Title | Convergence of equilibria of three-dimensional thin elastic beams |

Publication Type | Journal Article |

Year of Publication | 2008 |

Authors | Mora, MG, Müller, S |

Journal | Proc. Roy. Soc. Edinburgh Sect. A 138 (2008) 873-896 |

Abstract | A convergence result is proved for the equilibrium configurations of a three-dimensional thin elastic beam, as the diameter $h$ of the cross-section tends to zero. More precisely, we show that stationary points of the nonlinear elastic functional $E^h$, whose energies (per unit cross-section) are bounded by $Ch^2$, converge to stationary points of the $\\\\varGamma$-limit of $E^h/h^2$. 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. |

URL | http://hdl.handle.net/1963/1896 |

DOI | 10.1017/S0308210506001120 |

## Convergence of equilibria of three-dimensional thin elastic beams

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