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Contact Problems for Elastic Plates with Finite-Length Nonlinearly Deformable Stringers Glued to Their Boundaries

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Abstract

The problem to determine the mechanical field in a homogeneous half-plane supported by a finite homogeneous stringer, material of which obeys the nonlinear Hooke’s law, is considered. The contact between the plate and stringer is realized by a thin glue layer. The posed problem is reduced to a nonlinear singular integrodifferential equation. Using the Schauder fixed-point principle, we prove the existence of a solution to this equation. The uniqueness of the solution of the problem is proved. Using the small-parameter method, we obtain a system of recurrence linear singular integral equations of the first kind.

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Authors and Affiliations

  1. Tbilisi State University, Pazmadze Mathematical Institute, 0179, Tbilisi, Georgia

    N. N. Shavlakadze, O. M. Jokhadze & S. S. Kharibegashvili

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  1. N. N. Shavlakadze
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  2. O. M. Jokhadze
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  3. S. S. Kharibegashvili
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Correspondence to N. N. Shavlakadze.

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Translated by A. Muravnik

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Shavlakadze, N.N., Jokhadze, O.M. & Kharibegashvili, S.S. Contact Problems for Elastic Plates with Finite-Length Nonlinearly Deformable Stringers Glued to Their Boundaries. Mech. Solids 55, 1415–1422 (2020). https://doi.org/10.3103/S0025654420080269

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