Skip to main content

The Discontinuous Solution for the Piece-homogeneous Transversal Isotropic Medium

  • Chapter
Modern Analysis and Applications

Part of the book series: Operator Theory: Advances and Applications ((OT,volume 191))

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.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 129.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Hardcover Book
USD 169.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. G.Ya. Popov, The stress concentration near punches, sections, thin inclusions and supports. M.: Nauka, 1982.

    Google Scholar 

  2. 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.

    Google Scholar 

  3. O.F. Kryvyy, The tunnels inclusions in piece-homogeneous anisotropic medium. Math. methods and phys.-mech. fields. 50 2, (2007), 55–65.

    Google Scholar 

  4. 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.

    Google Scholar 

  5. S.G. Lekhnitskyy, The theory of elasticity of anisotropic solid. M.: Nauka, 1977.

    Google Scholar 

  6. 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.

    Article  Google Scholar 

  7. 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.

    Google Scholar 

  8. 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.

    Google Scholar 

  9. G. Bremerman, The distributions, complex variables and Fourier transforms. Mir, 1983.

    Google Scholar 

  10. D.F. Gakhov, The boundary problems. M: Nauka, 1977.

    Google Scholar 

  11. Yu.A. Brychkov, A.P. Prudnikow, The integral transformations of generalized functions. M: Nauka, 1977.

    Google Scholar 

  12. N.M. Gyunter, The theory of potential and its application to the basic problems of mathematical physics. M: Gos. Izd. Tekhniko-teoreticheskoy literatury, 1953.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints 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

Publish with us

Policies and ethics