bigon和bigon环的静态平衡和分岔的数值模拟
Numerical modeling of static equilibria and bifurcations in bigons and bigon rings
摘要：
在这项研究中，我们探讨了一个bigon和bigon环的力学从实验和数值模拟相结合。bigon是一个简单的弹性网络，由两个最初的直条组成，它们在每一端通过固定的交叉角相互交叉。bigon环是一种由一系列bigon排列成环的新型多稳态结构。我们发现，一个bigon环通常包含几个稳定态族，其中之一是一个多重覆盖环，这类似于带锯刀片的折叠行为。为了模拟bigons和bigon环，我们提出了一个数值框架，结合现有的几种技术来研究由薄条组成的弹性网络的力学。每个条带被建模为基尔霍夫杆，整个条带网络被配制为两点边值问题（BVP），可以通过通用BVP求解器来解决。结合数值延拓，我们应用数值框架研究了bigon和bigon环的静态平衡和分岔。数值计算和实验结果都表明，带的交叉角和截面的纵横比对双子的双稳性和双子环的多稳性有影响，而多稳性又取决于环中双子胞的数目.数值结果进一步揭示了bigon环中各种稳定态之间有趣的联系。我们的数值框架可以应用于一般的弹性杆网络，可能包含柔性关节，不同长度的自然弯曲条等。折叠和多稳态行为的bigon环可能会启发设计新的可展开和变形结构
英文摘要：
In this study, we explore the mechanics of a bigon and a bigon ring from a combination of experiments and numerical simulations. A bigon is a simple elastic network consisting of two initially straight strips that are deformed to intersect with each other through a fixed intersection angle at each end. A bigon ring is a novel multistable structure composed of a series of bigons arranged to form a loop. We find that a bigon ring usually contains several families of stable states and one of them is a multiply-covered loop, which is similar to the folding behavior of a bandsaw blade. To model bigons and bigon rings, we propose a numerical framework combining several existing techniques to study mechanics of elastic networks consisting of thin strips. Each strip is modeled as a Kirchhoff rod, and the entire strip network is formulated as a two-point boundary value problem (BVP) that can be solved by a general-purpose BVP solver. Together with numerical continuation, we apply the numerical framework to study static equilibria and bifurcations of the bigons and bigon rings. Both numerical and experimental results show that the intersection angle and the aspect ratio of the strip's cross section contribute to the bistability of a bigon and the multistability of a bigon ring; the latter also depends on the number of bigon cells in the ring. The numerical results further reveal interesting connections among various stable states in a bigon ring. Our numerical framework can be applied to general elastic rod networks that may contain flexible joints, naturally curved strips of different lengths, etc. The folding and multistable behaviors of a bigon ring may inspire the design of novel deployable and morphable structures
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