Bistability and equilibria of creased annular sheets and strips
Bistability and equilibria of creased annular sheets and strips
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DOI：
10.1016/j.ijsolstr.2022.111588
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发表时间：
2021-04
影响因子：
3.6
通讯作者：
Tian Yu
中科院分区：
文献类型：
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作者：
Tian Yu
有折痕的薄圆盘通常是光滑的，因为折痕可以被推过以形成稳定的锥形倒置状态，其弹性奇点对应于锥形表面的顶点。在最近的一项研究中，我们发现，这种双稳态可以通过在顶点周围切割一个洞来消除奇异性，这取决于洞的大小和形状。特别地，为了保持双稳态，圆孔通常不能超过盘尺寸的约20%。本文扩展了我们最近的工作，并基于以下观察在桌面模型的折痕盘与圆孔：（i）通过去除环形扇区来减小有折痕的盘的周长可以将孔尺寸增加到与盘一样大而不破坏双稳态性，（ii）利用单个折痕，圆孔可以与盘一样大而不损失双稳态性，以及（iii）通过沿折痕沿着的几乎任何地方反转盘，可以获得一族稳定的反转状态。一个不可扩展的带模型来研究这些现象。我们制定了一个最小的方面的折痕盘作为一个两点边值问题的折痕建模为非线性铰链，并使用数值延拓进行参数化研究。具体来说，我们专注于几何参数，其中包括一个角度deficit，确定圆周的磁盘，其余折痕角度，数量均匀分布的折痕，和aneccentricity，确定的位置上的孔折痕。我们的数值结果证实了定性观察（i）-（iii），并进一步揭示了这些几何参数之间的耦合所导致的意想不到的结果。我们的研究结果表明，通过改变一个简单的折痕盘的几何形状，可以获得令人惊讶的丰富的非线性行为，这揭示了新的光折纸，kirigami和变形结构的力学和设计。
A creased thin disk is generally bistable since the crease could be pushed through to form a stable cone-like inverted state with an elastic singularity corresponding to the vertex of the conical surface. In a recent study, we found that this bistability could be destroyed by removing the singularity through cutting a hole around the vertex, depending on the size and shape of the hole. Particularly, to maintain the bistability, a circular hole normally cannot exceed approximately 20% of the disk size. This paper extends our recent work and is based on the following observations in tabletop models of creased disks with circular holes: (i) reducing the circumference of the creased disk by removing an annular sector could increase the hole size to be as large as the disk without destroying the bistability, (ii) with a single crease, the circular hole could be as large as the disk without loss of the bistability, and (iii) a family of stable inverted states can be obtained by inverting the disk almost anywhere along the crease. An inextensible strip model is implemented to investigate these phenomena. We formulate a minimal facet of the creased disk as a two-point boundary value problem with the creases modeled as nonlinear hinges, and use numerical continuation to conduct parametric studies. Specifically, we focus on geometric parameters which include anangle deficitthat determines the circumference of the disk, the rest crease angle, the number of evenly distributed creases, and aneccentricitythat determines the position of the hole on the crease. Our numerical results confirm the qualitative observations in (i)-(iii) and further reveal unexpected results caused by the coupling between these geometric parameters. Our results demonstrate that by varying the geometry of a simply creased disk, surprisingly rich nonlinear behaviors can be obtained, which shed new light on the mechanics and design of origami, kirigami, and morphable structures.