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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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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N. Neustroeva

North-Eastern Federal University (NEFU) Institute of Mathematics and Informatics; Lavrent’ev Institute of Hydrodynamics

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Email: nnataliav@mail.ru
俄罗斯联邦, ul. Kulakovskogo 48, Yakutsk, 677000; pr. Akad. Lavrent’eva 15, Novosibirsk, 630090

N. Lazarev

North-Eastern Federal University (NEFU) Scientific Research Institute of Mathematics

Email: nnataliav@mail.ru
俄罗斯联邦, ul. Kulakovskogo 48, Yakutsk, 677000

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