Skip to main content
SpringerLink
Log in

The Discrete Cosserat Eigenfunctions for a Spherical Shell

  • Published:
Journal of Elasticity Aims and scope Submit manuscript

Abstract

The Papkovich-Neuber potential method is applied to obtain the discrete Cosserat eigenvalues and eigenvectors for the boundary value problems of displacement and traction for a spherical shell. The eigenvalues presented herein correct those obtained by the Cosserats.

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. R.J. Knops and L.E. Payne, Uniqueness Theorems in Linear Elasticity, Springer-Verlag, New York (1971).

    MATH  Google Scholar 

  2. E. Cosserat and F. Cosserat, Sur les equations de la theorie de l'elasticite. C. R. Acad. Sci. Paris 126(1898) 1089-1091.

    MATH  Google Scholar 

  3. E. Cosserat and F. Cosserat, Sur la deformation infiniment petite d'un corps elastique soumis a des forces donnees. C. R. Acad. Sci. Paris 133(1901) 271-273.

    Google Scholar 

  4. E. Cosserat and F. Cosserat, Sur la deformation infiniment petite d'un enveloppe spherique elastique. C. R. Acad. Sci. Paris 133(1901) 326-329.

    Google Scholar 

  5. S.G. Mikhlin, The spectrum of a family of operators in the theory of elasticity. Uspekhi Mat. Nauk(in Russian) 28(1973) 43-82; English translation: Russian Math. Surveys 28(1973) 45-88.

    MATH  Google Scholar 

  6. X. Markenscoff and M.V. Paukshto, The Cosserat spectrum in the theory of elasticity and applications. Proc. R. Soc. Lond. A 454(1998) 631-643.

    Article  MATH  MathSciNet  ADS  Google Scholar 

  7. W. Liu, X. Markenscoff and M.V. Paukshto, The Cosserat spectrum theory in thermoelasticity and application to the problem of heat flow past a spherical rigid inclusion. J. Appl. Mech. 65(1998) 614-618.

    Google Scholar 

  8. X. Markenscoff, W. Liu and M.V. Paukshto, Application of the Cosserat spectrum theory to viscoelasticity. J. Mech. Phys. Sol. 46(1998) 1969-1980.

    Article  MATH  MathSciNet  ADS  Google Scholar 

  9. A.I. Lur'e, Three-dimensional Problems of the Theory of Elasticity.Interscience Publishers, New York (1964).

    MATH  Google Scholar 

  10. W. Liu, The Cosserat Spectrum Theory and its Applications.Ph.D. Dissertation, University of California, San Diego and San Diego State University (1998).

Download references

Author information

Authors and Affiliations

  1. Department of Applied Mechanics and Engineering Sciences, University of California, San Diego, La Jolla, CA, 92093, U.S.A.

    Wensen Liu & Xanthippi Markenscoff

  2. San Diego State University, College of Engineering, San Diego, CA, 92182, U.S.A

    Wensen Liu

Authors
  1. Wensen Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Xanthippi Markenscoff
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Liu, W., Markenscoff, X. The Discrete Cosserat Eigenfunctions for a Spherical Shell. Journal of Elasticity 52, 239–255 (1998). https://doi.org/10.1023/A:1007574212023

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1007574212023

Search

Navigation