Nonlinear Dynamic Modeling for a Flexible Laminated Composite Appendage Attached to a Spacecraft Body Undergoing Deployment and Locking Motions

Abstract

A nonlinear dynamic modeling method is developed for a deployment and locking mechanism composed of laminated composite appendage. Unlike most formulations of linear models which ignore coupled and nonlinear terms resulting in a seriously improper response, the present model takes into account the effects of geometric nonlinearity and coupled deformations. In order to accurately obtain the dynamic response of laminated composited appendages, nonlinear strain-displacement relations for laminated plate/shell elements are presented, and the corresponding formulations are derived from the Piola–Kirchhoff stress tensor for evaluating the internal forces. Furthermore, the effect of contact and impact located at a spring hinge is investigated, which can achieve the actuating and locking functions. To study the dynamic behavior of contact-impact, the generalized contact-impact forces between the pin and locking groove are considered in the model. Meanwhile, the Jacobian matrices of geometric and momentum constraints are derived from hinge kinematics. Finally, the complete expressions including coupled deformation terms, nonlinear stiffness, additional stiffness terms, and contact-impact forces are presented, and a full analysis is achieved by using both the linear model and nonlinear model, respectively. Numerical simulation results are obtained to verify the dynamic effects of coupled deformation terms, the nonlinear stiffness and additional stiffness terms in the present model.