Circular inclusion in an infinite elastic medium with a circular inhomogeneity
- 1 January 1966
- journal article
- research article
- Published by Cambridge University Press (CUP) in Mathematical Proceedings of the Cambridge Philosophical Society
- Vol. 62 (1) , 113-127
- https://doi.org/10.1017/s0305004100039621
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.This publication has 4 references indexed in Scilit:
- Circular inclusion in an infinite elastic medium with a circular holeMathematical Proceedings of the Cambridge Philosophical Society, 1964
- Two-dimensional elastic inclusion problemsMathematical Proceedings of the Cambridge Philosophical Society, 1961
- The determination of the elastic field of an ellipsoidal inclusion, and related problemsProceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences, 1957
- An attempt to estimate the degree of precipitation hardening, with a simple modelProceedings of the Physical Society, 1940