Mathematical modeling and analysis of the stressed state in the orthotropic piezoelectric medium with a circle crack

Authors

  • Vitaliy Kirilyuk The Department of mechanics of stochastic nonhomogeneous media of the S. P. Timoshenko Institute of Mechanics of the NASU, Kyiv, Ukraine https://orcid.org/0000-0002-8513-0378
  • Olga Levchuk The Department of mechanics of stochastic nonhomogeneous media of the S. P. Timoshenko Institute of Mechanics of the NASU, Kyiv, Ukraine https://orcid.org/0000-0002-6514-6225
  • Olena Gavrilenko The Faculty of Informatics and Computer Science of 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.2308-8893.2017.3.11

Keywords:

mathematical modeling, coupled equations systems of electroelasticity, orthotropic piezoelectric materials, flat circle crack, uniform loading, stress intensity factors

Abstract

A mathematical model for the analysis of the stress state in an orthotropic electroelastic material with a circular (penny-shaped) crack is developed. The model is based on the consideration of the coupled system of electroelasticity equations. The problem on electric and stress states in orthotropic piezoelectric space with an elliptical crack under the force and electric loading was considered. The solution of the problem was obtained by means of using of the triple Fourier transform and Fourier image of Green's function for an infinite orthotropic piezoelectric medium. The 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 high efficiency of the used approach. Numerical experiments were conducted and distributions of stress intensity factors along elliptical crack front in orthotropic piezoelectric materials and elastic orthotropic materials under uniform force loading were investigated.

Author Biographies

Vitaliy Kirilyuk, The Department of mechanics of stochastic nonhomogeneous media of the S. P. Timoshenko Institute of Mechanics of the NASU, Kyiv

Vitaliy Kirilyuk,

senior scientist, Doctor of Phys.-Math. Sc., the lead scientist of the Department of mechanics of stochastic nonhomogeneous media of the S. P. Timoshenko Institute of Mechanics of the NASU, Kyiv, Ukraine.

Olga Levchuk, The Department of mechanics of stochastic nonhomogeneous media of the S. P. Timoshenko Institute of Mechanics of the NASU, Kyiv

Olga Levchuk,

Ph.D., Candidate of Phys.-Math. Sc., a senior scientist of the Department of mechanics of stochastic nonhomogeneous media of the S. P. Timoshenko Institute of Mechanics of the NASU, Kyiv, Ukraine.

Olena Gavrilenko, The Faculty of Informatics and Computer Science of National Technical University of Ukraine "Igor Sikorsky Kyiv Polytechnic Institute", Kyiv

Olena Gavrilenko,

Ph.D., Candidate of Phys.-Math. Sc., an associate professor at the Faculty of Informatics and Computer Science of National Technical University of Ukraine "Igor Sikorsky Kyiv Polytechnic Institute", Kyiv, Ukraine.

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Published

2017-09-29

Issue

No. 3 (2017)

Section

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

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