Origamis are becoming the inspiration of new adaptive structures applied for several purposes. One of the challenges of the design of the origami inspired structures is to deal with the large number of variables and degrees of freedom (DoFs) associated with such complex structures. Closed tessellations have a reduced number of DoF when compared to the opened ones. Besides, the coupling due to the closure of the tessellation promotes some periodicity along the structure. Symmetric behaviors allow the description of the structure from a unit cell behavior, establishing reduced-order models. This paper investigates the origami waterbomb pattern, exploring the unit cell behavior and its symmetries. Initially, kinematics analysis based on an equivalent mechanism approach establishes a reduced-order model associated with symmetry hypotheses. Afterward, mechanical analysis is investigated using a nonlinear finite element analysis through bar-and-hinge formulation. A comparison between both formulations is performed showing the range of validity of the reduced-order model description. The general conclusions are applied to a cylindrical tessellation under symmetric actuation showing the capability of the reduced-order model for the origami description. Results show that the rigid foldability hypothesis is the essential point for the equivalence between the two descriptions.

折纸正成为应用于多种用途的新型自适应结构的灵感来源。受折纸启发的结构设计的挑战之一是处理与此类复杂结构相关的大量变量和自由度 (DoF)。与打开的曲面细分相比，封闭的曲面细分具有减少的 DoF 数量。此外，由于镶嵌闭合引起的耦合促进了沿结构的一些周期性。对称行为允许从晶胞行为描述结构，建立降阶模型。本文研究了折纸水弹图案，探索了晶胞行为及其对称性。最初，基于等效机制方法的运动学分析建立了与对称假设相关的降阶模型。之后，通过杆和铰链公式，使用非线性有限元分析来研究机械分析。执行两种公式之间的比较，显示降阶模型描述的有效性范围。一般结论应用于对称驱动下的圆柱细分，显示了用于折纸描述的降阶模型的能力。结果表明，刚性可折叠性假设是两种描述之间等价的关键。一般结论应用于对称驱动下的圆柱细分，显示了用于折纸描述的降阶模型的能力。结果表明，刚性可折叠性假设是两种描述之间等价的关键。一般结论应用于对称驱动下的圆柱细分，显示了用于折纸描述的降阶模型的能力。结果表明，刚性可折叠性假设是两种描述之间等价的关键。