Calculus of Variations and Geometric Measure Theory

E. Davoli

Thin-walled beams with a cross-section of arbitrary geometry: derivation of linear theories starting from 3D nonlinear elasticity

created by davoli on 30 Jun 2011
modified on 30 Nov 2012


Inserted: 30 jun 2011
Last Updated: 30 nov 2012

Journal: Adv. Calc. Var.
Year: 2012


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