefore,a slack model of fiber rope is established.Compared with the traditional model,the slack model better reflects the static and dynamic characteristics of the fiber rope.The mechanical properties of the twisted wire rope are also analyzed.It is clear that there exists relative sliding between the wires with complex contact and friction during the process of movement and deformation.With the consideration of the practical geometric structure of twisted rope and analysis of the stick and slip friction force between the wires,the formulas of constant axial stiffness and variable bending stiffness are obtained.Consequently,the ANCF twisted rope model is established.By comparing with the detailed model,the correctness of the twisted rope model is verified.The twisted rope model possesses higher precision than the traditional model.Besides,since there is no need to build every wire in the twisted rope model and to calculate contact and friction forces in the numerical simulation,the twisted rope model has higher computation efficiency compared with the detailed model.In order to further improve the computation accuracy and efficiency in cable dynamics,an adaptive ANCF(AANCF,Adaptive ANCF)method is proposed,which improves the accuracy and efficiency by updating the distribution or type of element adaptively.The AANCF computation strategy is given,and the key problems such as error estimation,element updating strategy and evaluation of simulation results are discussed.The difference between AANCF method and adaptive finite element method is analyzed and compared.The AANCF cable computation model is proposed,of which the element description error is analyzed,and the criteria,method and procedure of element dividing and merging are given.Results of numerical simulation indicate that the AANCF model changes the element distribution at the suitable time and area,which improves the efficiency of cable dynamics while the precision guaranteed,but there exists sundden changes in system energy.Therefore,the continuity of the cable motion state before and after element updating is analyzed through theoretical method.It is found that the key factor that affects the continuity is the jump values of nodal displacement and gradient.Based on this,the continuity of AANCF cable is optimized and the CO-AANCF cable model is obtained.Numerical simulation shows that the model reduces the rapid energy change,which further improves the continuity and accuracy of the adaptive computation.