Problem of equilibrium of the timoshenko plate containing a crack on the boundary of an elastic inclusion with an infinite shear rigidity |
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Authors: | N. P. Lazarev |
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Affiliation: | 1489. Institute of Mathematics, North-East Federal University, Yakutsk, 677000, Russia 2489. Lavrent’ev Institute of Hydrodynamics, Siberian Branch, Russian Academy of Sciences, Novosibirsk, 630090, Russia
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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. |
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