Thin-walled beams: the case of an open multi-rectangular cross-section

In this paper we present an asymptotic analysis of the three-dimensional problem for a thin linearly elastic cantilever Omega_ε = omega_ε × (0, l) with rectangular cross-section omega_ε of sides ε and ε^2, as ε 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.