Thin-walled beams: a derivation of Vlassov theory via Gamma-convergence

This paper deals with the asymptotic analysis of the three-dimensional problem for a linearly elastic cantilever having an open cross-section which is the union of rectangles with sides of order epsilon and epsilon^2, as epsilon 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 Vlassov model for thin-walled beams.