Mathematical modeling of contact interaction of two electroelastic half-spaces under compression with rigid disc-shaped inclusion between them

Authors

  • V. S. Kirilyuk The Department of Mechanics of Stochastically Inhomogeneous Media of S.P. Timoshenko Institute of Mechanics of National Academy of Sciences of Ukraine, Kyiv, Ukraine https://orcid.org/0000-0002-8513-0378
  • Olga I. Levchuk The Department of Mechanics of Stochastically Inhomogeneous Media of S.P. Timoshenko Institute of Mechanics of National Academy of Sciences of Ukraine, Kyiv, Ukraine https://orcid.org/0000-0002-6514-6225
  • Оlena V. Gavrilenko The Department of Computer-Aided Management and Data Processing Systems of the Faculty of Informatics and Computer Science of the National Technical University of Ukraine "Igor Sikorsky Kyiv Polytechnic Institute", Kyiv, Ukraine https://orcid.org/0000-0003-0413-6274

DOI:

https://doi.org/10.20535/SRIT.2308-8893.2018.2.09

Keywords:

mathematical modeling, coupled system of equations of electroelasticity, piezoelectric half-space, rigid disc-shaped inclusion, parameters of contact interaction

Abstract

A mathematical model is developed for analyzing the contact interaction of two electroelastic transversely isotropic half-spaces under compression in the presence of a rigid disc-like inclusion of a constant thickness between them. The model is based on a consideration of the coupled system of electroelasticity equations for each of the piezoelectric half-spaces. The analytical solution of the problem is obtained by means of a general representation of solutions of the equations of electroelasticity on the basis of harmonic functions, reducing the problem to the consideration of the integral equation and the expansion of the unknown function with respect to a small parameter. As a particular case, the contact parameters for the two elastic transversely-isotropic half-spaces follow from the expressions obtained (if there is an inclusion between them). Numerical studies have been carried out, the influence of the connectedness of force and electric fields on the parameters of the contact interaction was studied.

Author Biographies

V. S. Kirilyuk, The Department of Mechanics of Stochastically Inhomogeneous Media of S.P. Timoshenko Institute of Mechanics of National Academy of Sciences of Ukraine, Kyiv

Vitaliy Semenovich Kirilyuk,

Doctor of Sciences (Physics and Mathematics), a senior researcher at the Department of Mechanics of Stochastically Inhomogeneous Media of S.P. Timoshenko Institute of Mechanics of National Academy of Sciences of Ukraine, Kyiv, Ukraine.

Olga I. Levchuk, The Department of Mechanics of Stochastically Inhomogeneous Media of S.P. Timoshenko Institute of Mechanics of National Academy of Sciences of Ukraine, Kyiv

Olga Ivanivna Levchuk,

Candidate of Sciences (Ph.D.), a senior researcher at the Department of Mechanics of Stochastically Inhomogeneous Media of S.P. Timoshenko Institute of Mechanics of National Academy of Sciences of Ukraine, Kyiv, Ukraine.

Оlena V. Gavrilenko, The Department of Computer-Aided Management and Data Processing Systems of the Faculty of Informatics and Computer Science of the National Technical University of Ukraine "Igor Sikorsky Kyiv Polytechnic Institute", Kyiv

Оlena Valeriyivna Gavrilenko,

candidate of physical and mathematical sciences, an associate professor at the Department of Computer-Aided Management and Data Processing Systems of the Faculty of Informatics and Computer Science of the National Technical University of Ukraine "Igor Sikorsky Kyiv Polytechnic Institute", Kyiv, Ukraine.

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Published

2018-06-20

Issue

No. 2 (2018)

Section

Mathematical methods, models, problems and technologies for complex systems research

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