Hostname: page-component-78c5997874-94fs2 Total loading time: 0 Render date: 2024-11-05T09:53:03.162Z Has data issue: false hasContentIssue false
  • English
  • Français

Circular inclusion in an infinite elastic medium with a circular inhomogeneity

Published online by Cambridge University Press:  24 October 2008

R. D. Bhargava  and
O. P. Kapoor
R. D. Bhargava
Affiliation:
Indian Institute of Technology, Kanpur (India)
O. P. Kapoor
Affiliation:
Indian Institute of Technology, Kanpur (India)
Get access Rights & Permissions [Opens in a new window]

Abstract

In a previous paper ((l)) the authors gave the solution for the two-dimensional circular inclusion problem in a medium containing a circular cavity. This paper seeks to solve the more general problem of a similar inclusion when the cavity is replaced by an inhomogeneity which could be of a different elastic material. The solution consists in finding three sets of suitable complex potential functions ø(z) and ψ(z) for three regions: the inhomogeneity, the inclusion and the rest of the material. The solution depends upon the evaluation of the complex potentials for a material containing the inhomogeneity when on the former a finite force is acting at some fixed point. It may be noted that two sets of ø(z) and ψ(z) have to be found in this case: one for the inhomogeneity and the other for the rest of the material. This may be taken as an auxiliary problem.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 62 , Issue 1 , January 1966 , pp. 113 - 127
Copyright
Copyright © Cambridge Philosophical Society 1966

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)Bhargava, R. D. and Kapoor, O. P.Proc. Cambridge Philos. Soc. 60 (1964), 675–682.CrossRefGoogle Scholar
(2)Bhargava, R. D. and Jaswon, M. A.Proc. Cambridge Philos. Soc. 57 (1961), 669–680.Google Scholar
(3)Eshelby, J. D.Proc. Boy. Soc., Ser. A 241 (1957), 376–396.Google Scholar
(4)Mott, N. F. and Nabarro, F. R. N.Proc. Phys. Soc. 52 (1940), 90–92.CrossRefGoogle Scholar
(5)Muskhelishvili, N. I.Some basic problems of the mathematical theory of elasticity (Noordhoff; Groningen, 1953).Google Scholar