Skip to main content
Log in

The indentation of a transversely isotropic half-space by a rigid punch

  • Brief Reports
  • Published:
Zeitschrift für angewandte Mathematik und Physik Aims and scope Submit manuscript

Zusammenfassung

Der Verfasser gibt eine allgemeine Lösung für die Verteilung des Druckes zwischen einem axialsymmetrischen Stempel und einem transversal-isotropen Halbraum. Es wird gezeigt, dass die Verteilung des Druckes für den flachen Stempel mit allgemeiner Belastung unabhängig ist von den elastischen Eigenschaften des Halbraums und auch genau dieselbe, als ob der Halbraum isotrop wäre.

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

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

References

  1. J. Boussinesq,Application des potentials... (Paris 1885).

  2. A. E. H. Love,Boussinesq's Problem for a Rigid Cone, Quart. appl. Math.10, 161 (1939).

    MathSciNet  MATH  Google Scholar 

  3. G. Schubert, Zur Frage der Druckverteilung unter elastisch gelagerten Tragwerken, Ingen.-Arch.13, 132 (1942).

    Article  MathSciNet  Google Scholar 

  4. J. W. Harding andI. N. Sneddon,The Elastic Stresses Produced by the Indentation of the Plane Surface of a Semi-Infinite Elastic Solid by a Rigid Punch, Proc. Camb. phil. Soc.41, 16 (1945).

    Article  MathSciNet  Google Scholar 

  5. I. N. Sneddon,Boussinesq's Problem for a Flat-Ended Cylinder, Proc. Camb. phil. Soc.42, 29 (1946).

    Article  MathSciNet  Google Scholar 

  6. I. N. Sneddon,Boussinesq's Problem for a Rigid Cone, Proc. Camb. phil. Soc.44, 492 (1948).

    Article  MathSciNet  Google Scholar 

  7. A. E. Green,On Boussinesq's Problem and Penny-Shaped Cracks, Proc. Camb. phil. Soc.45, 251 (1949).

    Article  MathSciNet  Google Scholar 

  8. H. A. Elliott,Three-Dimensional Stress Distributions in Hexagonal Aeolotropic Crystals, Proc. Camb. phil. Soc.44, 522 (1948).

    Article  MathSciNet  Google Scholar 

  9. H. A. Elliott,Axial Symmetric Stress Distributions in Aeolotropic Hexagonal Crystals. The Problem of the Plane and Related Problems, Proc. Camb. phil. Soc.45, 621 (1949).

    Article  MathSciNet  Google Scholar 

  10. R. T. Shield,Notes on Problems in Hexagonal Aeolotropic Materials, Proc. Camb. phil. Soc.47, 401 (1951).

    Article  MathSciNet  Google Scholar 

  11. L. E. Payne,On Axially Symmetric Crack and Punch Problems for a Medium with Transverse Isotropy, Proc. Camb. phil. Soc.50, 466 (1954).

    Article  MathSciNet  Google Scholar 

  12. H. D. Conway,The Indentation of an Orthotropic Half-Plane, ZAMP6, 402 (1955).

    MathSciNet  MATH  Google Scholar 

  13. H. Okubo,The Stress Distribution in a Semi-Infinite Domain Having a Plane Boundary and Compressed by a Rigid Body, Z. angew. Math. Mech.20, 271 (1940).

    Article  MathSciNet  Google Scholar 

  14. J. H. Michell,The Stress in an Aeolotropic Elastic Solid with an Infinite Plane Boundary, Proc. Lond. math. Soc.32, 247 (1900).

    Article  MathSciNet  Google Scholar 

  15. A. E. H. Love,The Mathematical Theory of Elasticity, 4th edition (Cambridge University Press 1927), 160 p.

  16. E. F. Gurnee Solution of an Integral Equation Arising in Optical Studies of Oriented Filaments, J. appl. Phys.26, 918 (1955).

    Article  MathSciNet  Google Scholar 

  17. H. Borowicka, Über ausmittig belastete starre Platten auf elastisch-isotropem Untergrund, Ingen.-Arch.14, 1 (1943).

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Conway, H.D. The indentation of a transversely isotropic half-space by a rigid punch. Journal of Applied Mathematics and Physics (ZAMP) 7, 80–85 (1956). https://doi.org/10.1007/BF01600729

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01600729

Keywords

Navigation