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

• Ia. M. Pasternak Lutsk National Technical University
• H. T. Sulym Pidstryhach Institute for Applied Problems of Mechanics and Mathematics National Academy of Sciences of Ukraine
Keywords: thread-like inclusion, integral equation, regularization

### Abstract

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.

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Published
12.10.2021
How to Cite
Pasternak , I. M., and H. T. Sulym. “Integral Equation of Elastic Medium Containing a Deformable Thread-Like Inclusion”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 73, no. 10, Oct. 2021, pp. 1391-03, doi:10.37863/umzh.v73i10.6785.
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Research articles