Hostname: page-component-586b7cd67f-t7czq Total loading time: 0 Render date: 2024-11-24T12:03:27.188Z Has data issue: false hasContentIssue false
  • English
  • Français

Plane elastostatic boundary value problems (II). The role of inversion

Published online by Cambridge University Press:  26 February 2010

V. T. Buchwald
V. T. Buchwald
Affiliation:
The Dept. of Applied Mathematics, The University, Sydney.
Get access

Summary

It is shown that in a certain sense, inversion transforms biharmonic functions into biharmonic functions. The first boundary value problem of elastostatics is also largely unchanged by this transformation, and known solutions can be used to obtain new results for inverse regions. As an example, the problem of a stress free dumb-bell shaped hole in an infinite plate is solved.

Type
Research Article
Information
Mathematika , Volume 10 , Issue 1 , June 1963 , pp. 29 - 34
Copyright
Copyright © University College London 1963

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

1. Muskhelishvili, N. I., Some basic problems of the mathematical theory of elasticity, translated by Radok, J. B. M. (Nordoff, Groningen, 1953).Google Scholar
2. Sokolnikoff, I. S., Mathematical Theory of Elasticity, 2nd Ed. (McGraw-Hill, New York, 1956), 157.Google Scholar
3. Buchwald, V. T., “Plane elastostatic boundary value problems (I)”, Mathematika, 10 (1963), 25–28.Google Scholar
4. Jeffery, G. B., Phil. Trans. Roy. Soc., A., 221 (1921), 265.Google Scholar
5. Mindlin, R. D., Proc. Soc. Exp. Stress Analysis, 5 (1948), 56.Google Scholar
6. , C. B.Ling, J. Math. Phys., 26 (1947), 284.CrossRefGoogle Scholar
7. Green, A. E. and , W. Zerna, Theoretical elasticity (Oxford, 1954), 306.Google Scholar
8. Davies, G. A. O., to appear in Aero. Quart.Google Scholar