The authors presented an interesting consideration of an axisymmetric frictionless contact problem with the aid of mathematical software MATHEMATICA. Evidently, the use of modern analytical software gives a possibility to obtain new results, check known solutions, and correct possible misprints. However, some papers in the field should be added to their reference list.

In 1939 an analytical solution for a punch described by a monomial function of r of a positive even degree α was obtained by Shtaerman 1. It is worth mentioning that after A. E. H. Love had obtained his solution, the problem for conical punch was also solved by Lur’e 2 in 1941. The problem for a punch described by a monomial function of r of an arbitrary real degree α was solved by Galin (see Chap. 2, paragraph 5 in Ref. 3). Then this problem was also analyzed by Sneddon 4. In 1957 the problem was analyzed by Segedin 5 for a punch whose shape is represented by a series (a polynomial function of r) with integer degrees α. For a punch described by a fractional power series of r, the problem was analyzed in Ref. 6. The analysis in Ref. 6 was based on the Galin’s solution (3). It was shown that the solution can be also used in the case when the punch is a transversally isotropic solid and the half space has homogeneous initial stresses. In particular, a formula similar to formula (17) was obtained.

1.
Shtaerman
,
I. Ya.
,
1939
, “
On the Hertz Theory of Local Deformations Resulting From the Pressure of Elastic Solids
,”
,
25
, pp.
360
362
(in Russian).
1.
Lur’e
,
A. I.
,
1941
, “
Some Contact Problems of the Theory of Elasticity
,”
Prikl. Mat. Mekh.
,
5
, pp.
383
408
(in Russian);
2.
Lur’e, A. I., 1964, Three-Dimensional Problems of the Theory of Elasticity, Interscience Publishers, New York.
1.
Galin, L. A., 1953, Contact Problems in the Theory of Elasticity, Gostekhizdat, Moscow-Leningrad. (English translation by H. Moss, edited by I. N. Sneddon, North Carolina State College, Departments of Mathematics and Engineering Research, NSF Grant No. G16447, 1961).
2.
Sneddon
,
I. N.
,
1965
, “
The Relation Between Load and Penetration in the Axisymmetric Boussineq Problem for a Punch of Arbitrary Profile
,”
Int. J. Eng. Sci.
,
3
, pp.
47
57
.
3.
Segedin
,
C. M.
,
1957
, “
The Relation Between Load and Penetration for a Spherical Punch
,”
Mathematika
,
4
, pp.
156
161
.
4.
Borodich
,
F. M.
,
1990
, “
Hertz Contact Problems for Elastic Anisotropic Half-Space With Initial Stress
,”
Soviet Appl. Mechanics
,
26
, pp.
126
132
.