Straight rod with different order of thickness

Georges Griso (1) , Manuel Villanueva Pesqueira (2)

1 LJLL - Laboratoire Jacques-Louis Lions
2 DMA - Departamento de Matemática Aplicada [Madrid]

In this paper, we consider rods whose thickness vary linearly between $\eps$ and $\eps^2$. 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 $u=U_e + \bar{u}$, where $U_e$ stands for the translation-rotations of the cross-sections and $\bar{u}$ 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.

Domaines: Analyse numérique [math.NA]

Georges Griso, Manuel Villanueva Pesqueira. Straight rod with different order of thickness. Asymptotic Analysis, 2016. ⟨hal-01240748⟩