Inserted: 27 apr 2006
Last Updated: 26 feb 2007
Journal: Journal of Elasticity
This paper deals with the asymptotic analysis of the three-dimen\-sional problem for a linearly elastic cantilever having an open cross-section which is the union of rectangles with sides of order $\varepsilon$ and $\varepsilon^2$, as $\varepsilon$ goes to zero. Under suitable assumptions on the given loads and for homogeneous and isotropic material, we show that the three-dimensional problem $\Gamma$-converges to the classical one-dimensional Vlas\-sov model for thin-walled beams.
Keywords: $\Gamma$-convergence, dimension reduction, thin-walled cross-section beams, linear elasticity