By combining Stroh’s formalism and the method of analytical continuation, several mixed-typed boundary value problems of an anisotropic elastic half-plane are studied in this paper. First, we consider a set of rigid punches of arbitrary profiles indenting into the surface of an anisotropic elastic half-plane with no slip occurring. Illustrations are presented for the normal and rotary indentation by a flat-ended punch. A sliding punch with or without friction is then considered under the complete or incomplete indentation condition.
Issue Section:
Technical Papers
1.
Chen
W. T.
1969
, “Stresses in Some Anisotropic Materials Due to Indentation and Sliding
,” International Journal of Solids and Structures
, Vol. 5
, pp. 191
–214
.2.
England, A. H., 1971, Complex Variable Methods in Elasticity, Wiley Interscience, London.
3.
Fabrikant
V. I.
1986
a, “Flat Punch of Arbitrary Shape on an Elastic Half-space
,” International Journal of Engineering Science
, Vol. 24
, pp. 1731
–1740
.4.
Fabrikant
V. I.
1986
b, “Inclined Flat Punch of Arbitrary Shape on an Elastic Half-space
,” ASME JOURNAL OF APPLIED MECHANICS
, Vol. 53
, pp. 798
–806
.5.
Galin, L. A., 1961, Contact Problems in the Theory of Elasticity, translation by I. N. Sneddon, North Carolina State College, Raleigh, N.C.
6.
Gladwell
G. M. L.
1976
, “On Some Unbonded Problems in Plane Elasticity Theory
,” ASME JOURNAL OF APPLIED MECHANICS
, Vol. 43
, pp. 263
–267
.7.
Gladwell
G. M. L.
England
A. H.
1977
, “Orthogonal Polynomial Solutions to Some Mixed Boundary Value Problems in Elasticity Theory
,” Quarterly Journal of Mechanics and Applied Mathematics
, Vol. 30
, pp. 175
–185
.8.
Gladwell
G. M. L.
1978
, “Polynomial Solutions for an Ellipse on an Anisotropic Elastic Half-Space
,” Quarterly Journal of Mechanics and Applied Mathematics
, Vol. 31
, pp. 251
–260
.9.
Gladwell, G. M. L., 1980, Contact Problems in the Classical Theory of Elasticity, Sijthoff and Noordhoff.
10.
Green, A. E., and Zerna, W., 1954, Theoretical Elasticity, Clarendon Press, Oxford, UK.
11.
Hasebe
N.
Okumura
M.
Nakamura
T.
1989
, “Frictional Punch and Crack in Plane Elasticity
,” ASCE Journal of Engineering Mechanics
, Vol. 115
, pp. 1137
–1149
.12.
Hwu
C.
1992
, “Thermoelastic Interface Crack Problems in Dissimilar Anisotropic Media
,” International Journal of Solids and Structures
, Vol. 29
, pp. 2077
–2090
.13.
Hwu
C.
1993
, “Explicit Solutions for the Collinear Interface Crack Problems
,” International Journal of Solids and Structures
, Vol. 30
, pp. 301
–312
.14.
Jaffar
M. J.
Savage
M. D.
1988
, “On the Numerical Solution of Line Contact Problems Involving Bonded and Unbonded Strips
,” Journal of Strain Analysis
, Vol. 23
, pp. 67
–77
.15.
Johnson, K. L., 1985, Contact Mechanics, Cambridge University Press, Cambridge, U.K.
16.
Klintworth
J. W.
Stronge
W. L.
1990
, “Plane Punch Indentation of Anisotropic Elastic Half Space
,” ASME JOURNAL OF APPLIED MECHANICS
, Vol. 57
, pp. 84
–90
.17.
Kuo
C. H.
Keer
L. M.
1992
, “Contact Stress Analysis of a Layered Transversely Isotropic Half-Space
,” Journal of Tribology
, Vol. 114
, pp. 253
–262
.18.
Lin
W.
Kuo
C. H.
Keer
L. M.
1991
, “Analysis of a Transversely Isotropic Half-Space Under Normal and Tangential Loadings
,” Journal of Tribology
, Vol. 113
, pp. 335
–338
.19.
Muskhelishvili, N. I., 1954, Some Basic Problems of the Mathematical Theory of Elasticity, Noordhoff, Groningen, The Netherlands.
20.
Okumura
M.
Hasebe
N.
Nakamura
T.
1990
, “Crack Due to Wedge-shaped Punch with Friction
,” ASCE Journal of Engineering Mechanics
, Vol. 116
, pp. 2173
–2185
.21.
Pan
Y. C.
Chou
T. W.
1979
, “Green’s Function Solutions for Semi-infinite Transversely Isotropic Materials
,” International Journal of Engineering Science
, Vol. 17
, pp. 545
–551
.22.
Shibuya
T.
Koizumi
T.
Kawamura
N.
Gladwell
G. M. L.
1989
, “The Contact Problem Between an Elliptical Punch and an Elastic Half-space with Friction
,” JSME International Journal, Series I
, Vol. 32
, pp. 192
–198
.23.
Shield
R. T.
1987
, “Variational Principles for Some Nonstandard Elastic Problems
,” ASME JOURNAL OF APPLIED MECHANICS
, Vol. 54
, pp. 768
–771
.24.
Stroh
A. N.
1958
, “Dislocations and Cracks in Anisotropic Elasticity
,” Philosophical Magazine
, Vol. 7
, pp. 625
–646
.25.
Stroh
A. N.
1962
, “Steady State Problems in Anisotropic Elasticity
,” Journal of Mathematics and Physics
, Vol. 41
, pp. 77
–103
.26.
Suo
Z.
1990
, “Singularities, Interfaces and Cracks in Dissimilar Anisotropic Media
,” Proceedings of the Royal Society, London
, Vol. A427
, pp. 331
–358
.27.
Ting
T. C. T.
1982
, “Effects of Change of Reference Coordinates on the Stress Analysis of Anisotropic Elastic Materials
,” International Journal of Solids and Structures
, Vol. 18
, pp. 139
–152
.28.
Ting
T. C. T.
1986
, “Explicit Solution and Invariance of the Singularities at an Interface Crack in Anisotropic Composites
,” International Journal of Solids and Structures
, Vol. 22
, pp. 965
–983
.29.
Ting
T. C. T.
1988
, “Some Identities and the Structures of Ni in the Stroh Formalism of Anisotropic Elasticity
,” Quarterly Journal of Applied Mathematics
, Vol. 46
, pp. 109
–120
.30.
Tsiang
T. H.
Mandell
J. F.
1985
, “Bearing/Contact for Anisotropic Materials
,” AIAA Journal
, Vol. 23
, pp. 1273
–1277
.31.
Willis
J. R.
1966
, “Hertzian Contact of Anisotropic Bodies
,” Journal of the Mechanics and Physics of Solids
, Vol. 14
, pp. 163
–176
.
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