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

A Saint-Venant principle for nonlinear elasticity

  • 98 Accesses

  • 30 Citations

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

References

  1. 1.

    Adams, R. A., Sobolev Spaces, Academic Press, New York 1975.

  2. 2.

    Ball, J. M., Constitutive inequalities and existence theorems in nonlinear elastostatics. Nonlinear Analysis and Mechanics: Heriot-Watt Symposium Vol. I, pp. 187–238. Pitman. London 1977.

  3. 3.

    Biollay, Y., First boundary value problem in elasticity: Bounds for the displacements in Saint-Venant's principle. ZAMP. 31, 556–567, 1980.

  4. 4.

    Breuer, S., & J. J. Roseman, On Saint-Venant's principle in three-dimensional non-linear elasticity. Arch. Rational Mech. Anal. 63, 191–203, 1977.

  5. 5.

    Ericksen, J. L., On the formulation of St-Venant's problem. Nonlinear Analysis and Mechanics: Heriot-Watt Symposium Vol. I, pp. 158–186. Pitman. London 1977.

  6. 6.

    Fichera, G., Il principio di Saint-Venant: intuizione dell'ingegnere e rigore del matematico. Rend. Mat. 10, (Ser VI), 1–24, 1977.

  7. 7.

    Fichera, G., Remarks on Saint-Venant's principle. Complex Analysis and its Applications. I.N. Vekua Anniversary Volume. 543–554, Moscow 1978.

  8. 8.

    Horgan, C. O., Plane entry flows and energy estimates for the Navier-Stokes equations. Arch. Rational Mech. Anal. 68, 359–381, 1978.

  9. 9.

    Horgan, C. O., & W. E. Olmstead, Exponential decay estimates for a class of nonlinear Dirichlet problems. Arch. Rational Mech. Anal. 71, 231–235, 1979.

  10. 10.

    Horgan, C. O., & L. T. Wheeler, Spatial decay estimates for the heat equation via the maximum principle. Z. Angew. Math. Phys. 27, 371–376, 1976.

  11. 11.

    Horgan, C. O., & L. T. Wheeler, Exponential decay estimates for second-order quasilinear elliptic equations. J. Math. Anal. Appl. 59, 267–277, 1977.

  12. 12.

    Horgan, C. O., & L. T. Wheeler, Spatial decay estimates for the Navier-Stokes equations with application to the problem of entry flow. SIAM J. Appl. Math. 35, 97–116, 1978.

  13. 13.

    Knowles, J. K., On Saint-Venant's principle in the two-dimensional linear theory of elasticity. Arch. Rational Mech. Anal. 21, 1–22, 1966.

  14. 14.

    Knowles, J. K., A note on the spatial decay of a minimal surface over a semi-infinite strip. J. Math. Anal. Appl. 59, 29–32, 1977.

  15. 15.

    Muncaster, R. G., Saint-Venant's problem in nonlinear elasticity: a study of cross sections. Nonlinear Analysis and Mechanics: Heriot-Watt Symposium Vol. IV, p. 17–75. Pitman. London 1979.

  16. 16.

    Neapolitan, R. E., & W. S. Edelstein, Further study of Saint-Venant's principle in linear viscoelasticity. Z. Angew. Math. Phys. 24, 283–337, 1973.

  17. 17.

    Neapolitan, R. E., & W. S. Edelstein, A priori bounds for the secondary boundary value problem in linear viscoelasticity. SIAM J. Appl. Math. 28, 559–564, 1975.

  18. 18.

    Oleinik, O. A., & G. A. Yosifian, Boundary value problems for second order elliptic equations in unbounded domains and Saint-Venant's principle. Ann. della Scu. Norm. Sup. Pisa, IV2, 269–290, 1977.

  19. 19.

    Roseman, J. J., A pointwise estimate for the stress in a cylinder and its application to Saint-Venant's principle. Arch. Rational Mech. Anal. 21, 23–48, 1966.

  20. 20.

    Roseman, J. J., The principle of Saint-Venant in linear and nonlinear plane elasticity. Arch. Rational Mech. Anal. 26, 142–162, 1967.

  21. 21.

    Roseman, J. J., Phragmén-Lindelöf theorems for some nonlinear elliptic partial differential equations. J. Math. Anal. Appl. 43, 587–602, 1973.

  22. 22.

    Roseman, J. J., The rate of decay of a minimum surface defined over a semi-infinite strip. J. Math. Anal. Appl. 46, 545–554, 1974.

  23. 23.

    Toupin, R. A., Saint-Venant's principle. Arch. Rational Mech. Anal. 18, 83–96, 1965.

  24. 24.

    Villaggio, P., Energetic bounds in finite elasticity. Arch. Rational Mech. Anal. 45, 282–293, 1972.

Download references

Author information

Additional information

Communicated by R. A. Toupin

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Knops, R.J., Payne, L.E. A Saint-Venant principle for nonlinear elasticity. Arch. Rational Mech. Anal. 81, 1–12 (1983). https://doi.org/10.1007/BF00283164

Download citation

Keywords

  • Neural Network
  • Complex System
  • Nonlinear Dynamics
  • Electromagnetism
  • Nonlinear Elasticity