Using a variational approach we rigorously deduce a nonlinear model for inextensible rods from three-dimensional nonlinear elasticity, passing to the limit as the diameter of the rod goes to zero. The theory obtained is analogous to the Föppl–von Kármán theory for plates. We also derive an asymptotic expansion of the solution and compare it to a similar expansion which Murat and Sili obtained starting from three-dimensional linear elasticity.
A nonlinear model for inextensible rods as a low energy Gamma-limit of three-dimensional nonlinear elasticity
Mora, M. G.;
2004-01-01
Abstract
Using a variational approach we rigorously deduce a nonlinear model for inextensible rods from three-dimensional nonlinear elasticity, passing to the limit as the diameter of the rod goes to zero. The theory obtained is analogous to the Föppl–von Kármán theory for plates. We also derive an asymptotic expansion of the solution and compare it to a similar expansion which Murat and Sili obtained starting from three-dimensional linear elasticity.File in questo prodotto:
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