Modélisation de la jonction entre un corps élastique tridimensionnel et une plaque. (Modeling of the junction between a three-dimensional elastic body and a plate). (French) Zbl 0632.73015

Ciarlet, Philippe G.; Le Dret, Hervé; Nzengwa, Robert

C. R. Acad. Sci., Paris, Sér. I 305, 55-58 (1987).

The paper proves a theorem which shows that the solution of a three- dimensional problem of linear elasticity-posed on a domain consisting of (i) a plate of thickness \(2\epsilon\), the Lamé constants of its material varying as \(\epsilon^{-3}\); and (ii) a solid whose Lamé constants are independent of \(\epsilon\)- converges with \(\epsilon\) approaching 0 to the solution of a variational problem posed simultaneously on a three-dimensional open set with a slot and a two- dimensional open set.

Reviewer: S.K.Lakshmana Rao

MSC:

74S30	Other numerical methods in solid mechanics (MSC2010)
74B20	Nonlinear elasticity
74K20	Plates

Keywords:

variable Lame constants; uniform Lame constants; three-dimensional problem