Integral equation of elastic medium containing a deformable thread-like inclusion

UDC 517.968.23: 539.3 In this study, we propose a method of mathematical modeling of deformable thread-like (wire) inclusions based on replacing their influence on the elastic medium with the tension/compression forces distributed along their axis. We derive a regularized integral equation of the pr...

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Bibliographic Details
Date:2026
Main Authors: Pasternak , Ia. M., Sulym, H. T., Пастернак, Я. М., Сулим, Г. Т.
Format: Article
Language:Ukrainian
Published: Institute of Mathematics, NAS of Ukraine 2026
Online Access:https://umj.imath.kiev.ua/index.php/umj/article/view/6785
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Journal Title:Ukrains’kyi Matematychnyi Zhurnal
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Ukrains’kyi Matematychnyi Zhurnal
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Summary:UDC 517.968.23: 539.3 In this study, we propose a method of mathematical modeling of deformable thread-like (wire) inclusions based on replacing their influence on the elastic medium with the tension/compression forces distributed along their axis. We derive a regularized integral equation of the problem, which is external with respect to the inhomogeneity, and also a mathematical model of inhomogeneity, which, taking into account the contact conditions, makes it possible to determine the desired distribution of forces along the axis of inhomogeneity. An approach to solving these equations is proposed. For the case of a rectilinear elastic thread-like inclusion, an approximate solution of the problem is obtained in a close analytical form.
DOI:10.37863/umzh.v73i10.6785