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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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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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Authors and Affiliations

  1. Institute of Mathematics, North-East Federal University, Yakutsk, 677000, Russia

    N. P. Lazarev

  2. Lavrent’ev Institute of Hydrodynamics, Siberian Branch, Russian Academy of Sciences, Novosibirsk, 630090, Russia

    N. P. Lazarev

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  1. N. P. Lazarev
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Correspondence to N. P. Lazarev.

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Original Russian Text © N.P. Lazarev.

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Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 54, No. 2, pp. 179–189, March–April, 2013.

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Lazarev, N.P. Problem of equilibrium of the timoshenko plate containing a crack on the boundary of an elastic inclusion with an infinite shear rigidity. J Appl Mech Tech Phy 54, 322–330 (2013). https://doi.org/10.1134/S0021894413020181

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  • DOI: https://doi.org/10.1134/S0021894413020181

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