The problems of a concentrated point force in an infinite medium (Kelvin's problem), or applied normal to the boundary of a half-space (Boussinesq's problem), as well as the corresponding problems for a concentrated couple, are solved to second order for incompressible isotropic elastic solids. The solutions are based on a simplified form of the second-order equations, obtained previously, and use of the Love's function representation for axisymmetric problems in the linear theory.

Issue Section:
Technical Papers
Topics:
Elasticity, Solids
1.
Carroll
M. M.
, and
Rooney
F. J.
,
1984
, “
Simplification of the Second Order Problem for Incompressible Solids
,”
Quart. J. Mech. Appl. Math.
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261
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272
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2.
Chan
C.
, and
Carlson
E. E.
,
1970
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Second-Order Incompressible Elastic Torsion
,”
In. J. Engng. Sci
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8
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415
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430
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3.
Hill
J. M.
,
1973
, note on “
Second-Order incompressible Elastic Torsion
,”
Int. J. Engng. Sci.
, Vol.
11
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331
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336
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4.
Little, R. M., 1973, Elasticity, Prentice-Hall, Englewood Cliffs, NJ.
5.
Selvadurai, A. P. S., 1970, “Problems in Second-Order Elasticity,” Ph.D. thesis, The University of Nottingham.
6.
Sneddon, I. N., 1951, Fourier Transforms, McGraw-Hill, New York.
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