This review article (Part II) is a sequel to an earlier one (Part I) that dealt with means of removal and interpretation of stress singularities in elasticity, as well as their asymptotic and numerical analysis. It reviews contributions to the literature that have actually effected asymptotic identifications of possible stress singularities for specific configurations. For the most part, attention is focused on 2D elastostatic configurations with constituent materials being homogeneous and isotropic. For such configurations, the following types of stress singularity are identified: power singularities with both real and complex exponents, logarithmic intensification of power singularities with real exponents, pure logarithmic singularities, and log-squared singularities. These identifications are reviewed for the in-plane loading of angular elastic plates comprised of a single material in Section 2, and for such plates comprised of multiple materials in Section 3. In Section 4, singularity identifications are examined for the out-of-plane shear of elastic wedges comprised of single and multiple materials, and for the out-of-plane bending of elastic plates within the context of classical and higher-order theory. A review of stress singularities identified for other geometries is given in Section 5, axisymmetric and 3D configurations being considered. A limited examination of the stress singularities identified for other field equations is given as well in Section 5. The paper closes with an overview of the status of singularity identification within elasticity. This Part II of the review has 227 references.
Issue Section:
Review Articles
1.
Sinclair
GB
2004
), Stress singularities in classical elasticity—I: Removal, interpretation, and analysis
, Appl. Mech. Rev.
57
, 251
-298
.2.
Williams
ML
1952
), Stress singularities resulting from various boundary conditions in angular corners of plates in extension
, ASME J. Appl. Mech.
19
, 526
–528
.3.
Dempsey
JP
Sinclair
GB
1979
), On the stress singularities in the plane elasticity of the composite wedge
, J. Elast.
9
, 373
–391
.4.
Rao AK (1958), A study into the problem of diffusion of loads, Doctoral Dissertation, Univ of London, London, UK.
5.
Johnson KL (1985), Contact Mechanics, Cambridge Univ Press, Cambridge, UK.
6.
Winkler E (1867), Theory of Elasticity and Strength, (German), H Dominicus Press, Prague, Austria.
7.
Oravas
GA
1964
), Review Number 4988
, Appl. Mech. Rev.
17
, 684
684
.8.
Euler
L
1774
), The pressure in planes from weights that settle (Latin
), Novi Commun Acad Petropolit
18
, 283
–329
.9.
Nuller
BM
1974
), Deformation of an elastic wedge reinforced by a beam
, J. Appl. Math. Mech.
38
, 823
–829
.10.
Ting
TCT
1985
), Asymptotic solution near the apex of an elastic wedge with curved boundaries
, Q. Appl. Math.
42
, 467
–476
.11.
Gregory
RD
1979
), Green’s functions, bi-linear forms, and completeness of the eigenfunctions for the elastostatic strip and wedge
, J. Elast.
9
, 283
–309
.12.
Knowles
JK
Pucik
TA
1973
), Uniqueness for plane crack problems in linear elastostatics
, J. Elast.
3
, 155
–160
.13.
Lighthill MJ (1975), Introduction to Fourier Analysis and Generalized Functions, Cambridge Univ Press, Cambridge, UK.
14.
Kolossoff G (1910), On an application of the theory of complex variables to the two-dimensional problem of elasticity theory, Doctoral Dissertation, St Petersburg, Russia.
15.
Kolossoff
G
1914
), On some properties of the plane problem of elasticity theory (German
), Z. Math. Phys.
62
, 384
–409
.16.
Inglis
CE
1913
), Stresses in a plate due to the presence of cracks and sharp corners
, Soc. Nav. Archit. Mar. Eng., Trans.
55
, 219
–241
.17.
Neuber H 1946, Theory of Notch Stresses, JW Edwards Co, Ann Arbor MI.
18.
Kitover
KA
1952
), On the use of special systems of biharmonic functions for the solution of some problems in the theory of elasticity (Russian
), Prikl. Mat. Mekh.
16
, 739
–748
.19.
Kalandiia
AI
1969
), Remarks on the singularity of elastic solutions near corners
, J. Appl. Math. Mech.
33
, 127
–131
.20.
Seweryn
A
Molski
K
1996
), Elastic stress singularities and corresponding generalized stress intensity factors for angular corners under various boundary conditions
, Eng. Fract. Mech.
55
, 529
–556
.21.
Dempsey JP (1978), On the stress singularities in the plane elasticity of the composite wedge, Doctoral Dissertation, Univ of Auckland, Auckland, New Zealand.
22.
Gdoutos
EE
Theocaris
PS
1975
), Stress concentrations at the apex of a plane indentor acting on an elastic half plane
, ASME J. Appl. Mech.
