Hostname: page-component-cd9895bd7-q99xh Total loading time: 0 Render date: 2024-12-26T12:49:14.622Z Has data issue: false hasContentIssue false
  • English
  • Français

An elastostatic circle theorem

Published online by Cambridge University Press:  24 October 2008

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

Abstract

An isotropic infinite plane containing a circular inhomogeneity is subjected to an arbitrary loading condition. Assuming that the unperturbed elastic field is known, it is proved that the disturbed Papkovich potentials are expressible in terms of the potentials for the homogeneous plane. This knowledge can save considerable labour in the actual construction of the elastic field for the composite plane. The results are applied to some particular problems which include that of an arc displacement discontinuity in the composite plane. This example has as yet not been solved explicity by other methods and reveals that the displacement field at the cavity surface is independent of the elastic constants.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 73 , Issue 1 , January 1973 , pp. 269 - 277
Copyright
Copyright © Cambridge Philosophical Society 1973

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)Aderogba, K. Ph.D. Thesis, University of Nottingham (1971).Google Scholar
(2)Aderogba, K. and Berry, D. S.J. Mech. Phys. Solids 19 (1971), 285.CrossRefGoogle Scholar
(3)Aderogba, K. To appear in Proc. Roy. Soc. Edinburgh, series A (1972).Google Scholar
(4)Berry, D. S.J. Mech. Phys. Solids (1960), 280.CrossRefGoogle Scholar
(5)Berry, D. S. and Sales, T. W.J. Mech. Phys. Solids. 9 (1961), 52.CrossRefGoogle Scholar
(6)Berry, D. S. and Sales, T. W.J. Mech. Phys. Solids. 10 (1962), 73.CrossRefGoogle Scholar
(7)Bhargava, R. A. and Kapoor, O. P.Proc. Cambridge Philos. Soc. 62 (1966), 113.CrossRefGoogle Scholar
(8)Cholton, F.Math. Gaz. 51 (1967), 120.CrossRefGoogle Scholar
(9)Dundurs, J.J. Appl. Math. Mech. 36 (1969), 650.Google Scholar
(10)Dundurs, J. and Hetenyi, M.J. Appl. Math. Mech. 28 (1961), 103.Google Scholar
(11)Eubanks, R. A. and Sternberg, E.J. Rat. Mech. Analysis. 5 (1956), 735.Google Scholar
(12)Ludford, G. S. S., Martinek, J. and Yeh, G. C. H.Proc. Cambridge Philos. Soc. 51 (1955), 389.CrossRefGoogle Scholar
(13)Milne-Thomson, L. M.Proc. Cambridge Philos. Soc. 36 (1940), 246.CrossRefGoogle Scholar
(14)Rongved, L.J. Appl. Math. Mech. 24 (1957), 252.Google Scholar
(15)Rongved, L. and Frasier, J. T.J. Appl. Math. Mech. 25 (1958), 125.Google Scholar
(16)Sternberg, E. and Rosenthal, F.J. Appl. Math. Mech. 19 (1952), 413.Google Scholar
(17)Sternberg, E. and Eubanks, R. A.Proc. 2nd U.S. Nat. Cong. Appl. Mech. (1954), 237.Google Scholar