Integral Equation of the Elastic Medium Containing a Deformable Thread-Like Inclusion

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...

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Bibliographic Details
Published in:Ukrainian mathematical journal 2022-03, Vol.73 (10), p.1607-1621
Main Authors: Pasternak, Ia. M., Sulym, H. T.
Format: Article
Language:English
Subjects:
Algebra
Analysis
Applications of Mathematics
Elastic deformation
Elastic media
Formability
Geometry
Inclusions
Inhomogeneity
Integral equations
Mathematical analysis
Mathematics
Mathematics and Statistics
Numerical analysis
Statistics
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Summary: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.
ISSN:0041-5995
1573-9376
DOI:10.1007/s11253-022-02017-1