双稳态预应力圆柱壳的折断
Snapping of Bistable, Prestressed Cylindrical Shells
摘要：
双稳态壳可以在两个稳定构型之间可逆地改变，而能量输入非常小。了解这些结构的形状和快速通过标准对于设计利用不稳定性实现功能的设备至关重要。通过拉伸和粘结多层弹性板制造的双稳态圆柱壳将包含残余应力，该残余应力将影响壳体的形状和引起折断所需的刺激的大小。使用非欧壳理论的框架，我们首先预测的平均曲率的近圆柱壳形成任意预拉伸的双层板的一层相对于另一个。然后，从一个残余应力的圆柱体，我们确定的刺激量需要触发两个配置之间的抢购通过数值模拟和理论相结合。我们证明了预应力的作用，通过的标准，并突出的重要作用，高斯曲率的边界层的外壳中起着支配壳的稳定性。
英文摘要：
Bistable shells can reversibly change between two stable configurations with very little energetic input. Understanding what governs the shape and snap-through criteria of these structures is crucial for designing devices that utilize instability for functionality. Bistable cylindrical shells fabricated by stretching and bonding multiple layers of elastic plates will contain residual stress that will impact the shell's shape and the magnitude of stimulus necessary to induce snapping. Using the framework of non-Euclidean shell theory, we first predict the mean curvature of a nearly cylindrical shell formed by arbitrarily prestretching one layer of a bilayer plate with respect to another. Then, beginning with a residually stressed cylinder, we determine the amount of the stimuli needed to trigger the snapping between two configurations through a combination of numerical simulations and theory. We demonstrate the role of prestress on the snap-through criteria, and highlight the important role that the Gaussian curvature in the boundary layer of the shell plays in dictating shell stability.
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