Proceedings of the Royal Society of Edinburgh: Section A Mathematics

Research Article

Asymptotic models for curved rods derived from nonlinear elasticity by Γ-convergence

Lucia Scardiaa1

a1 SISSA, Via Beirut 2–4, 34014 Trieste, Italy (scardia@sissa.it)

Abstract

We study the problem of the rigorous derivation of one-dimensional models for a thin curved beam starting from three-dimensional nonlinear elasticity. We describe the limiting models obtained for different scalings of the energy. In particular, we prove that the limit functional corresponding to higher scalings coincides with the one derived by dimension reduction starting from linearized elasticity.

(Received January 29 2007)

(Accepted October 09 2008)