Inserted: 14 mar 2011
Last Updated: 11 jan 2017
Journal: Mathematical Models and Methods in Applied Sciences (M3AS)
In this paper we report the second part of our results concerning the rigorous derivation of a hierarchy of one-dimensional models for thin-walled beams with rectangular cross-section. Denoting by $h$ and $\delta_h$ the length of the sides of the cross-section of the beam, we analyse the limit behaviour of a non-linear elastic energy which scales as $\varepsilon_h^2$ when $\varepsilon_h/\delta_h\to0$.
Keywords: $\Gamma$-convergence, dimension reduction, nonlinear elasticity, thin-walled cross-section beams