Deformations of a 2D Elastica under a random distribution of normal loads

We describe the deformations of a 2D elastic structure (beam, rod or filament) subjected to randomly distributed local orthogonal forces. The fiber is in quasistatic equilibrium condition when a given force distribution is acting on it. To analyze the effects of force fluctuations on the observed configurations, we study the behavior of the bending moment at the origin and the filament curvature, as a function of nominal values of the local mean forces and small, moderate and large fluctuations around them.