We consider a thin elastic strip of height h and we show that stationary points of the nonlinear elastic energy whose energy (per unit height) is of order h^2 converge to stationary points of the Euler-Bernoulli functional. The proof uses a rigidity estimate for low-energy deformations and a compensated compactness argument in a singular geometry. In addition, possible concentration effects are ruled out by a careful truncation argument.
Convergence of equilibria of planar thin elastic beams
Mora, M. G.;
2007-01-01
Abstract
We consider a thin elastic strip of height h and we show that stationary points of the nonlinear elastic energy whose energy (per unit height) is of order h^2 converge to stationary points of the Euler-Bernoulli functional. The proof uses a rigidity estimate for low-energy deformations and a compensated compactness argument in a singular geometry. In addition, possible concentration effects are ruled out by a careful truncation argument.File in questo prodotto:
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