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Convergence of equilibria of planar thin elastic beams

TitleConvergence of equilibria of planar thin elastic beams
Publication TypeJournal Article
Year of Publication2007
AuthorsMora, MG, Müller, S, Schultz, MG
JournalIndiana Univ. Math. J. 56 (2007) 2413-2438

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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