@article {2008,
title = {Convergence of equilibria of three-dimensional thin elastic beams},
journal = {Proc. Roy. Soc. Edinburgh Sect. A 138 (2008) 873-896},
number = {SISSA;69/2006/M},
year = {2008},
abstract = {A convergence result is proved for the equilibrium configurations of a three-dimensional thin elastic beam, as the diameter $h$ of the cross-section tends to zero. More precisely, we show that stationary points of the nonlinear elastic functional $E^h$, whose energies (per unit cross-section) are bounded by $Ch^2$, converge to stationary points of the $\\\\varGamma$-limit of $E^h/h^2$. 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 M{\"u}ller 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.},
doi = {10.1017/S0308210506001120},
url = {http://hdl.handle.net/1963/1896},
author = {Maria Giovanna Mora and Stefan M{\"u}ller}
}