Abstract This paper studies the snap-through of a pinned-clamped elastica when the support of the clamped end can be moved arbitrarily in plane. The universal snap curve, which describes the critical boundary conditions of the pinned-clamped elasticas, is firstly obtained by determining the saddle-node bifurcation points of the moment-rotation response curves. Based on the universal snap curve, the stability of the pinned-clamped elastica can be determined, when the support at the clamped end is moved. The critical boundary can also be directly obtained, where the elastica loses stability and the snap-through occurs between the non-inverted shape and the inverted shape. The study here can be useful to reveal the snap-through behavior for some other complex systems where movable supports exist.

中文翻译：

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卡紧端可任意移动支撑的带销卡紧松紧带的卡扣

摘要 本文研究了被夹紧端的支撑可以在平面内任意移动时的带销夹紧弹性件的卡穿问题。首先通过确定弯矩-旋转响应曲线的鞍形节点分岔点来获得通用捕捉曲线，该曲线描述了固定夹紧弹性体的临界边界条件。根据万能卡扣曲线，可以确定当被夹紧端的支撑移动时，被销夹紧的弹力绳的稳定性。也可以直接获得临界边界，其中弹性体失去稳定性，在非倒置形状和倒置形状之间发生快速穿透。此处的研究可用于揭示存在可移动支撑的其他一些复杂系统的快速通过行为。