Parametric study of planar flexible deployable structures consisting of Scissor-like elements using a novel multibody dynamic analysis methodology

A general methodology for the dynamic modeling and analysis of planar flexible deployable structures consisting of scissor-like elements (SLEs) is presented. This modeling method is based on a comprehensive consideration of the symmetry and array characteristics of deployable structure and on an improved absolute node coordinate formulation (ANCF), which can model the warping of beam section using the locking-free shear deformable beam element. An effective node separation method is proposed to reduce the number of degrees of freedom of the dynamic equation in the ANCF framework, eliminate the constraint equations within and between SLEs and obtain a compact matrix. This reduction method has good adaptability and can be extended to all kinds of scissor deployable structures with array characteristics, whether they are planar or spatial structures. In addition, the modified generalized \(\alpha\) method is utilized to solve the motion equations of deployable structure and eliminate the false high-frequency response generated in the calculation process. Finally, the methodology is validated using a cantilever beam case, and the parametric dynamic response of 2 × 2 and 1 × 2 deployable structures is implemented in this paper. The obtained results show that flexibility has an important impact on the dynamic characteristics of large deployable structures, and the deployable structure is unstable near \(0^{ \circ }\) and \(90^{ \circ }\), and its safe working angle is \(17^{ \circ }\)–\(75^{ \circ }\). It is necessary to carry out parametric research on this structures in the design stage because the prediction of these parameters such as initial configuration and component materials can improve the stability and deployment accuracy of deployable structures in orbit.