Skip to main content
SpringerLink
Log in

Transverse deformations associated with rectilinear shear in elastic solids

  • Published:
Journal of Elasticity Aims and scope Submit manuscript

Abstract

The rectilinear deformation of an incompressible, isotropic clastic solid is, in general, characterized by the two planar fields of pressure and displacement magnitude, and these are, in turn, restricted by the three, generally independent, differential equations of equilibrium. The over-determined nature of this situation suggests the possibility that transverse deformations may accompany rectilinear shear—a possibility not supported by the linear theory. Within this context we consider the class of equilibrium non-linear clasticity problems which is associated with cylindrical domains whose various boundaries each are displaced rigidly along their generators. An approximation scheme is developed for determining the cross sectional deformation and a specific example for a cylinder with eccentric circular cross section is given.

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. Ericksen, J. L., Overdetermination of the speed in rectilinear motion of non-Newtonian fluids. Quart. Appl. Math. 14 (1956) 318–321.

    Google Scholar 

  2. Fosdick, R. L., & J.Serrin, Rectilinear steady flow of simple fluids. Proc. Roy. Soc. Lond. A 332 (1973) 311–333.

    Google Scholar 

  3. Truesdell, C., & W.Noll, The Non-Linear Field Theories of Mechanics. Flügge's Handbuch der Physik, III/3. Berlin-Heidelberg-New York: Springer 1965.

    Google Scholar 

  4. Kao, B. G., & R. L. Fosdick, Rectilinear Shearing states in non-linear elastic solids and simple fluids. In preparation.

  5. Duffing, G., Beitrag zur Theorie der Flüssigkeitbewegung zwischen Zapfen und Lager. Z. Angew. Math. Mech. 4 (1924) 296–314.

    Google Scholar 

  6. Kudriavtzev, N. V., Flexure of a round plate with an eccentric hole by a concentrated load. Comp. Rend. (Doklady) de l'Académie des Sciences de l'URSS 53 (1946) 103–106.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Aerospace Engineering and Mechanics, University of Minnesota, 55455, Minneapolis, Minnesota, USA

    R. L. Fosdick

  2. Theoretical and Applied Mechanics, Cornell University, 14853, Ithaca, New York, USA

    B. G. Kao

Authors
  1. R. L. Fosdick
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. B. G. Kao
    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

Fosdick, R.L., Kao, B.G. Transverse deformations associated with rectilinear shear in elastic solids. J Elasticity 8, 117–142 (1978). https://doi.org/10.1007/BF00052477

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00052477

Keywords

Search

Navigation