Hostname: page-component-cd9895bd7-dk4vv Total loading time: 0 Render date: 2024-12-25T13:23:57.406Z Has data issue: false hasContentIssue false
  • English
  • Français

Plane stress theories

Published online by Cambridge University Press:  24 October 2008

F. P. Sayer  and
C. C. Calder
F. P. Sayer
Affiliation:
Department of Theoretical Mechanics, University of Bristol
C. C. Calder
Affiliation:
College of Technology, Portsmouth
Get access Rights & Permissions [Opens in a new window]

Extract

Tiffen and Lowe in two recent papers (4,5) have developed exact theories for the bending and stretching of generally loaded elastic plates using the moments of the fundamental equations of infinitesimal elasticity. The two theories depend on the choice of independent variables so that a pair of functions, denoted by and are independent. The choice is correct in (4) but not in (5). This paper pro-poses a modification to the forms of the functions and in (5) and then shows that the modified forms are independent. The subsequent alteration to (5), as will be seen, involves only the biharmonic function χ Apart from a minor algebraic adjustment the rest of the theory, containing the real and complex eigenfunctions and particular integral, is preserved. It should be noted that the modified theory like the original is obtained entirely from the moment equations.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 63 , Issue 4 , October 1967 , pp. 1369 - 1378
Copyright
Copyright © Cambridge Philosophical Society 1967

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.The elastic equilibrium of isotropic plates and cylinders. Proc. Roy. Soc. Ser. A 195 (1949), 533–552.Google Scholar
(2)Stevenson, A. C.Phil. Mag. 33 (1942), 639–661.CrossRefGoogle Scholar
(3)Tiffen, R.Quart. J. Mech. Appl. Math. 14 (1961), 59–74.CrossRefGoogle Scholar
(4)Tiffen, R. and Lowe, P. G.Proc. London Math. Soc. 13 (1963), 653–671.CrossRefGoogle Scholar
(5)Tiffen, R. and Lowe, P. G.J. London Math. Soc. 40 (1965), 72–86.CrossRefGoogle Scholar