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DOI: 10.34229/KCA2522-9664.24.1.16
UDC 519.6, 539.3
B.E. Panchenko1, Yu.D. Kovalev2, T.O. Kalinina3,
I.N. Saiko4, L.M. Bukata5


1 Odesa I.I. Mechnykov National University, Odesa, Ukraine

 pr-bob@ukr.net

2 State University of Intellectual Technologies and Communications, Odesa, Ukraine

 kovalev@ukr.net

3 State University of Intellectual Technologies and Communications, Odesa, Ukraine

 kalininat384@gmail.com

4 V.M. Glushkov Institute of Cybernetics, National Academy of Sciences of Ukraine, Kyiv, Ukraine

 igor.sayko1988@gmail.com

5 State University of Intellectual Technologies and Communications, Odesa, Ukraine

 ygrikluda@gmail.com

MATHEMATICAL MODELING IN STATIC THREE-DIMENSIONAL
BOUNDARY-VALUE PROBLEMS:
A SKEW-SYMMETRIC PROBLEM FOR A LAYER WEAKENED
BY A THROUGH HOLE WITH SLIDING SEALING OF ITS ENDS

Abstract. Spatial static boundary-value problems of mathematical physics for a layer with a non-circular cylindrical through hole have hardly been solved using the method of singular integral equations (SIE) despite the fact that numerous fundamental theoretical issues have been developed. Methods for the calculation of spectral characteristics are also absent. The paper provides an overview of the methods for solving these problems. A new mathematical model has been constructed, and a new method based on a system of three SIEs has been developed and tested numerically. As a result of a high-precision numerical study, it was found that with an increase in the thickness of the layer, an increase in the relative circumferential stress occurs. In the case of a circular hole, a shift of the maximum relative circumferential stress from the ends to the depth of the layer is observed. In the case of an elliptical hole, with a decrease in one of the radii, an increase in the relative circumferential stress is also observed.

Keywords: three-dimensional boundary-value problems, singular integral equations, numerical experiment, static bending, a through hole.


full text

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