On an approach to solving the integral equation of a crack problem in a layered medium

Authors

  • Telyatnikov I.S. Federal Research Centre the Southern Scientific Centre of the Russian Academy of Sciences, Russian Federation ORCID iD 0000-0001-8500-2133

UDC

539.3

EDN

VDTBCO

DOI:

10.31429/vestnik-23-1-86-96

Abstract

One of the areas of research in mixed elasticity theory is the construction of mathematical models of the dynamics of defects in elastic media and the solution of problems describing these models. These include problems involving the vibrations of layered media with cracks. A layer or layered medium with a crack or system of cracks serves as a model for various natural structures, such as geological ones, as well as structural elements. Seismology is a traditional application of such models. This paper examines a method for solving problems of integral equations involving the excitation of harmonic vibrations in a package of layers with a free upper face and a lower face rigidly connected to a rigid base, caused by vibration of the faces of a finite-sized crack. To solve the integral equations after transforming their integral operator, the authors used the fictitious absorption method. The paper presents the results of model calculations for an axisymmetric problem formulated by an integral equation involving the vibration of an interface tensile crack in a two-layer elastic medium. Developed methods for solving static and problems for absorbing media, as well as highly viscous media with time-invariant properties, can be used to construct auxiliary solutions employed in the method of fictitious perturbations. The accuracy of the approximate solutions obtained by applying the method of fictitious perturbations is determined by the accuracy of the solutions to the static problems.

Keywords:

layer package, circular planar crack, block element method, integral equation, fictitious absorption method

Funding information

The work was carried out within the framework of the State Assignment of the Southern Scientific Center of the Russian Academy of Sciences (00-25-13, state registration number 125011200152-6).

Author info

  • Ilya S. Telyatnikov

    канд. физ.-мат. наук, старший научный сотрудник лаборатории математики и механики Южного научного центра РАН

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Issue

Vol. 23 (2026) No. 1

Pages

86-96

Section

Mechanics

Dates

Submitted

February 10, 2026

Accepted

March 17, 2026

Published

March 24, 2026

How to Cite

[1]
Telyatnikov, I.S., On an approach to solving the integral equation of a crack problem in a layered medium. Ecological Bulletin of Research Centers of the Black Sea Economic Cooperation, 2026, т. 23, № 1, pp. 86–96. DOI: 10.31429/vestnik-23-1-86-96

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