Equilibria of a clamped Euler beam (Elastica) with distributed load:   large deformations
  We present some novel equilibrium shapes of a clamped Euler beam (Elastica from now on) under uniformly distributed dead load orthogonal to the straight reference configuration. We characterize the properties of the minimizers of total energy, determine the corresponding Euler-Lagrange conditions and prove, by means of direct methods of calculus of variations, the existence of curled local minimizers. Moreover, we prove some sufficient conditions for stability and instability of particular solutions of the Euler-Lagrange conditions that can be applied to numerically found curled shapes. 
Alessandro Della Corte, Francesco dell'Isola, Raffaele Esposito, Mario   Pulvirenti
math-ph math.MP