Modeling of contact interaction of a heated plane rigid elliptical punch with a transversally isotropic elastic half-space

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

DOI:

https://doi.org/10.20535/SRIT.2308-8893.2020.3.10

Keywords:

mathematical model, contact interaction, elastic half-space, transversally-isotropic material, plane elliptical punch, heating, stress distribution, domain of material separation

Abstract

On the base of a rigorous mathematical model, the problem of the contact interaction of a heated flat punch of an elliptical section with a transversely isotropic elastic half-space is investigated. It is assumed that the half-space surface is the isotropy plane of a transversely isotropic material, and also that there is a smooth (without friction) contact. Expressions of contact stresses and displacements of a heated flat elliptical punch are found explicitly. In the form of a simple inequality, a condition for separating the elastic material from the surface of a flat elliptical punch is obtained. Numerical calculations are carried out. Contact interaction of a heated flat punch is studied taking into account the separation of material from the punch.

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.

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Published

2020-12-07

Issue

No. 3 (2020)

Section

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

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