Springer Nature is making SARS-CoV-2 and COVID-19 research free. View research | View latest news | Sign up for updates

On Green's functions and Saint-Venant's principle in the linear theory of viscoelasticity

  • 111 Accesses

  • 11 Citations

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

References

  1. [1]

    Gurtin, M. E., & Eli Sternberg, On the linear theory of viscoelasticity. Arch. Rational Mech. Anal. 11, 4, 291 (1962).

  2. [2]

    Gurtin, M. E., Variational principles in the linear theory of viscoelasticity. Arch. Rational Mech. Anal. 13, 179 (1963).

  3. [3]

    Sternberg, Eli, & M. E. Gurtin, Uniqueness in the theory of thermo-rheologically simple ablating viscoelastic solids, in: Progress in Applied Mechanics — The Prager Anniversary Volume. New York: Macmillan 1963.

  4. [4]

    Sternberg, Eli, On the analysis of thermal stresses in viscoelastic solids. Technical Report No. 19, Contract Nonr-562(25), Brown University, February 1963. To appear in Proc., International Conference on High-Temperature Structures and Materials. New York: Columbia University 1963.

  5. [5]

    Love, A. E. H., A Treatise on the Mathematical Theory of Elasticity, Fourth Ed. New York: Dover Publications 1944.

  6. [6]

    Mises, R. v., On Saint-Venant's principle. Bull. Amer. Math. Soc. 51, 555 (1945).

  7. [7]

    Sternberg, Eli, On Saint-Venant's principle. Quart. Appl. Math. 11, 4, 393 (1954).

  8. [8]

    Sternberg, Eli, & R. A. Eubanks, On the concept of concentrated loads and an extension of the uniqueness theorem in the linear theory of elasticity. J. Rational Mech. Anal. 4, 1, 135 (1955).

  9. [9]

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

  10. [10]

    Natanson, I. P., Theory of Functions of a Real Variable, translated by Leo F. Boron. New York: Frederick Ungar Publishing Company 1955.

  11. [11]

    Volterra, V., Sulle equazioni integro-differenziali della teoria dell'elasticità Atti della Reale Accademia dei Lincei 18, 2, 295 (1909).

  12. [12]

    Thomson, W., Note on the integration of the equations of equilibrium of an elastic solid. Cambridge and Doublin Math. J. 3, 87 (1884).

  13. [13]

    Lord Kelvin & P. G. Tait, Treatise on Natural Philosophy. Cambridge: Cambridge University Press 1923.

  14. [14]

    Lee, E. H., Stress analysis in visco-elastic bodies. Quart. Appl. Math. 13, 2, 183 (1955).

  15. [15]

    De Saint-Venant, B., Mémoire sur la torsion des prismes. Mém. Savants Étrangers, Paris, 1855.

  16. [16]

    Boussinesq, J., Application des potentiels à l'étude de l'équilibre et du mouvement des solides élastiques. Paris: Gauthiers-Villars 1885.

  17. [17]

    Fredholm, I, Sur les équations de l'équilibre d'un corps solide élastique. Acta Math. 23, 1 (1900).

Download references

Author information

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Sternberg, E., Al-Khozaie, S. On Green's functions and Saint-Venant's principle in the linear theory of viscoelasticity. Arch. Rational Mech. Anal. 15, 112–146 (1964). https://doi.org/10.1007/BF00249521

Download citation

Keywords

  • Neural Network
  • Complex System
  • Nonlinear Dynamics
  • Electromagnetism
  • Linear Theory