Skip to main content
Log in

On the traction problem of dead loading in linear elasticity with initial stress

  • 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

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

Instant access to the full article PDF.

References

  • Aubin, J.-P., 1972, Approximation of Elliptic Boundary-Value Problems, Wiley-Interscience, New York.

    Google Scholar 

  • Aubin, J.-P., 1979, Applied Functional Analysis, John Wiley, New York.

    Google Scholar 

  • Bažant, Z. P., 1971, A correlation study of formulations of incremental deformation and stability of continuous bodies, ASME J. Appl. Mech., 38, pp. 919–928.

    Google Scholar 

  • Bharatha, S. & Levinson, M., 1978, Signorini's perturbation scheme for a general reference configuration in finite elastostatics, Arch. Rational Mech. Anal, 67, pp. 365–394.

    Google Scholar 

  • Biot, M. A., 1939, Nonlinear theory of elasticity and the linearized case for a body under initial stress, Phil. Mag., 27, Series 7, pp. 468–489.

    Google Scholar 

  • Biot, M. A., 1965, Mechanics of Incremental Deformations, John Wiley, New York.

    Google Scholar 

  • Capriz, G. & Podio Guidugli, P., 1979, The role of Fredholm conditions in Signorini's perturbation method, Arch. Rational Mech. Anal., 70, pp. 261–288.

    Google Scholar 

  • Carlson, D. E. & Man, C.-S., 1992, On the traction problem in linear elasticity with initial stress, in Characterization of Mechanical Properties of Materials (Lu, W.-Y. & Man, C.-S., eds.), MD-Vol. 33, Amer. Soc. Mech. Engrs., New York, pp. 83–92.

    Google Scholar 

  • Cauchy, A.-L., 1829, Sur l'équilibre et le mouvement intérieur des corps considérés comme des masses continues, Exercices de Mathématique, 4, pp. 293–319.

    Google Scholar 

  • Del Piero, G., 1980, Lower bounds for the critical loads of elastic bodies, J. Elasticity, 10, pp. 135–143.

    Google Scholar 

  • Eringen, A. C. & Şuhubi, E. S., 1974, Elastodynamics, Vol. 1, Academic Press, New York.

    Google Scholar 

  • Grisvard, P., 1985, Elliptic Problems in Nonsmooth Domains, Pitman, Boston.

    Google Scholar 

  • Gurtin, M. E., 1972, The linear theory of elasticity, in Handbuch der Physik, Vol. VIa/2 (Truesdell, C., ed.), Springer, Berlin, pp. 1–295.

    Google Scholar 

  • Holden, J. T., 1964, Estimation of critical loads in elastic stability theory, Arch. Rational Mech. Anal., 17, pp. 171–183.

    Google Scholar 

  • Hoger, A., 1986, On the determination of residual stress in an elastic body, J. Elasticity, 16, pp. 303–324.

    Google Scholar 

  • Ieşan, D., 1989, Prestressed Bodies, Longman, Essex, England.

    Google Scholar 

  • Knops, R. J. & Payne, L. E., 1971, Uniqueness Theorems in Linear Elasticity, Springer, Berlin.

    Google Scholar 

  • Le Dret, H., 1987, Structure of the set of equilibrated loads in nonlinear elasticity and applications to existence and nonexistence, J. Elasticity, 17, pp. 123–141.

    Google Scholar 

  • Lu, W., 1992, Ultrasonic stress and texture measurement of thin sheet under biaxial loading, in Characterization of Mechanical Properties of Materials (Lu, W.-Y., & Man, C.-S., eds.), MD-Vol. 33, Amer. Soc. Mech. Engrs., New York, pp. 53–66.

    Google Scholar 

  • Man, C.-S. & Lu, W. Y., 1987, Towards an acoustoelastic theory for measurement of residual stress, J. Elasticity, 17, pp. 159–182.

    Google Scholar 

  • Man, C.-S. & Lu, W., 1992, An acoustoelastic theory for measurement of stress in inhomogeneous and weakly anisotropic thin sheets, in Review of Progress in Quantitative Nondestructive Evaluation, Vol. 11 (Thompson, D. O. & Chimenti, D. E., eds.), Plenum Press, New York, 1992, pp. 1975–1982.

    Google Scholar 

  • Man, C.-S. Lu, W., Gu, Q. & Tang, W., 1992, Ultrasonic measurement of stress in weakly anisotropic thin sheets, J. Acoust. Soc. Am., 91, pp. 2643–2653.

    Google Scholar 

  • Marlow, R. S., 1992, On the stress in an internally constrained elastic material, J. Elasticity, 27, pp. 97–131.

    Google Scholar 

  • Murdoch, A. I., 1978, Radial vibrations of a gravitating sphere with a material boundary, Q. J. Mech. Appl. Math., 31, pp. 531–542.

    Google Scholar 

  • Nečas, J., 1965, L'application de l'égalité de Rellich aux systèmes elliptiques du deuxième ordre, J. de Math. Pures et Appl., 44, pp. 133–147.

    Google Scholar 

  • Nečas, J. & Hlaváček, I., 1981, Mathematical Theory of Elastic and Elastico-PlasticBodies: An Introduction, Elsevier, Amsterdam.

    Google Scholar 

  • Spector, S. J., 1980, On uniqueness in finite elasticity with general loading, J. Elasticity, 10, pp. 145–161.

    Google Scholar 

  • Tang, W. & Lu, W., 1992, A new theory of acoustoelasticity for thin plate problems, in Developments in Theoretical and Applied Mechanics, Vol. XVI (Antar, B., et al., eds.), The University of Tennessee Space Institute, Manchester, Tennessee, pp. II.1.15-II.1.22.

    Google Scholar 

  • Trefftz, E., 1933, Zur Theorie der Stabilität des elastischen Gleichgewichts, Z. Angew. Math. Mech., 12, pp. 160–165.

    Google Scholar 

  • Truesdell, C. & Noll, W., 1965, The Non-linear Field Theories of Mechanics, Vol. III/3 of Handbuch der Physik, Springer, Berlin.

    Google Scholar 

  • Valent, T., 1988, Boundary Value Problems of Finite Elasticity, Springer, New York.

    Google Scholar 

  • Wan, Y. H. & Marsden, J. E., 1984, Symmetry and bifurcation in three-dimensional elasticity. Part III: Stressed reference configurations, Arch. Rational Mech. Anal., 84, pp. 203–233.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

Communicated by C.-C. Wang

Rights and permissions

Reprints and permissions

About this article

Cite this article

Man, C.S., Carlson, D.E. On the traction problem of dead loading in linear elasticity with initial stress. Arch. Rational Mech. Anal. 128, 223–247 (1994). https://doi.org/10.1007/BF00386246

Download citation

  • Accepted:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00386246

Keywords

Navigation