Mathematical modeling of the stress state of an orthotropic piezoelectric material with a spheroidal cavity under internal pressure

Authors

  • Vitaly 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
  • Olena 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
  • Mykhailo K. Sukach Kyiv National University of Construction and Architecture, Kyiv, Ukraine https://orcid.org/0000-0003-0485-4073

DOI:

https://doi.org/10.20535/SRIT.2308-8893.2019.3.10

Keywords:

mathematical modeling, orthotropic piezoelectric material, system of electro-elasticity equations, spheroidal cavity, internal pressure, stress state

Abstract

On the basis of mathematical modeling, the stress state of an orthotropic electro-elastic space with a spheroidal cavity under internal pressure is investigated. The solution of the problem is obtained by using the Eshelby equivalent method, generalized to the case of an orthotropic piezoelectric material, and the integral representation of the Green’s function for an orthotropic electroelastic space. Testing of the algorithm for solving the problem for a special case (for a transversely isotropic electrical-elastic material with a spheroidal cavity) confirms its effectiveness. The numerical studies of the stress state in an orthotropic electroelastic material with a cavity under internal pressure were carried out, characteristic patterns of the stress distribution were found.

Author Biographies

Vitaly 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

Vitaly Semenovich Kirilyuk,

senior researcher, Doctor of Sciences (Physics and Mathematics), a leading 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.

Olena 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

Olena Valersiyvna Gavrilenko,

Ph.D., an associated 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.

Mykhailo K. Sukach, Kyiv National University of Construction and Architecture, Kyiv

Mykhailo K. Sukach,

Doctor of Technical Sciences, a professor at the Department of construction machinery of Kyiv National University of Construction and Architecture, Kyiv, Ukraine.

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Published

2019-10-07

Issue

No. 3 (2019)

Section

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

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