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
Abstract:
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
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