Mathematical modeling of the electrostressed state in the orthotropic piezoelectric space with an arbitrary orientated circle crack under uniaxial tension

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

DOI:

https://doi.org/10.20535/SRIT.2308-8893.2018.3.06

Keywords:

mathematical modeling, coupled equations systems of electroelasticity, orthotropic piezoelectric materials, circular crack, arbitrary orientation, uniaxial tension, stress state

Abstract

A mathematical model for the analysis of the stress state in an orthotropic electroelastic material with an arbitrary orientated circular crack is developed. The model is based on the consideration of the coupled system of equations of static electroelasticity. The problem on electric and stress states in orthotropic piezoelectric space with an arbitrary orientated circular crack under homogeneous loads was considered. The solution of the problem was obtained by means of the triple Fourier transform and Fourier image of Green's function for an infinite anisotropic piezoelectric medium. This approach was tested in the case of the location crack in the isotropy plane of transversely isotropic piezoelectric material for which there was an exact solution of the problem. The comparison of the calculated results confirmed the efficiency of the used approach. Numerical experiments were carried out and distributions of stress intensity factors along the front of the arbitrary orientated circular crack in orthotropic piezoelectric materials under the uniaxial tension were 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.

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Published

2018-10-16

Issue

No. 3 (2018)

Section

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

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