Asymptotic behavior of solutions of the anisotropic heterogeneous linearized elasticity system in thin cylinders. (Comportement asymptotique des solutions du système de l’élasticité linéarisée anisotrope hétérogène dans des cylindres minces.) (French. Abridged English version) Zbl 0929.74010

Murat, François; Sili, Ali

C. R. Acad. Sci., Paris, Sér. I, Math. 328, No. 2, 179-184 (1999).

Summary: We study the convergence of the solution \(u^\varepsilon\) of an anisotropic, heterogeneous, linearized elasticity problem in a cylinder, the diameter of which tends to zero. We prove, in particular, that \(u^\varepsilon-(u +\varepsilon v+\varepsilon^2w)\) strongly converges to zero (in a sense which is specified in the paper), where \((u,v,w)\) is the unique solution of an elliptic system of partial differential equations.

MSC:

74B05	Classical linear elasticity
35Q72	Other PDE from mechanics (MSC2000)

Keywords:

convergence; elliptic system