Some answers on this site, such as this one, refer to something called aeroelastic deformation.
What is it and how does it affect aircraft construction? Are there any famous lessons learned on this topic as far as aircraft construction goes?
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Aeroelasticity is the elastic deformation of a structure caused by aerodynamic forces. An example is the flexing of a wing. The change of the shape of the structure has in turn an effect on the aerodynamics.
Aeroelastic effects can be static, such as the upward deflection of a wing under the influence of lift, or dynamic.
In the static case, the aerodynamic for cause the structure to deform. If the structure is very flexible this can cause a stability problem: the deformation causes an increases of the aerodynamic load, that will in turn increases the deformation until the structure fail.
In dynamic cases there is an interaction between the aerodynamic forces, the inertial forces and the deformation of the structure. Usually the dynamic behaviour is transient and damped.
When the dynamic behaviour is undamped (the aerodynamic forces add more energy than is dissipated in the transforming structure) an increasing vibration will occur. This is called flutter. Flutter is unwanted the because the resulting severe vibrations can cause structural damage.
Here is an example of flutter on a small aeroplane:
The earliest form of aerolastic deformation gave rise to the famous control reversal of the aircraft trying to break the 'sound barrier'.
At high airspeeds, moving the elevator up created such a large force on the aft end of the tailplane ('stabiliser') that it twisted (which it wasn't designed/expected to do). The twisting pushed the aft end of the tailplane down, which gave the tailplane a net 'upwards' shape, and so the aircraft pitched down when the elevator was moved to give a pitch up.
A similar problem happened in roll, the aileron forcing the wing to twist in torsion, and thus the aileron acted as a tab with the wing itself acting as the aileron.
Measures now are...
* more metal in the structure
* moving stabiliser
* not using tip-mounted ailerons at high speed.