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.

介绍了由剪刀状元件 (SLE) 组成的平面柔性可展开结构的动态建模和分析的一般方法。该建模方法综合考虑了可展开结构的对称性和阵列特性，并基于改进的绝对节点坐标公式（ANCF），可以使用无锁定剪切变形梁单元对梁截面翘曲进行建模。提出了一种有效的节点分离方法，以减少ANCF框架中动态方程的自由度数，消除SLE内部和SLE之间的约束方程，获得紧凑矩阵。这种缩减方法具有很好的适应性，可以推广到各种具有阵列特性的剪刀式可展开结构，无论是平面结构还是空间结构。\(\alpha\)方法用于求解可展开结构的运动方程，消除计算过程中产生的虚假高频响应。最后，使用悬臂梁案例验证了该方法，并在本文中实现了 2 × 2 和 1 × 2 可展开结构的参数化动力响应。所得结果表明，柔度对大型可展开结构的动力特性有重要影响，可展开结构在\(0^{\circ}\)和\(90^{\circ}\)附近不稳定，其安全工作角度为\(17^{ \circ }\) – \(75^{ \circ }\). 有必要在设计阶段对这种结构进行参数化研究，因为对初始构型和部件材料等参数的预测可以提高可展开结构在轨的稳定性和展开精度。