Mathematical modeling of the stress state in an orthotropic electroelastic space with an arbitrary oriented 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 B. Viter The Department of Information Systems and Technologies of the Faculty of Transport and Information Technologies of the National Transport University, Kyiv, Ukraine https://orcid.org/0000-0003-4109-005X
  • Lesia V. Kharytonova The Department of Information Systems and Technologies of the Faculty of Transport and Information Technologies of the National Transport University, Kyiv, Ukraine https://orcid.org/0000-0002-0108-6702

DOI:

https://doi.org/10.20535/SRIT.2308-8893.2020.2.10

Keywords:

mathematical modeling, orthotropic piezoelectric material, coupled system of equations of electroelasticity, spheroidal cavity, arbitrary orientation, inner pressure, stress state

Abstract

The stress state of an orthotropic electro-elastic space with an arbitrary oriented spheroidal cavity under internal pressure is investigated based on mathematical modeling. The problem's solution is obtained by using the Eshelby equivalent method, generalized to the case of orthotropic piezoelectric material, and the integral representation of the Green function for an anisotropic electroelastic space. Testing the algorithm for solving the problem on 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 stress distribution were revealed.

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 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 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 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 B. Viter, The Department of Information Systems and Technologies of the Faculty of Transport and Information Technologies of the National Transport University, Kyiv

Mykhailo Viter,

Candidate of Physical and Mathematical Sciences (Ph.D.), an associate professor at the Department of Information Systems and Technologies of the Faculty of Transport and Information Technologies of the National Transport University, Kyiv, Ukraine.

Lesia V. Kharytonova, The Department of Information Systems and Technologies of the Faculty of Transport and Information Technologies of the National Transport University, Kyiv

Lesia Kharytonova,

Candidate of Physical and Mathematical Sciences (Ph.D.), an associate professor at the Department of Information Systems and Technologies of the Faculty of Transport and Information Technologies of the National Transport University, Kyiv, Ukraine.

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Published

2020-09-25

Issue

No. 2 (2020)

Section

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

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