Using an analytical solution of the Euler’s Elastica, we stumbled upon peculiar shapes of a cantilever beam subject to a large value of shear follower force at the free end. Intrigued by whether such shapes existed or not, we set out to realise an experimental apparatus to validate our predictions. Attaining such system, in reality, is not at all a trivial task. Indeed, it has represented a tremendous experimental challenge for decades, due to the emergence of unstable configurations. After various attempts, we were finally able to conceive and realise a device capable of generating a perpendicular follower force to the beam via air-thrust. We compared the measurement of the forces and the deformation of the beam obtained experimentally with the analytical solution of the Euler’s Elastica in dimensionless form. Since the experiments are quasi-static, the aerodynamic effect induced by the air flow are negligible; this is confirmed by the excellent agreement between the experimental results and both theoretical and numerical prediction. During the experiments, we observed a high susceptibility to perturbations around a dimensionless load of 41.5. We used finite element simulations with an explicit time integration scheme to carry out a stability analysis. Our analysis confirmed the appearance of an unstable configuration for a load of 40.5. Therefore, by carefully tuning the apparatus, we could reach load values higher than the unstable load, at around 120. For such levels of forces, the solution of the Elastica prescribes hook-like shapes that we show experimentally for the first time in this paper. These results can find several applications, for instance, the design of soft-actuators, the realisation of more efficient drilling pipes for underwater, or underground, well or the design of biomedical equipment, such as catheters.

使用欧拉弹性的解析解，我们偶然发现了悬臂梁的特殊形状在自由端受到较大的剪切随动力的作用。对这种形状是否存在感兴趣，我们着手设计一种实验设备来验证我们的预测。实际上，获得这样的系统绝非易事。实际上，由于不稳定配置的出现，它已经代表了数十年来的巨大实验挑战。经过各种尝试，我们终于能够构思并实现一种能够通过空气推力对梁产生垂直从动力的装置。我们将实验获得的力的测量和梁的变形与欧拉弹性的解析解进行了比较无量纲形式。由于实验是准静态的，因此气流引起的空气动力影响可以忽略不计；实验结果与理论和数值预测之间的极好的一致性证实了这一点。在实验过程中，我们观察到在41.5的无量纲载荷附近对扰动的敏感性很高。我们使用带有显式时间积分方案的有限元模拟来进行稳定性分析。我们的分析证实了负载为40.5时出现不稳定配置的情况。因此，通过仔细调整设备，我们可以达到比不稳定负载高的负载值，约为120。对于这种水平的力，Elastica的解是规定了本文首次通过实验展示的钩状形状。这些结果可以找到几种应用，例如，软致动器的设计，水下或地下井的高效钻杆的实现或生物医学设备（如导管）的设计。