Geodesic
An equilibrium problem for the Timoshenko-type plate containing a~crack on the boundary of a~rigid inclusion
Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 6 (2013) no. 1, pp. 53-62.

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An equilibrium problem for an elastic Timoshenko type plate containing a rigid inclusion is considered. On the interface between the elastic plate and the rigid inclusion, there is a vertical crack. It is assumed that at both crack faces, boundary conditions of inequality type are considered describing a mutual non-penetration of the faces. A solvability of the problem is proved, and a complete system of boundary conditions is found. It is also shown that the problem is the limit one for a family of other problems posed for a wider domain and describing an equilibrium of elastic plates with a vertical crack as the rigidity parameter goes to infinity.
Keywords: crack, Timoshenko-type plate, rigid inclusion, energy functional, mutual non-penetration condition. 
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Nyurgun P. Lazarev. An equilibrium problem for the Timoshenko-type plate containing a~crack on the boundary of a~rigid inclusion. Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 6 (2013) no. 1, pp. 53-62. http://geodesic.mathdoc.fr/item/JSFU_2013_6_1_a5/

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