In the present paper, we propose a method aimed at the mathematical simulation of deformable threadlike (wire) inclusions based on the replacement of their influence on the elastic medium by tensile/compressive forces distributed along their axes. We construct a regularized integral equation of the problem external with respect to the inhomogeneity and develop mathematical models of inhomogeneity that take into account the conditions of contact and enable one to determine the required distribution of forces along the axis of inhomogeneity. An approach to the solution of the posed problems is proposed. For the case of a rectilinear elastic thread-like inclusion of finite length, we obtain an approximate solution of the problem in the closed analytic form.
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 73, No. 10, pp. 1391–1403, October, 2021. Ukrainian DOI: https://doi.org/10.37863/umzh.v73i10.6785.
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Pasternak, I.M., Sulym, H.T. Integral Equation of the Elastic Medium Containing a Deformable Thread-Like Inclusion. Ukr Math J 73, 1607–1621 (2022). https://doi.org/10.1007/s11253-022-02017-1
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DOI: https://doi.org/10.1007/s11253-022-02017-1