Straight rod with different order of thickness

Article type: Research Article

Authors: Griso, G.^a | Villanueva-Pesqueira, Manuel^{b; *}

Affiliations: [a] Laboratoire J.-L. Lions – CNRS, Université Pierre et Marie Curie, Paris, France | [b] Departamento de Matemática Aplicada, Facultad de Matemáticas, Universidad Complutense de Madrid, Madrid, Spain

Correspondence: [*] Corresponding author: Manuel Villanueva-Pesqueira, Departamento de Matemática Aplicada, Facultad de Matemáticas, Universidad Complutense de Madrid, 28040 Madrid, Spain. E-mail: manuelvillanueva@mat.ucm.es.

Abstract: In this paper, we consider rods whose thickness vary linearly between ϵ and ϵ2. 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+u¯, where Ue stands for the translation-rotations of the cross-sections and 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.

Keywords: linear elasticity, rods

DOI: 10.3233/ASY-151313

Journal: Asymptotic Analysis, vol. 94, no. 3-4, pp. 255-291, 2015