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- W2952742476 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 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 Muller 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." @default.
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- W2952742476 date "2006-12-18" @default.
- W2952742476 modified "2023-10-01" @default.
- W2952742476 title "Convergence of equilibria of three-dimensional thin elastic beams" @default.
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