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The torsion of a semi-infinite elastic solid by an elliptical stamp

Published online by Cambridge University Press:  18 May 2009

Mumtaz K. Kassir
Mumtaz K. Kassir
Affiliation:
The City CollegeThe City UniversityNew York N.Y. 10031, U.S.A.
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The problem of determining, within the limits of the classical theory of elasticity, the displacements and stresses in the interior of a semi-infinite solid (z ≧ 0) when a part of the boundary surface (z = 0) is forced to rotate through a given angle ω about an axis which is normal to the undeformed plane surface of the solid, has been discussed by several authors [7, 8, 9, 1, 11, and others]. All of this work is concerned with rotating a circular area of the boundary surface and the field equation to be solved is, essentially, J. H. Mitchell's equation for the torsion of bars of varying circular cross-sections.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 9 , Issue 1 , January 1968 , pp. 36 - 45
Copyright
Copyright © Glasgow Mathematical Journal Trust 1968

References

REFERENCES

1.Collins, W. D., The forced torsional oscillations of an elastic half-space and an elastic stratum. Proc. London Math. Soc., (3) 12 (1962), 226–244.CrossRefGoogle Scholar
2.Kassir, M. K. and Sih, G. C., Three-dimensional stress distribution around an elliptical crack under arbitrary loadings, J. Appl Mech., 33 (1966), 601–611.CrossRefGoogle Scholar
3.Kassir, M. K. and Sih, G. C., Geometric discontinuities in elastostatics, J. Math. Mech., 16 (1967), 927–948.Google Scholar
4.Luré, A. I., Three-dimensional problems of the theory of elasticity (English Translation), John Wiley (New York, 1964), 68–144.Google Scholar
5.Mindlin, R. D., Compliance of elastic bodies in contact, J. Appl. Mech., 16 (1949), 259–268.CrossRefGoogle Scholar
6.Ramsey, A. S., An introduction to the theory of Newtonian attraction, First Edn, Cambridge University Press (Cambridge, 1940), 161–184.Google Scholar
7.Reissner, E., Freie und enzwungene Torsionschwingungen des elastischen Halbraumes, Ing.-Arch. 8 (1937), 229–245.Google Scholar
8.Reissner, E. and Sagoci, H. F., Forced torsional oscillations of an elastic half-space, I, J. Appl. Phys. 15 (1944), 652–654.CrossRefGoogle Scholar
9.Sneddon, I. N., The Reissner-Sagoci problem, Proc. Glasgow Math. Assoc., 7 (1966), 136–144.CrossRefGoogle Scholar
10.Whittaker, E. T. and Watson, G. N., Modern analysis, Fourth Edn, Cambridge University Press (Cambridge, 1962), 548–552.Google Scholar
11.Yu, Yi-Yuan, Torsion of a semi-infinite body and a large thick plate, Quart. J. Mech. Appl. Math., 7 (1954), 287–298.CrossRefGoogle Scholar