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Differentiation of the energy functional in the equilibrium problem for a Timoshenko plate with a crack on the boundary of an elastic inclusion

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Abstract

Under consideration is the equilibrium of a composite plate containing a through vertical crack of variable length at the interface between thematrix and the elastic inclusion. The deformation of the matrix is described by the Timoshenko model, and the deformation of the elastic inclusion, by the Kirchhoff–Love model. Some formula is obtained for the derivative of the energy functional with respect to the crack length.

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Authors and Affiliations

  1. North-Eastern Federal University (NEFU) Institute of Mathematics and Informatics, ul. Kulakovskogo 48, Yakutsk, 677000, Russia

    N. V. Neustroeva

  2. Lavrent’ev Institute of Hydrodynamics, pr. Akad. Lavrent’eva 15, Novosibirsk, 630090, Russia

    N. V. Neustroeva

  3. North-Eastern Federal University (NEFU) Scientific Research Institute of Mathematics, ul. Kulakovskogo 48, Yakutsk, 677000, Russia

    N. P. Lazarev

Authors
  1. N. V. Neustroeva
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  2. N. P. Lazarev
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Correspondence to N. V. Neustroeva.

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Original Russian Text © N.V. Neustroeva, N.P. Lazarev, 2017, published in Sibirskii Zhurnal Industrial’noi Matematiki, 2017, Vol. XX, No. 2, pp. 59–70.

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Neustroeva, N.V., Lazarev, N.P. Differentiation of the energy functional in the equilibrium problem for a Timoshenko plate with a crack on the boundary of an elastic inclusion. J. Appl. Ind. Math. 11, 252–262 (2017). https://doi.org/10.1134/S1990478917020119

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