Abstract
The method of the reduction of the problems about the inter-phase defects in the piece-homogeneous transversal isotropic medium to the systems of the 2D singular integral equations is proposed. The method is based on the proposed way of solving the boundary Riemann problem in the space of the generalized functions of the slow growth in part of the variables and the discontinuous solution of the equations of the inhomogeneous transversal isotropic elasticity obtained with the help of this method.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
G.Ya. Popov, The stress concentration near punches, sections, thin inclusions and supports. M.: Nauka, 1982.
V.V. Yefimov, A.F. Kryvyy, G.Ya. Popov, The problems about the stress concentration near the circular defect in the compound elastic medium. Izvestiya Rossijskoi Akademii Nauk. Mehanika tverdogo tela. 2 (1998), 42–58.
O.F. Kryvyy, The tunnels inclusions in piece-homogeneous anisotropic medium. Math. methods and phys.-mech. fields. 50 2, (2007), 55–65.
A.F. Kryvyy, The fundamental solution for the four-component anisotropic plane. Visnyk Odeskogo derzhavnogo universytetu. Phys.-math. sciences. v. 8 2, (2003), 140–149.
S.G. Lekhnitskyy, The theory of elasticity of anisotropic solid. M.: Nauka, 1977.
H.A. Elliot, Axial symmetric stress distribution in aelotropic hexagonal crystals. The problem of the plane and related problems. Proc. Cambridge Phil. Soc. 45 (1949), 621–630.
H.C. Hu, On the three-dimensional problems of the theory of elasticity of a transversely isotropic body. Deta Sci. Sinica. 2 (1953), 145–151.
Yu.A. Brychkov, About the smoothness concerning of variables solutions of the linear differential equations with partial derivatives. Differential equations. v. 10 2, (1974), 281–289.
G. Bremerman, The distributions, complex variables and Fourier transforms. Mir, 1983.
D.F. Gakhov, The boundary problems. M: Nauka, 1977.
Yu.A. Brychkov, A.P. Prudnikow, The integral transformations of generalized functions. M: Nauka, 1977.
N.M. Gyunter, The theory of potential and its application to the basic problems of mathematical physics. M: Gos. Izd. Tekhniko-teoreticheskoy literatury, 1953.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2009 Birkhäuser Verlag Basel/Switzerland
About this chapter
Cite this chapter
Kryvyy, O. (2009). The Discontinuous Solution for the Piece-homogeneous Transversal Isotropic Medium. In: Adamyan, V.M., et al. Modern Analysis and Applications. Operator Theory: Advances and Applications, vol 191. Birkhäuser Basel. https://doi.org/10.1007/978-3-7643-9921-4_25
Download citation
DOI: https://doi.org/10.1007/978-3-7643-9921-4_25
Publisher Name: Birkhäuser Basel
Print ISBN: 978-3-7643-9920-7
Online ISBN: 978-3-7643-9921-4
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)