Dynamic Analysis Of Space Deployable Structures Based On Zu's Algorithm

Large deployable structures are widely used in aerospace.Due to its large structure and light weight,the structures are flexible.During the process of deployment,the rigid body rotation motion which is low frequency and the elastic deformation which is high frequency are coupled.At the same time,there are a large number of hinge constraints between the flexible bodies,and the dynamic equations of the flexible bodies are the stiff differential algebraic equations(DAEs).The stiff equations require higher numerical stability,and the differential algebraic equations require no constraint violation problem.This paper,based on the idea of the Zu's method,guarantees the constraint on the time lattice and relaxes the constraints between the time lattice,and uses the symplectic algorithm to solve the dynamic equation.A large number of truss structures exist in space deployable systems,which play a supporting and stabilizing role during the process of structural deployment and assembly.In this paper,the dynamic analysis of the deployable structure based on scissor-like element is carried out.The time finite element and Zu's method are used to solve the differential algebraic equations,the time finite element is symplectic,and the Zu's method guarantees no constraint violation.Many researches show that the traditional multi-body dynamic method based on the small rotation and small deformation assumptions can't lead to accurate results for the nonlinear dynamic of flexible structures with large rotational and large deformation.The nonlinear finite element based on the Absolute Node Coordinate Formulation uses the node positions and the slope vector as the generalized coordinates,not the rotation angle,the system mass matrix remains constant and the centrifugal and coriolis forces vanish.It's very suitable for modeling flexible multi-body systems undergoing large deformation and large rotation.The validity of the symplectic Runge-Kutta method based on the Zu's method is proved by the flexible double pendulum example,and the dynamic analysis of the space deployable plate structures is calculated by this method.The Udwadia-Kalaba method is used to control the track of the flexible structure,which is modeled by the two-dimensional shear deformation beam element based on the Absolute Node Coordinate Formulation.The target trajectory is considered as the system constraint and The analytical expression of the servo control force can be obtained without the Lagrange multiplier.It is verified that the control method has good control effect on flexible structures with large deformation.