Convergence of equilibria of planar thin elastic beams

2006/04/26 by Maria Giovanna Mora, Mora, Maria Giovanna, Stefan Mueller +3 · 1 citation
Mathematics · #FOS: Mathematics #Functional Analysis (math.FA) #math.FA

paper · pdf · doi:10.48550/arxiv.math/0604554

19 pages

arxiv created 2006/04/26 · arxiv updated 2009/12/01

Abstract

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 h² 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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