Straight rod with different order of thickness

In this paper, we consider rods whose thickness vary linearly between and . 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 = Ue + ū, where Ue stands for the translation-rotations of the cross-sections and ū 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.