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Energy functional derivative with respect to the length of a curvilinear oblique cut in the equilibrium problem for a Timoshenko plate

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Abstract

This paper describes the dependence of the solution of the equilibrium problem for a Timoshenko plate and the total energy functional of the plate on the perturbation of an oblique crack. The nonlinearity of the problem is caused by the boundary conditions in the form of inequalities (conditions such as the Signorini conditions), which describe mutual nonpenetration of the opposite crack faces. The continuous dependence of the solution of the problem on the perturbation of the crack length is established. A formula for the energy functional derivative of the perturbation of the crack length is obtained.

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Authors and Affiliations

  1. Scientific Research Institute of Mathematics of the North-Eastern Federal University, Yakutsk, 677000, Russia

    N. P. Lazarev

  2. Lavrentyev Institute of Hydrodynamics, 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.

Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 56, No. 6, pp. 119–131, November–December, 2015.

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Lazarev, N.P. Energy functional derivative with respect to the length of a curvilinear oblique cut in the equilibrium problem for a Timoshenko plate. J Appl Mech Tech Phy 56, 1038–1048 (2015). https://doi.org/10.1134/S0021894415060140

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  • DOI: https://doi.org/10.1134/S0021894415060140

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