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Exact solutions of some singular integro-differential equations related to adhesive contact problems of elasticity theory

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Abstract

The problem of constructing an exact solution of singular integro-differential equations related to problems of adhesive interaction between elastic thin semi-infinite homogeneous patch and elastic plate is investigated. For the patch loaded with horizontal forces the usual model of the uniaxial stress state is valid. Using the methods of the theory of analytic functions and integral transformation, the singular integro-differential equation is reduced to the Riemann boundary value problem of the theory of analytic functions. The exact solution of this problem and asymptotic estimates of tangential contact stresses are obtained.

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Authors and Affiliations

  1. A. Razmadze Mathematical Institute, Tbilisi State University, Tamarashvili str. 6, 0177, Tbilisi, Georgia

    Nugzar Shavlakadze

  2. Department of Computer Sciences, Faculty of Exact and Natural Sciences, Iv.Javakhishvili Tbilisi State University, 2, University st., 0143, Tbilisi, Georgia

    Nana Odishelidze

  3. Department of Applied Physics II, Polytechnic School, Malaga University, Campus Teatinos, s/n, 29071, Málaga, Spain

    Francisco Criado-Aldeanueva

Authors
  1. Nugzar Shavlakadze
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  2. Nana Odishelidze
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  3. Francisco Criado-Aldeanueva
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Correspondence to Francisco Criado-Aldeanueva.

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Shavlakadze, N., Odishelidze, N. & Criado-Aldeanueva, F. Exact solutions of some singular integro-differential equations related to adhesive contact problems of elasticity theory. Z. Angew. Math. Phys. 71, 115 (2020). https://doi.org/10.1007/s00033-020-01350-4

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  • DOI: https://doi.org/10.1007/s00033-020-01350-4

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