Calculus of Variations and Geometric Measure Theory

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


Published Paper

Inserted: 26 apr 2006
Last Updated: 9 nov 2007

Journal: Indiana Univ. Math. J.
Volume: 56
Pages: 2413-2438
Year: 2007


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