On one approach to the solution of miscellaneous problems of the theory of elasticity
https://doi.org/10.29235/1561-2430-2021-57-3-263-273
Abstract
Herein, a miscellaneous contact problem of the theory of elasticity in the upper half-plane is considered. The boundary is a real semi-axis separated into four parts, on each of which the boundary conditions are set for the real or imaginary part of two desired analytical functions. Using new unknown functions, the problem is reduced to an inhomogeneous Riemann boundary value problem with a piecewise constant 2 × 2 matrix and four singular points. A differential equation of the Fuchs class with four singular points is constructed, the residue matrices of which are found by the logarithm method of the product of matrices. The single solution of the problem is represented in terms of Cauchy-type integrals when the solvability condition is met.
About the Authors
V. V. Amel’kin
Belarusian State University
Belarus
Belarus
Vladimir V. Amel’kin – Dr. Sc. (Physics and Mathematics), Professor, Professor of the Department of Differential Equations and Systemic Analysis
4, Nezavisimosti Ave, 220030, Minsk
M. N. Vasilevich
Belarusian State University
Belarus
Belarus
Michail N. Vasilevich – Ph. D. (Physics and Mathematics), Associate Professor of the Department of General Mathematics and Informatics
4, Nezavisimosti Ave, 220030, Minsk
L. A. Khvostchinskaya
Belarusian State Agrarian Technical University
Belarus
Belarus
Ludmila A. Khvostchinskaya – Ph. D. (Physics and Mathematics), Associate Professor of the Department of Higher Mathematics
99, Nezavisimosti Ave, 220023, Minsk
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