Elastic analysis of an axisymmetric stress field perturbed by a spheroidal inhomogeneity
Author:
W. T. Chen
Journal:
Quart. Appl. Math. 28 (1971), 517-525
DOI:
https://doi.org/10.1090/qam/99772
MathSciNet review:
QAM99772
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Abstract: An infinite elastic medium contains an elastic spheroidal inclusion. Both materials are transversely isotropic. Assuming that the stress field in the absence of any inhomogeneity is prescribed, it is desired to calculate the modification caused by the inclusion. This paper presents a general solution to this elasticity problem with the restriction that the prescribed stress field is axisymmetric. The analysis is based upon some new identities in Legendre functions, which are derived in this paper. The solution is in the form of combinations of Legendre functions. An example of a spheroidal cavity in a tension field is given.
E. Sternberg, Three-dimensional stress concentrations in the theory of elasticity, Applied Mechanics Reviews, vol. 11, 1958, pp. 1–4
- J. D. Eshelby, Elastic inclusions and inhomogeneities, Progress in Solid Mechanics, Vol. II, North-Holland, Amsterdam, 1961, pp. 87–140. MR 0134510
W. T. Chen, Axisymmetric stress distribution around spheroidal inclusions and cavities in a transversely isotropic material, J. Appl. Mech. 35, Trans. ASME E 90, 770–773 (1968)
G. P. Sendeckyj, Ellipsoidal inhomogeneity problem, Ph.D. dissertation, Northwestern University, 1967 (University Microfilms Order No. 67–15, 337)
Yu. M. Podil’chuk, Deformation of an axisymmetrically loaded elastic spheroid, Prikl. Mat. Meh. 29, 85–91 (1965)
- A. E. Green and W. Zerna, Theoretical elasticity, Oxford, at the Clarendon Press, 1954. MR 0064598
- E. W. Hobson, The theory of spherical and ellipsoidal harmonics, Chelsea Publishing Company, New York, 1955. MR 0064922
E. Sternberg, Three-dimensional stress concentrations in the theory of elasticity, Applied Mechanics Reviews, vol. 11, 1958, pp. 1–4
J. D. Eshelby, Elastic inclusions and inhomogeneities, Progress in Solid Mechanics, vol. 2, North–Holland, Amsterdam, 1961, pp. 87–140
W. T. Chen, Axisymmetric stress distribution around spheroidal inclusions and cavities in a transversely isotropic material, J. Appl. Mech. 35, Trans. ASME E 90, 770–773 (1968)
G. P. Sendeckyj, Ellipsoidal inhomogeneity problem, Ph.D. dissertation, Northwestern University, 1967 (University Microfilms Order No. 67–15, 337)
Yu. M. Podil’chuk, Deformation of an axisymmetrically loaded elastic spheroid, Prikl. Mat. Meh. 29, 85–91 (1965)
A. E. Green and W. Zerna, Theoretical elasticity, Clarendon Press, Oxford, 1954, p. 180
E. W. Hobson, The theory of spherical and ellipsoidal harmonics, Chelsea, New York, 1955
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Article copyright:
© Copyright 1971
American Mathematical Society
