N. P. Lazarev, “Problem of equilibrium of the Timoshenko plate containing a crack on the boundary of an elastic inclusion with an infinite shear rigidity”, Prikl. Mekh. Tekh. Fiz., 2013, Volume 54, Issue 2,Pages <nobr>179

This article is cited in 8 papers

Problem of equilibrium of the Timoshenko plate containing a crack on the boundary of an elastic inclusion with an infinite shear rigidity

N. P. Lazarev^ab

^a Institute of Mathematics, North-East Federal University, Yakutsk, 677000, Russia
^b Lavrentyev Institute of Hydrodynamics of Siberian Branch of the Russian Academy of Sciences, Novosibirsk, 630090, Russia

Abstract: A problem of equilibrium of a composite plate consisting of a matrix and an elastic inclusion with a through crack along the boundary of this inclusion is studied. The matrix deformation is described by the Timoshenko model, and the elastic inclusion deformation is described by the Kirchhoff–Love model. Conditions of mutual non-penetration of the crack edges are imposed on the curve that describes the crack. Unique solvability of the variational problem is proved. A system of boundary conditions on the curve bounding (in the mid-plane) the elastic inclusion is obtained. A differential formulation of the problem equivalent to the initial variational formulation is given.

Keywords: plate, crack, non-penetration condition, variational problem, elastic inclusion.

UDC: 539.311

Received: 13.04.2012
Revised: 26.06.2012