## M. G. Mora - S. Müller - M. G. Schultz

# Convergence of equilibria of planar thin elastic beams

created by mora on 26 Apr 2006

modified on 09 Nov 2007

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BibTeX]

*Published Paper*

**Inserted:** 26 apr 2006

**Last Updated:** 9 nov 2007

**Journal:** Indiana Univ. Math. J.

**Volume:** 56

**Pages:** 2413-2438

**Year:** 2007

**Abstract:**

We consider a thin elastic strip $\Omega_h = (0,L) \times (-h/2, h/2)$, and we show that stationary points of the nonlinear elastic energy (per unit height) whose energy is bounded by $C h^2$ converge to stationary points of the Euler-Bernoulli functional. The proof uses the rigidity estimate for low-energy deformations by Friesecke, James, and Müller ({\it 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.

**Keywords:**
dimension reduction, nonlinear elasticity, thin beams, equilibrium configurations

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