Hostname: page-component-78c5997874-v9fdk Total loading time: 0 Render date: 2024-11-05T10:02:43.256Z Has data issue: false hasContentIssue false
  • English
  • Français

On the use of convected coordinate systems in the mechanics of continuous media

Published online by Cambridge University Press:  24 October 2008

A. S. Lodge
A. S. Lodge
Affiliation:
British Rayon Research Association58 Whitworth StreetManchester 1
Get access Rights & Permissions [Opens in a new window]

Extract

The use of a coordinate system convected with the moving medium for describing its mechanics, first proposed by Hencky (5), has since been extended by several authors, and has several advantages over the more conventional use of a coordinate system fixed in space; Brillouin(1) has shown that the relation between the strain-energy function for an ideally elastic solid and the stress tensor takes a very simple form when the latter is referred to a convected coordinate system; Oldroyd(8) has given a very general discussion of the formulation of rheological equations of state and has shown that the right invariance properties are most readily recognized when the equations are referred to a convected coordinate system; Green and Zerna (4) have similarly expressed the equations of motion and boundary conditions; and Gleyzal (2), and Green and Shield (3) have applied the formalism to certain problems in elasticity theory.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 47 , Issue 3 , July 1951 , pp. 575 - 584
Copyright
Copyright © Cambridge Philosophical Society 1951

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)Brillouin, L.Ann. Phys., Paris (10e Série), 3 (1925), 251.CrossRefGoogle Scholar
(2)Gleyzal, A.Quart. Appl. Math. 6 (1948), 429.CrossRefGoogle Scholar
(3)Green, A. E. and Shield, R. T.Proc. Roy. Soc. A, 202 (1950), 407.Google Scholar
(4)Green, A. E. and Zerna, W.Phil. Mag. 41 (1950), 313.CrossRefGoogle Scholar
(5)Hencky, H.Z. angew. Math. Mech. 5 (1925), 144.CrossRefGoogle Scholar
(6)Madelung, E.Die Mathematischen Hilfsmittel des Physikers (New York, 1943), p. 137.Google Scholar
(7)Murnaghan, F. D.American J. Math. 59 (1937), 235.CrossRefGoogle Scholar
(8)Oldroyd, J. G.Proc. Roy. Soc. A, 200 (1950), 523.Google Scholar
(9)Treloar, L. R. G.Trans. Faraday Soc. 39 (1943), 241.CrossRefGoogle Scholar
(10)Russell, R. J. The determination of the basic Theological constants governing the flow of pseudoplastic substances. (Ph.D. Thesis), Imperial College, London (1945).Google Scholar