Kravchuk A.S., Kravchuk A.I. Stress State of Elastic Thick-Walled Ring With Self-Balanced Pressures Distributed on Its Internal and External Borders
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http://dx.doi.org/10.15688/jvolsu1.2015.4.5
Kravchuk Aleksandr Stepanovich
Doctor of Physical and Mathematical Sciences, Associate Professor,
Professor of Department of Bio- and Nanomechanics,
Belarusian State University
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Prosp. Nezavisimosti, 4, 220030 Minsk, Republic of Belarus
Kravchuk Anzhelika Ivanovna
Candidate of Physical and Mathematical Sciences, Associate Professor,
Department of Web-technologies and Computer Modeling,
Belarusian State University
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Prosp. Nezavisimosti, 4, 220030 Minsk, Republic of Belarus
Abstract. For the first time with the help of the theory of analytic functions and Kolosov-Muskhelishvili formulas the problem of the two-dimensional theory of elasticity for a thickwalled ring with the uneven pressures, acting on its borders, was solved. The pressure on the inner and outer boundaries is represented by Fourier series. The authors represent the two complex functions which solve boundary problem in the form of Laurent series. The logarithmic terms in these series are absent because the boundary problem has the self-balancing loads on each boundary of ring. The coefficients in the Laurent series are calculated by the boundary conditions. Firstly, the equations were obtained in the general form. But the hypothesis about even distributions of pressures at borders of ring was used for constructing an example. It leads to the fact that all coefficients of analytic functions represented in Laurent series have to be only real. As a solving example, the representation of pressures in equivalent hypotrochoids was used. The application of the computer algebra system Mathematica greatly simplifies the calculation of the distribution of stresses and displacements in ring. It does not require manual formal separation of real and imaginary parts in terms of Kolosov-Muskhelishvili to display the distribution of the physical parameters. It separates them only for calculated numbers with the help of built-in functions.
Key words: analytic functions, Kolosov-Muskhelishvili formulas, complex numbers, elastic thick-walled ring, uneven pressure.
Stress State of Elastic Thick-Walled Ring With Self-Balanced Pressures Distributed on Its Internal and External Borders by Kravchuk A.S., Kravchuk A.I. is licensed under a Creative Commons Attribution 4.0 International License.
Citation in English: Science Journal of Volgograd State University. Mathematics. Physics. №4 (29) 2015 pp. 45-56
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