Calculus of Variations and Geometric Measure Theory

L. Freddi - A. Morassi - R. Paroni

Thin-walled beams: the case of the rectangular cross-section

created on 22 Jun 2004
modified by freddi on 02 Mar 2005


Published Paper

Inserted: 22 jun 2004
Last Updated: 2 mar 2005

Journal: Journal of Elasticity
Volume: 76
Pages: 45-66
Year: 2004


In this paper we present an asymptotic analysis of the three-dimen\-sional problem for a thin linearly elastic cantilever \hbox{$\Omega_\varepsilon = \omega_\varepsilon \times (0,l)$} with rectangular cross-section $\omega_\varepsilon $ of sides $\varepsilon $ and $\varepsilon ^2$, as $\varepsilon $ goes to zero. Under suitable assumptions on the given loads, we show that the three-dimensional problem converges in a variational sense to the classical one-dimensional model for extension, flexure and torsion of thin-walled beams.

Keywords: dimension reduction, thin-walled cross-section beams, linear elasticity, Gamna-convergence