Formulation Analyze Of Rigid-flexible Coupling Dynamics For Thin Plate Structure Multibody System With Large Deformation

With the development of science and technology, attention is gradually paid to the space exploration, because of the limitation of maintenance cost and transportation cost, the station of the main components is characterized by large size, thin-walled and light weight. In addition, because the flexible attachment on the space station is affected by the non-uniform and periodic solar radiation, both the top and bottom surfaces will produce a larger temperature difference that will cause large thermally induced elastic deformation. Up to now, the research of the rigid-flexible-thermal coupling model is based on the linear elastic theory which may lead to simulation error, therefore, the investigation of the rigid-flexible-thermal coupling dynamic formulation of flexible multibody system with large deformation is of significant importance. Furthermore, because composite materials is becoming more and more widely used in the space station, it is necessary to extend the research based on isotropic plate structure with large deformation to composite structure multibody system.In this paper, dynamic modeling theory of isotropic thin plate multibody system with large deformation is investigated. Based on Kirchhoff assumption that the normal vector is always perpendicular to the central surface, the relation among the in-plane strains, the curvatures, the absolute nodal coordinates and the absolute gradients are derived according to the definition of Green strain, and then the generalized elastic force vector and the differentiation of the elastic force vector with respect to the generalized coordinates are derived. Equations of motion of isotropic thin plate multibody system with large deformation are derived based on absolute nodal coordinate formulation.In order to investigate the rigid-flexible-thermal coupling effect, the relation between the heat flux and the absolute coordinates is also obtained, and then by leading into the constrained equations of the multibody system, the rigid-flexible-thermal coupling equations are derived, which are combined of the heat conduction equations and the Lagrange dynamic equations of the first kind. In order to improve the simulation efficiency, modified central difference method and generalized-? method are combined to solve the heat conduction equations and the dynamic equations, and then the discretized equations are solved by using Newton-Raphson method. Simulation example of satellite and plate multibody system applied with solar heat flux is used to verify the effectiveness of the formulation. Comparison of the results obtained by non-coupling method and rigid-flexible-thermal coupling method shows that the effect of the rigid body motion on the temperature gradient in the thickness direction and thermally induced deformation is significant, which should be taken into account. Furthermore, due to the inclusion of the geometric nonlinear terms, the influence of the axial deformation caused by the temperature increase on the transverse deformation is revealed.The dynamic model of the isotropic thin plate multibody system has been successfully extended to composite thin plate multibody system. Simulation of a composite thin plate applied with an external force is carried out. Comparison of the present simulation results with those obtained by ANSYS software verifies the accuracy and effectiveness of the formulation. Finally the proposed formulation is used for numerical simulation of composite solar array deployment mechanism. The vibration characteristics of the driving force and the constraint forces are analyzed in case of different panel layers.