Convergence of equilibria of three-dimensional thin elastic beams
Maria Giovanna Mora, Stefan G. Müller · Proceedings of the Royal Society of Edinburgh Section A Mathematics · 2008
A convergence result is proved for the equilibrium configurations of a three-dimensional thin elastic beam, as the diameter . This corresponds to a nonlinear one-dimensional model for inextensible rods, describing bending and torsion effects. The proof is based on the rigidity estimate for low-energy deformations by Friesecke, James and Müller and on a compensated compactness argument in a singular geometry. In addition, possible concentration effects of the strain are controlled by a careful truncation argument.