Calculus of Variations and Geometric Measure Theory

L. Freddi - A. Morassi - R. Paroni

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

created by freddi on 27 Apr 2006
modified on 26 Feb 2007


Published Paper

Inserted: 27 apr 2006
Last Updated: 26 feb 2007

Journal: Journal of Elasticity
Volume: 86
Number: 3
Pages: 263-296
Year: 2007


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