Convergence of equilibria of planar thin elastic beams
Functional Analysis
2007-05-23 v1
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 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.
Keywords
Cite
@article{arxiv.math/0604554,
title = {Convergence of equilibria of planar thin elastic beams},
author = {Maria Giovanna Mora and Stefan Mueller and Maximilian G. Schultz},
journal= {arXiv preprint arXiv:math/0604554},
year = {2007}
}
Comments
19 pages