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Junctions between three-dimensional and two-dimensional linear elastic structures. (English) Zbl 0661.73013
We consider a problem in three-dimensional linearized elasticity, posed over a domain consisting of a plate with thickness \(2\epsilon\), inserted into a solid whose Lamé constants are independent of \(\epsilon\). If the Lamé constants of the material constituting the plate vary as \(\epsilon^{-3}\), we show that the solution of the three-dimensional problem converges, as \(\epsilon\) approaches zero, to the solution of a coupled “pluri-dimensional” problem of a new type, posed simultaneously over a three-dimensional open set with a slit and a two-dimensional open set.
Reviewer: Ph.Ciarlet

74B99 Elastic materials
74K99 Thin bodies, structures