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Differentiation of the energy functional in the equilibrium problem for a Timoshenko plate containing a crack

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Abstract

The variational formulation of the equilibrium problem for a Timoshenko plate containing a vertical plane crack is considered. Nonpenetration conditions in the form of inequalities (Signorini type conditions) are specified on the crack faces. The behavior of the solution and the corresponding energy functional of the plate with variation in the crack length is analyzed. A formula for the derivative of the energy functional along the crack length is obtained. The solutions are found to continuously depend on the parameter characterizing the crack length.

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Authors and Affiliations

  1. Research Institute of Mathematics, Ammosov North-East Federal University, Yakutsk, 677000, 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. 53, No. 2, pp. 175–185, March–April, 2012.

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Lazarev, N.P. Differentiation of the energy functional in the equilibrium problem for a Timoshenko plate containing a crack. J Appl Mech Tech Phy 53, 299–307 (2012). https://doi.org/10.1134/S0021894412020198

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  • DOI: https://doi.org/10.1134/S0021894412020198

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