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Equilibrium of an Elastic Body with Closely Spaced Thin Inclusions

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Abstract

Problems with unknown boundaries describing an equilibrium of two-dimensional elastic bodies with two thin closely spaced inclusions are considered. The inclusions are in contact with each other, which means that there is a crack between them. On the crack faces, nonlinear boundary conditions of the inequality type that prevent the interpenetration of the faces are set. The unique solvability of the problems is proved. The passages to the limit as the stiffness parameter of thin inclusions tends to infinity are studied, and limiting models are analyzed.

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Authors and Affiliations

  1. Lavrentiev Institute of Hydrodynamics, Siberian Branch, Russian Academy of Sciences, 630090, Novosibirsk, Russia

    A. M. Khludnev

  2. Novosibirsk State University, 630090, Novosibirsk, Russia

    A. M. Khludnev

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  1. A. M. Khludnev
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Correspondence to A. M. Khludnev.

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Translated by I. Ruzanova

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Khludnev, A.M. Equilibrium of an Elastic Body with Closely Spaced Thin Inclusions. Comput. Math. and Math. Phys. 58, 1660–1672 (2018). https://doi.org/10.1134/S096554251810007X

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  • DOI: https://doi.org/10.1134/S096554251810007X

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