Equilibria of a clamped Euler beam (Elastica) with distributed load: large deformations
Mathematical Physics
2017-03-22 v2 math.MP
Abstract
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.
Cite
@article{arxiv.1610.07814,
title = {Equilibria of a clamped Euler beam (Elastica) with distributed load: large deformations},
author = {Alessandro Della Corte and Francesco dell'Isola and Raffaele Esposito and Mario Pulvirenti},
journal= {arXiv preprint arXiv:1610.07814},
year = {2017}
}