%0 Journal Article
%J Proc. Roy. Soc. Edinburgh Sect. A 138 (2008) 873-896
%D 2008
%T Convergence of equilibria of three-dimensional thin elastic beams
%A Maria Giovanna Mora
%A Stefan Müller
%X 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 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.
%B Proc. Roy. Soc. Edinburgh Sect. A 138 (2008) 873-896
%G en_US
%U http://hdl.handle.net/1963/1896
%1 2339
%2 Mathematics
%3 Functional Analysis and Applications
%$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2006-11-24T10:09:06Z\\nNo. of bitstreams: 1\\n69M-2006.pdf: 3633291 bytes, checksum: b5dba64c671bbcd8b87e52ce24963341 (MD5)
%R 10.1017/S0308210506001120