Hostname: page-component-586b7cd67f-gb8f7 Total loading time: 0 Render date: 2024-11-23T07:29:38.755Z Has data issue: false hasContentIssue false
  • English
  • Français

A note on a method of Milne-Thomson

Published online by Cambridge University Press:  09 April 2009

V. T. Buchwald
V. T. Buchwald
Affiliation:
Department of Applied Mathematics, University of Sydney.
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Milne-Thomson has used the method of analytic continuation to solve boundary value problems of the annulus in plane elastostatics. However, his use of Cauchy integrals is incorrect, and it is shown in this note that the solution is obtained in terms of Laurent Series expansions. The solution is equivalent to that of Muskhelishvili, but is simpler to use in some applications.

A similar approach is used to solve the boundary value problem of the infinite strip, the solution being given in terms of functions of a complex variable expressed as Fourier integrals.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 3 , Issue 1 , February 1963 , pp. 93 - 98
Copyright
Copyright © Australian Mathematical Society 1963

References

[1]Muskhelishvili, N. I., Some Basic problems of the mathematical theory of elasticity, chapter 1 (Translated by Radok, S. R. M., Noordhoff, Groningen, 1953).Google Scholar
[2]Milne-Thomson, L. M., Plane Elastic Systems (Spriniger-Verlag, Berlin, 1960) p. 130.CrossRefGoogle Scholar
[3]Davies, G. A. O., in preparation.Google Scholar
[4]Buchwald, V. T. and Davies, G. A. O., Quart. J. Mech. Appl. Math., in the press.Google Scholar
[5]Filon, L. N. G., Phil. Trans. A 201 (1903) 63.Google Scholar
[6]Hopkins, H. G., Proc. Camb. Phil. Soc., 46 (1949) 164.CrossRefGoogle Scholar
[7]Tiffen, R., Quart. J. Mech. appl. Math. 6, (1953), 344.CrossRefGoogle Scholar
[8]Tiffen, R., Quart. J. Mech. appl. Math. 8, (1955), 237.CrossRefGoogle Scholar
[9]Tichmarsh, Theory of Fourier Integrals, § 10.16, (Oxford University Press, 1937).Google Scholar