Convergence of equilibria of three-dimensional thin elastic beams
| dc.creator | Mora, Maria Giovanna | |
| dc.creator | Müller, Stefan | |
| dc.date | 2006-12-18 | |
| dc.date.accessioned | 2026-07-07T07:35:43Z | |
| dc.date.available | 2026-07-07T07:35:43Z | |
| dc.description | A convergence result is proved for the equilibrium configurations of a three-dimensional thin elastic beam, as the diameter h of the cross-section goes 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 Gamma-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. | |
| dc.description | 22 pages | |
| dc.identifier | https://arxiv.org/abs/math/0612519 | |
| dc.identifier | http://arxiv.org/abs/math/0612519 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/120187 | |
| dc.subject | Analysis of PDEs | |
| dc.subject | 74K10; 74B20; 74G10 | |
| dc.title | Convergence of equilibria of three-dimensional thin elastic beams | |
| dc.type | text |