In this paper, the response of a transversely isotropic half-space under the punch action of a set of rigid concentric annuli frictionless contacts is considered. By virtue of a compact potential representation and Hankel transforms, a set of ring-load Green’s functions for the axisymmetric equations of equilibrium are derived and shown to be expressible in terms of standard elliptic integrals. With the aid of a rigorous yet highly efficient numerical method, the integral equation is solved for the multi-interval singular mixed boundary value problem. Detailed solutions to illustrate the performance of the computational approach and the influence of the degree of anisotropy and contact conditions on the mechanics problem are presented.

References

References
1.
Johnson
,
J. L.
, 1986,
Contact Mechanics
,
Cambridge University Press
,
New York
.
2.
Kim
,
K.
,
Roesset
,
J. M.
, and
Tassoulas
,
J. L.
, 1987, “
Interaction Between Concentric Annular and Circular Foundations
,”
J. Geotech. Eng.
,
113
(
6
), pp.
555
567
.
3.
Melerski
,
E. S.
, 1997, “
Numerical Modeling of Elastic Interaction Between Circular Rafts and Cross Anisotropic Media
,”
Comput. Struct.
,
64
(
1-4
), pp.
567
578
.
4.
Tassoulas
,
J. L.
, and
Kausel
,
E.
, 1984, “
On the Dynamic Stiffness of Circular Ring Footings on an Elastic stratum
,”
Int. J. Numer. Analyt. Meth. Geomech.
,
8
(
5
), pp.
411
426
.
5.
Veletsos
,
A. S.
, and
Tang
,
Y.
, 1987, “
Vertical Vibration of Ring Foundations
,”
Earthquake Eng. Struct. Dyn.
,
15
, pp.
1
21
.
6.
Boddapati
,
K. M.
, and
Nazarian
,
S.
, 1994, “
Effects of Pavement-Falling Weight Deflectometer Interaction on Measured Pavement Response
,”
ASTM Spec. Tech. Publ.
,
1198
, pp.
326
340
.
7.
Guzina
,
B. B.
, and
Nintcheu
,
F. S.
, 2001, “
Axial Vibration of a Padded Annulus on a Semi-Infinite Viscoelastic Medium
,”
ASME J. Appl. Mech.
,
68
(
6
), pp.
923
928
.
8.
Uzan
,
J.
,
Lytton
,
R. L.
, and
Germann
,
F. P.
, 1989, “
General Procedure for Back Calculating Layer Moduli
,”
ASTM Spec. Tech. Publ.
,
1026
, pp.
217
228
.
9.
Harding
,
J. W.
, and
Sneddon
,
I. N.
, 1945, “
The Elastic Stresses Produced by the Indentation of the Plane Surface of a Semi-Infinite Elastic Solid by a Rigid Punch
,”
Proc. Cambridge Philos. Soc.
,
41
, pp.
16
26
.
10.
Sneddon
,
I. N.
, 1966, “
The Reissner-Sagoci Problem
,”
Proc. Glasg. Math. Assoc.
,
7
, pp.
136
144
.
11.
Keer
,
L. M.
, 1967, “
Mixed Boundary Value Problems for an Elastic Half-Space
,”
Proc. Camb. Phil. Soc.
,
63
, pp.
1379
1386
.
12.
Michell
,
J. H.
, 1900 “
The Stress in an Aeolotropic Elastic Solid With an Infinite Plane Boundary
,”
Proc. London Math. Soc.
,
32
, pp.
247
258
.
13.
Fabrikant
,
V. I.
, 1989,
Applications of Potential Theory in Mechnics, A Selection of New Results
,
Kluwer Academic Publications
,
The Netherlands
.
14.
Egorov
,
K. E.
, 1965, “
Calculations of Bed for Foundation With Ring Footing
,”
Proceedings of the Sixth International Conference on Soil Mechanics and Foundation Engineering
, Vol.
2
, pp.
41
45
.
15.
Shield
,
T. W.
, and
Bogy
,
D. B.
, 1989, “
Some Axisymmetric Problems for Layered Elastic Media. II: Solutions for Annular Indenters and Cracks
,”
ASME J. Appl. Mech.
,
56
, pp.
807
813
.
16.
Dhawan
,
G. K.
, 1979, “
Transversely Isotropic Half-Space Indented by a Flat Annular Rigid Stamp
,”
Acta Mech.
,
31
(
3-4
), pp.
291
299
.
17.
Pak
,
R. Y. S.
, and
Ashlock
,
J. C.
, 2007, “
Method of Adaptive-Gradient Elements for Computational Mechanics
,”
J. Eng. Mech.
,
133
(
1
), pp.
87
97
.
18.
Lekhnitskii
,
S. G.
, 1981,
Theory of Anisotropic Elastic Bodies
,
Holden-Day Publishing Co.
,
San Francisco
.
19.
Eskandari-Ghadi
,
M.
, 2005, “
A Complete Solutions of the Wave Equations for Transversely Isotropic Media
,”
J. Elast.
,
81
, pp.
1
19
.
20.
Eskandari-Ghadi
,
M.
,
Pak
,
R. Y. S.
, and
Ardeshir-Behrestaghi
,
A.
, 2008, “
Transversely Isotropic Elastodynamic Solution of a Finite Layer on an Infinite Subgrade Under Surface Loads
,”
Soil Dyn. Earthquake Eng.
,
28
, pp.
986
1003
.
21.
Turner
,
J. R.
, 1980, “
Contact on a Transversely Isotropic Half-Space, or Between Two Transversely Isotropic Bodies
,”
Int. J. Solids Struct.
,
16
, pp.
409
419
.
22.
Eskandari-Ghadi
,
M.
,
Pak
,
R. Y. S.
, and
Ardeshir-Behrestaghi
,
A.
, 2009, “
Elastostatic Green’s Functions for an Arbitrary Internal Load in a Transversely Isotropic Bi-Material Full-Space
,”
Int. J. Eng. Sci.
,
47
(
4
), pp.
631
641
.
23.
Eason
,
G.
,
Noble
,
B.
, and
Sneddon
,
I. N.
, 1955, “
On Certain Integrals of Lipschitz-Hankel Type Involving Products of Bessel Functions
,”
Philos. Trans. R. Soc. London, Ser. A
,
247
(
935
), pp.
529
551
.
24.
Heuman
,
C.
, 1941, “
Tables of Complete Elliptic Integrals
,”
J. Math. Phys.
,
20
, pp.
127
206
.
25.
Pak
,
R. Y. S.
,
Simmons
,
B. M.
, and
Ashlock
,
J. C.
, 2008, “
Tensionless Contact of a Flexible Plate and Annulus With a Smooth Half-Space by Integral Equations
,”
Int. J. Mech. Sci.
,
50
, pp.
1004
1011
.
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