Hostname: page-component-848d4c4894-pjpqr Total loading time: 0 Render date: 2024-06-30T04:08:07.165Z Has data issue: false hasContentIssue false
  • English
  • Français

On eigenstresses in a semi-infinite solid

Published online by Cambridge University Press:  24 October 2008

K. Aderogba
K. Aderogba
Affiliation:
Engineering Analysis Unit, University of Lagos, Nigeria
Get access Rights & Permissions [Opens in a new window]

Abstract

A uniform eigenstrain is prescribed within a spherical subregion of an isotropic linearly elastic half-space. Combining an application of potential theory with the stress-function approach of Papkovitch and Neuber, and starting with Eshelby's well-known solution for the homogeneous infinite solid, it is shown that the residual problem of potential to be solved is the determination of Boussinesq's first and second three-dimensional logarithmic potentials of volume distributions. Although explicit results are supplied only for the case of a spherical inclusion, the dependence of the solution on the infinite solid solution holds good for an arbitrarily shaped transforming inclusion. This can be established on the basis of the principle of superposition, considering that an arbitrary volume is essentially made up from an infinite spectrum of spherical regions.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 80 , Issue 3 , November 1976 , pp. 555 - 562
Copyright
Copyright © Cambridge Philosophical Society 1976

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)Mindlin, R. D. and Cheng, D. H.J. Appl. Phys. 21 (1950), 931.Google Scholar
(2)Eshelby, J. D.Proc. Roy. Soc. London A 241 (1957), 376.Google Scholar
(3)Eshelby, J. D.Proc. Roy. Soc. London A 252 (1959), 561.Google Scholar
(4)Eseelby, J. D.Progress in Solid Mechanics 2 (1961), 89.Google Scholar
(5)Neuber, H.Kerbspannungslehre, 2nd edn. (Berlin; Springer-Verlag, 1958).Google Scholar
(6)Kellogg, O. D.Foundations of potential theory (Berlin; Springer-Verlag, 1929).Google Scholar
(7)Sobolev, S. L.Partial differential equations of mathematical physics (Pergamon Press, 1964).Google Scholar
(8)Sneddon, I. N.Proc. Cambridge Philos. Soc. 40 (1944), 229.Google Scholar
(9)List, R. D. and Silberstein, J. P. O.Proc. Cambridge Philos. Soc. 62 (1966), 303.Google Scholar
(10)Jaswon, M. A. and Bhargava, R. D.Proc. Cambridge Philos. Soc. 57 (1961), 669.Google Scholar
(11)Mindlin, R. D.Proc. First Midwestern Conference on solid mechanics (1953), 56.Google Scholar
(12)Lure, A. I.Three-dimensional problems of the theory of elasticity (Interscience Publishers, 1964), 74.Google Scholar
(13)Aderogba, K. J.Engineering Mathematics 10 (1976), 143.Google Scholar
(14)Blake, J. R.Proc. Cambridge Philos. Soc. 70 (1971), 303.Google Scholar