Decomposition of curved rod displacements using Bernoulli-Navier displacements. Application to different loads of curved rods.

In this paper, we present a mathematical approach of thin curved rods within the framework of linear elasticity. We show that any displacement of a curved rod is the sum of a Bernoulli-Navier displacement and residual displacements (including shearing and warping in the most complete decomposition). We give estimates of the terms of the decompositions with respect to δ and the L 2 norm of the strain tensor. Next, we present different loads applied to a curved rod and give the asymptotic behaviors of the corresponding linearized elasticity problems.