Unified Modeling Method for Large Space Structures Using Absolute Nodal Coordinate

A unified rigid-flexible coupled modeling method for large flexible space structures is proposed based on absolute nodal coordinate formulation (ANCF). The explicit formulas of gravitational potential energy and generalized gravitational force are developed, which are simple to use and apply to all ANCF elements. First, the shape functions of all kinds of ANCF elements are written as a unified form by using the Kronecker product. Then, the equations of motion are derived through Hamilton's principle. A Taylor series expansion is adopted to obtain the explicit expression of gravitational potential energy. Also, a simplified model of the gravitational force is proposed to improve simulation efficiency. Finally, two case studies are presented to validate the proposed modeling method, including a two-dimensional Euler-Bernoulli beam in elliptic orbits and a thin plate in a circular orbit. The effects of orbital eccentricity on the orbital and attitude accuracies of the proposed method, the mutual effects between the attitude motion and structural vibrations, and the effects of the flexibility on the attitude controller of the beam are also investigated. Simulation results show that the proposed modeling method takes gravitational force as well as gravity gradient torque into account accurately. The simplified model is recommended because of its accuracy and time efficiency.