**Inserted:** 30 jun 2011

**Last Updated:** 30 nov 2012

**Journal:** Adv. Calc. Var.

**Year:** 2012

**Abstract:**

The subject of this paper is the rigorous derivation of lower dimensional models for a nonlinearly elastic thin-walled beam whose cross-section is given by a thin tubular neighbourhood of a smooth curve. Denoting by $h$ and $\delta_h$, respectively, the diameter and the thickness of the cross-section, we analyse the case where the scaling factor of the elastic energy is of order $\epsilon_h^2$, with $\epsilon_h/\delta_h^2\rightarrow \ell\in [0,+\infty)$. Different linearized models are deduced according to the relative order of magnitude of $\delta_h$ with respect to $h$.

**Keywords:**
Gamma-convergence, dimension reduction, nonlinear elasticity, Thin-walled beams

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