Skip to main content
SpringerLink
Log in

On the numerical evaluation of two-and three-dimensional cauchy principal-value integrals

Über die numerische Bestimmung von zwei-und dreidimensionalen Cauchy-Hauptwert-Integralen

  • Contributed Papers
  • Published:
Acta Mechanica Aims and scope Submit manuscript

Summary

In the present paper two techniques are introduced for the numerical evaluation of either two-, or three-dimensional Cauchy principal-value integrals defined either over a shallow Lyapunov shell, or a closed Lyapunov domain respectively. A Gaussian cubature formula was established for the evaluation of these integrals which makes use of the concept of the finite-part integrals. Several numerical and theoretical applications are given to illustrate the results.

Zusammenfassung

In dieser Arbeit wurden zwei Methoden für die numerische Bestimmung von zwei-oder dreidimensionalen Cauchy-Hauptwert-Integralen eingeführt. Diese Integrale wurden entweder über eine flache Lyapounov-Schale oder ein geschlossenes Lyapunov-Gebiet definiert. Eine Gaußsche Quadraturformel, die das Konzept der finiten Integrale benutzt, wurde für die Bestimmung dieser Integrale gebildet. Um die Resultate zu veranschaulichen wurden verschiedene numerische und theoretische Anwendungen gegeben.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Kupradze, V. D.: Potential methods in the theory of elasticity, 1st ed., p. 33. Israel Program for Scientific Translations 1965.

  2. Mikhlin, S. G.: Multidimensional singular integrals and integral equations, 1st ed., p. 10. Oxford: Pergamon Press 1965.

    Google Scholar 

  3. Theocaris, P. S., Kazantzakis, J. G.: On the solution of the three-dimensional problem of a plane Crack of arbitrary shape. Int. J. of Fracture14, R117-R119 (1978).

    Google Scholar 

  4. Theocaris, P. S., Ioakimidis, N. I., Kazantzakis, J. G.: On the numerical evaluation of two-dimensional principal value integrals. Int. J. Num. Meth. Engng.15, 611–634 (1980).

    Google Scholar 

  5. Kazantzakis, J. G., Theocaris, P. S.: The evaluation of certain two dimensional singular integrals used in three-dimensional elasticity. Int. J. Solids Structures15, 203–207 (1979).

    Google Scholar 

  6. Stroud, A. H.: Approximate calculation of multiple integrals, 1st ed. Englewood Cliffs, N. J.: Prentice-Hall 1971.

    Google Scholar 

  7. Theocaris, P. S.: On the numerical solution of Cauchy-type singular integral equations. Serdica, Bulg. Math. Publ.2, 252–275 (1976).

    Google Scholar 

  8. Ioakimidis, N. I., Theocaris, P. S.: On the numerical evaluation of Cauchy principal value integrals. Rev. Roum. Sci. Tech.-Méc. Appl.22, 803–818 (1977).

    Google Scholar 

  9. Cruse, T. A.: Application of the boundary integral equation method to three-dimensional stress analysis. Comp. and Struct.3, 509–517 (1973).

    Google Scholar 

  10. Kutt, H. R.: On the numerical evaluation of finite part integrals involving an algebraic singularity. Special report No WISK 179, The National Research Institute for Mathematical Sciences, Pretoria, 1975. (Available also from NTIS.)

    Google Scholar 

  11. Davis, P. J., Rabinowits, P.: Methods of numerical integration, 1st ed., pp. 268–275. New York: Academic Press 1975.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Theoretical and Applied Mechanics, The National Technical University of Athens, 5, K. Zographou street, Zographou, (624), Athens, Greece

    P. S. Theocaris & J. G. Kazantzakis

Authors
  1. P. S. Theocaris
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. J. G. Kazantzakis
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

With 2 Figures

Rights and permissions

Reprints and permissions

About this article

Cite this article

Theocaris, P.S., Kazantzakis, J.G. On the numerical evaluation of two-and three-dimensional cauchy principal-value integrals. Acta Mechanica 39, 105–115 (1981). https://doi.org/10.1007/BF01173196

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01173196

Keywords

Search

Navigation