Hostname: page-component-cd9895bd7-8ctnn Total loading time: 0 Render date: 2024-12-25T13:17:57.823Z Has data issue: false hasContentIssue false
  • English
  • Français

Rods, plates and shells

Published online by Cambridge University Press:  24 October 2008

A. E. Green ,
N. Laws  and
P. M. Naghdi
A. E. Green
Affiliation:
University of Newcastle upon Tyne and University of California, Berkeley
N. Laws
Affiliation:
University of Newcastle upon Tyne and University of California, Berkeley
P. M. Naghdi
Affiliation:
University of Newcastle upon Tyne and University of California, Berkeley
Get access Rights & Permissions [Opens in a new window]

Abstract

We discuss non-linear thermodynamical theories of rods and shells using the three-dimensional theory of classical continuum mechanics as a starting point. The three-dimensional theory is reduced to a two-dimensional theory for a shell, or plate, and a one-dimensional theory for a rod by employing an exact expansion for the displacement but an approximation for the temperature. For elastic rods and shells a method of approximation is suggested which brings the respective theories into correspondence with those of Green and Laws (1) and Green, Naghdi and Wain-wright(2).

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 64 , Issue 3 , July 1968 , pp. 895 - 913
Copyright
Copyright © Cambridge Philosophical Society 1968

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

(1)Green, A. E. and Laws, N.Proc. R. Soc. Ser. A 283 (1966), 145.Google Scholar
(2)Green, A. E., Naghdi, P. M. and Wainwright, W. L.Arch. Rational Mech. Anal. 20 (1965), 287.CrossRefGoogle Scholar
(3)Laws, N.Quart. J. Mech. Appl. Math. 20 (1967), 167.CrossRefGoogle Scholar
(4)Green, A. E. and Naghdi, P. M.Proc. Cambridge Philos. Soc. 63 (1967), 537 and 63(1967),922.CrossRefGoogle Scholar
(5)Green, A. E., Laws, N. and Naghdi, P. M.Arch. Rational Mech. Anal. 25 (1967), 285.CrossRefGoogle Scholar
(6)Cohen, H.Internat. J. Engng Sci. 4 (1966), 511.CrossRefGoogle Scholar
(7)Cohen, H. and de Silva, C. N.J. Mathematical Phys. 7 (1966), 960.CrossRefGoogle Scholar
(8)Antman, S. S. and Warner, W. H.Arch. Rational Mech. Anal. 23 (1966), 135.CrossRefGoogle Scholar
(9)Green, A. E. and Naghdi, P. M.Quart. J. Mech. Appl. Math. (In the press.)Google Scholar