We present an asymptotic analysis of the three-dimensional problem for a thin linearly elastic cantilever Ωε = εω × (0, ℓ) as ε goes to zero. By assuming ω 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.
A simple variational derivation of slender rods theory
FREDDI, Lorenzo;
2007-01-01
Abstract
We present an asymptotic analysis of the three-dimensional problem for a thin linearly elastic cantilever Ωε = εω × (0, ℓ) as ε goes to zero. By assuming ω 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.File in questo prodotto:
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