Convergence of equilibria of three-dimensional thin elastic beams

Maria Giovanna Mora, Stefan Müller

Type: Article

Publication Date: 2008-07-28

Citations: 33

DOI: https://doi.org/10.1017/s0308210506001120

Abstract

A convergence result is proved for the equilibrium configurations of a three-dimensional thin elastic beam, as the diameter . This corresponds to a nonlinear one-dimensional model for inextensible rods, describing bending and torsion effects. The proof is based on the rigidity estimate for low-energy deformations by Friesecke, James and Müller and on a compensated compactness argument in a singular geometry. In addition, possible concentration effects of the strain are controlled by a careful truncation argument.

Locations

Proceedings of the Royal Society of Edinburgh Section A Mathematics - View
arXiv (Cornell University) - View - PDF

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