Multiple equilibrium states of a curved-sided hexagram: Part II—Transitions between states
Multiple equilibrium states of a curved-sided hexagram: Part II—Transitions between states
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DOI：
10.1016/j.jmps.2023.105407
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发表时间：
2023-07
影响因子：
5.3
通讯作者：
Lu Lu-Lu;Jize Dai;Sophie Leanza;J. Hutchinson;R. Zhao
中科院分区：
文献类型：
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作者：
Lu Lu-Lu;Jize Dai;Sophie Leanza;J. Hutchinson;R. Zhao
具有多个平衡态的曲面图在可折叠建筑、可展开航天结构和变形软机器人等工程应用中具有巨大的潜力。在第一部分中，利用经典的基于能量变分的稳定性准则研究了曲边六边形的弹性稳定性，并确定了圆杆和矩形杆各状态稳定性的自然曲率范围。在这里，我们结合多段Kirchhoff杆模型、有限元模拟和实验来研究曲边六角图四个基本平衡态之间的跃迁。四种平衡态，即星形、菊花形、三圈线和三圈“8”，在它们的初始状态都带有均匀的弯矩，这些弯矩的大小取决于它们的自然曲率和它们的初始曲率。这些平衡状态之间的转换是通过在其拐角或边缘施加弯曲载荷来触发的。研究发现，曲边六角图的稳定平衡态之间的转变既受自然曲率的影响，也受加载位置的影响。在特定的自然曲率范围内，星形、菊花和三环八卦可以通过在不同位置弯曲而相互转换。在此基础上，我们确定了在高厚比为4的矩形截面上实现这三种平衡状态+折叠三圈线状态之间过渡的自然曲率范围和载荷条件。这一部分的结果也验证了第一部分中曲边六角图四种平衡状态的弹性稳定范围。我们预计，本工作将为多功能可展开可折叠结构的设计提供一个新的视角。
Curved-sided hexagrams with multiple equilibrium states have great potential in engineering applications such as foldable architectures, deployable aerospace structures, and shape-morphing soft robots. In Part I, the classical stability criterion based on energy variation was used to study the elastic stability of the curved-sided hexagram and identify the natural curvature range for the stability of each state with circular and rectangular rod cross-sections. Here, we combine a multi-segment Kirchhoff rod model, finite element simulations, and experiments to investigate the transitions between four basic equilibrium states of the curved-sided hexagram. The four equilibrium states, namely the star hexagram, the daisy hexagram, the 3-loop line, and the 3-loop "8", carry uniform bending moments in their initial states, and the magnitudes of these moments depend on the natural curvatures and their initial curvatures. Transitions between these equilibrium states are triggered by applying bending loads at their corners or edges. It is found that transitions between the stable equilibrium states of the curved-sided hexagram are influenced by both the natural curvature and the loading position. Within a specific natural curvature range, the star hexagram, the daisy hexagram, and the 3-loop "8" can transform among one another by bending at different positions. Based on these findings, we identify the natural curvature range and loading conditions to achieve transition among these three equilibrium states plus a folded 3-loop line state for one specific ring having a rectangular cross-section with a height to thickness ratio of 4. The results obtained in this part also validate the elastic stability range of the four equilibrium states of the curved-sided hexagram in Part I. We envision that the present work could provide a new perspective for the design of multi-functional deployable and foldable structures.