Elastic instability

Elastic instability is a form of instability occurring in elastic systems, such as buckling of beams and plates subject to large compressive loads.

Consider as a simple example a rigid beam of length L, hinged in one end and free in the other, and having an angular spring attached to the hinged end. The beam is loaded in the free end by a force F acting in the compressive axial direction of the beam, see the figure to the right.

Assuming a clockwise angular deflection ${\displaystyle \theta }$, the clockwise moment exerted by the force becomes ${\displaystyle M_{F}=FL\sin \theta }$. The moment equilibrium equation is given by

${\displaystyle FL\sin \theta =k_{\theta }\theta }$

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