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arXiv · 1605.07871

Straight rod with different order of thickness

Georges Griso·Manuel Villanueva Pesqueira
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Abstract

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.

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Georges Griso, Manuel Villanueva Pesqueira. 2016-05-19. Straight rod with different order of thickness. https://arxiv.org/abs/1605.07871

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