Calculus of Variations and Geometric Measure Theory

L. Freddi - A. Londero - R. Paroni

A simple variational derivation of slender rods theory

created by freddi on 29 Nov 2006
modified on 17 Oct 2007


Published Paper

Inserted: 29 nov 2006
Last Updated: 17 oct 2007

Journal: Applied and Industrial Mathematics in Italy II, Series in Mathermatics for Applied Sciences. World Scientific
Volume: 75
Pages: 363-374
Year: 2007


We present an asymptotic analysis of the three-dimensional problem for a thin linearly elastic cantilever \hbox{$\Omega_\varepsilon = \varepsilon\omega \times (0,\ell)$} as $\varepsilon$ goes to zero. By assuming $\omega$ simply connected and under suitable assumptions on the given loads, we show that the 3D problem converges in a variational sense to the classical dimensional models for extension, flexure and torsion of slender rods.

Keywords: $\Gamma$-convergence, linear elasticity, thin beams, slender rods