Convergence of equilibria of planar thin elastic beams

Details Convergence of equilibria of planar thin elastic beams Convergence of equilibria of planar thin elastic beams

2006-04-26

arxiv.org/abs/math/0604554v1

Mathematics

Functional Analysis

19 pages

Scientific paper

We consider a thin elastic strip of thickness h and we show that stationary points of the nonlinear elastic energy (per unit height) whose energy is of order h^2 converge to stationary points of the Euler-Bernoulli functional. The proof uses the rigidity estimate for low-energy deformations by Friesecke, James, and Mueller (Comm. Pure Appl. Math. 2002), and a compensated compactness argument in a singular geometry. In addition, possible concentration effects are ruled out by a careful truncation argument.

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