Skip to main content
SpringerLink
Log in

A generalization of the Beltrami stress functions in continuum mechanics

  • Published:
Archive for Rational Mechanics and Analysis Aims and scope Submit manuscript

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

References

  • 1863Airy, G. B.: On the strains in the interior of beams. Phil. Trans. Roy. Soc. London153, 49–80.

    Google Scholar 

  • 1870Maxwell, J. C.: On reciprocal figures, frames, and diagrams of force. Trans. Roy. Soc. Edinburgh26, 1–40.

    Google Scholar 

  • 1873Maxwell, J. C.: A Treatise on Electricity and Magnetism. Oxford.

  • 1892Morera, G.: Soluzione generale delle equazioni indefinite dell'equilibrio di un corpo continuo. Atti Accad. Nazl. Lincei1, 137–141.

    Google Scholar 

  • 1892Beltrami, E.: Osservazioni sulla Nota precedente. Att. Accad. Nazl. Lincei1, 141–142.

    Google Scholar 

  • 1912Gwyther, R. F.: The formal specification of the elements of stress in cartesian and in cylindrical and spherical polar coordinates. Mem. Manchester Lit. Phil. Soc.56, 10.

    Google Scholar 

  • 1929Kellogg, O. D.: Foundations of Potential Theory. Berlin: Springer.

    Google Scholar 

  • 1929Lichtenstein, L.: Grundlagen der Hydromechanik. Berlin: Springer.

    Google Scholar 

  • 1934Finzi, B.: Integrazione delle equazioni indefinite della meccanica dei sistemi continui. Atti Accad. Nazl. Lincei19, 6, 578–584.

    Google Scholar 

  • 1945Kuzmin, R. O.: On Maxwell's and Morera's formulae in the theory of elasticity. C. R. Acad. Sci. URSS (Doklady)49, 326–328.

    Google Scholar 

  • 1948Weber, C.: Spannungsfunktionen des dreidimensionalen Kontinuums. Z. Angew. Math. Mech.28, 193–197.

    Google Scholar 

  • 1949Krutkov, Y. A.: The Tensor of Stress-functions and General Solutions in Elastostatics [in Russian]. Moscow.

  • 1950Blokh, V. I.: Stress-functions in the theory of elasticity (in Russian). Prikl. Mat. Mekh.14, 415–422.

    Google Scholar 

  • 1950Morinaga, K., & T.Nôno: On stress-functions in general coordinates. J. Sci. Hiroshima Univ. A14, 181–194.

    Google Scholar 

  • 1953Schaefer, H.: Die Spannungsfunktionen des dreidimensionalen Kontinuums und des elastischen Körpers. Z. Angew. Math. Mech.33, 356–362.

    Google Scholar 

  • 1954Langhaar, H., & M.Stippes: Three-dimensional stress functions. J. Franklin Inst.258, 371–382.

    Google Scholar 

  • 1954Ornstein, W.: Stress functions of Maxwell and Morera. Quart. Appl. Math.2, 198–201.

    Google Scholar 

  • 1954Günther, W.: Spannungsfunktionen und Verträglichkeitsbedingungen der Kontinuumsmechanik. Abh. Braunschweig. Wiss. Ges.6, 207–219.

    Google Scholar 

  • 1954Kröner, E.: Die Spannungsfunktionen der dreidimensionalen isotropen Elastizitätstheorie139, 175–188.

    Google Scholar 

  • 1955Marguerre, K.: Ansätze zur Lösung der Grundgleichungen der Elastizitätstheorie. Z. Angew. Math. Mech.35, 241–263.

    Google Scholar 

  • 1956Dorn, W. S., & A.Schild: A converse of the virtual work theorem for deformable solids. Quart. Appl. Math.14, 2, 209–213.

    Google Scholar 

  • 1959Truesdell, C.: Invariant and complete stress functions for general continua. Arch. Rational Mech. Anal.4, 1–29.

    Google Scholar 

  • 1960Rieder, G.: Topologische Fragen in der Theorie der Spannungsfunktionen. Abh. Braunschweig. Wiss. Ges.7, 4–65.

    Google Scholar 

  • 1960Sternberg, E.: On some recent developments in the linear theory of elasticity. Structural Mechanics. New York: Pergamon.

    Google Scholar 

  • 1962Courant, R.: Partial differential equations, Vol. 2 of Methods of Mathematical Physics by R.Courant & D.Hilbert. New York: Interscience.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Brown University, Providence, Rhode Island

    M. E. Gurtin

Authors
  1. M. E. Gurtin
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Communicated by E.Sternberg

Rights and permissions

Reprints and permissions

About this article

Cite this article

Gurtin, M.E. A generalization of the Beltrami stress functions in continuum mechanics. Arch. Rational Mech. Anal. 13, 321–329 (1963). https://doi.org/10.1007/BF01262700

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01262700

Keywords

Search

Navigation