Extreme deformations of the cantilever Euler Elastica under transverse aerodynamic load

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 an 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 transverse 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 agreement between the experimental results and both theoretical and numerical predictions. During the experiments, we observed a high susceptibility to perturbations around a dimensionless load of 41.15. 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 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.