TY - JOUR
T1 - Convergence of equilibria of three-dimensional thin elastic beams
JF - Proc. Roy. Soc. Edinburgh Sect. A 138 (2008) 873-896
Y1 - 2008
A1 - Maria Giovanna Mora
A1 - Stefan Müller
AB - 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.
UR - http://hdl.handle.net/1963/1896
U1 - 2339
U2 - Mathematics
U3 - Functional Analysis and Applications
ER -