Straight rod with different order of thickness

摘要

In this paper, we consider rods whose thickness vary linearly between epsilon and epsilon(2). Our aim is to study the asymptotic behavior of these rods in the framework of the linear elasticity. We use a decomposition method of the displacement fields of the form u = U-e + (u) over bar, where U-e stands for the translation-rotations of the cross-sections and (u) over bar is related to their deformations. We establish a priori estimates. Passing to the limit in a fixed domain gives the problems satisfied by the bending, the stretching and the torsion limit fields which are ordinary differential equations depending on weights.