42
, 688
–692
.23.
Sinclair
GB
1996
), On the influence of cohesive stress-separation laws on elastic stress singularities
, J. Elast.
44
, 203
–221
.24.
Ro¨ssle
A
2000
), Corner singularities and regularity of weak solutions for the two-dimensional Lame´ equations on domains with angular corners
, J. Elast.
60
, 57
–75
.25.
Ro¨sel
R
1987
), On the wedge/notch eigenvalues
, Int. J. Fract.
33
, 61
–71
.26.
Karp
SN
Karal
FC
1962
), The elastic-field behavior in the neighborhood of a crack of arbitrary angle
, Commun. Pure Appl. Math.
15
, 413
–421
.27.
Sinclair GB, Khatod HN, and Rummel CW (2003), On the removal of stress singularities from sharp corners, Proc of the 19 Canadian Congress of Applied Mechanics, Vol. 1, Calgary, Alberta, 1, 94–95.
28.
Williams
ML
1953
), Discussion of ‘Stress singularities resulting from various boundary conditions in angular corners of plates in extension,Discussion of ‘Stress singularities resulting from various boundary conditions in angular corners of plates in extension,’
ASME J. Appl. Mech.
20
, 590
590
.29.
Ricci L (1951), Table of Minimum Roots of an Equation of Interest in Solid Mechanics (Italian), Pubblicazioni No 296, Istituto per le Applicazioni del Calcolo, Rome, Italy.
30.
Klingbeil NW (1996), private communication.
31.
England
AH
1971
), On stress singularities in linear elasticity
, Int. J. Eng. Sci.
9
, 571
–585
.32.
Smallwood BS (1996), private communication.
33.
Dempsey
JP
1995
), Power-logarithmic stress singularities at bi-material corners and interface cracks
, J. Adhes. Sci. Technol.
9
, 253
–265
.34.
Sinclair
GB
1999
), Logarithmic stress singularities resulting from various boundary conditions in angular corners of plates in extension
, ASME J. Appl. Mech.
66
, 556
–560
.35.
Browning
RV
Ju
FD
1977
), Stress singularities at an elastic crack with arbitrary surface loads, including possible fracture mechanics applications
, J. Math. Anal. Appl.
58
, 482
–496
.36.
ANSYS personnel (1995), ANSYS User’s Manual, Revision 5.2, Vol I, ANSYS Inc, Canonsburg, PA.
37.
ABAQUS personnel (1997), ABAQUS Standard User’s Manual, Revision 5.7, Vol I, Hibbitt, Karlsson and Sorensen, Inc, Pawtucket, RI.
38.
Sinclair
GB
Epps
BE
2002
), On the logarithmic stress singularities induced by the use of displacement shape functions in boundary conditions in submodelling
, Commun. Numer. Methods Eng.
18
, 121
–130
.39.
Dempsey
JP
1981
), The wedge subjected to tractions: A paradox resolved
, J. Elast.
11
, 1
–10
.40.
Sinclair
GB
1998
), Further paradoxes in generalized Levy problems
, J. Elast.
50
, 253
–259
.41.
Levy
M
1898
), On the elastic equilibrium of a masonry dam of triangular cross section (French
), Acad. Sci., Paris, C. R.
127
, 10
–15
.42.
Timoshenko SP, and Goodier JN (1970), Theory of Elasticity, 3rd Edition, McGraw-Hill, New York, NY.
43.
Fillunger
P
1912
), Three important plane states of stress for wedge-shaped bodies (German
), Z. Angew. Math. Mech.
60
, 275
–285
.44.
Ting
TCT
1984
), The wedge subjected to tractions: A paradox re-examined
, J. Elast.
14
, 235
–247
.45.
Sternberg
E
Koiter
WT
1959
), Discussion of “The wedge under a concentrated couple: A paradox in the two-dimensional theory of elasticity,”
ASME J. Appl. Mech.
26
, 472
–474
.46.
Sneddon IN (1951), Fourier Transforms, McGraw-Hill, New York, NY.
47.
Brock
LM
1979
), Frictionless indentation by a rigid wedge: The effect of tangential displacements in the contact zone
, Int. J. Eng. Sci.
17
, 365
–372
.48.
Rao
AK
1971
), Stress concentrations and singularities at interface corners
, Z. Angew. Math. Mech.
51
, 395
–406
.49.
Erdogan
F
Gupta
GD
1972
), Stresses near a flat inclusion in bonded dissimilar materials
, Int. J. Solids Struct.
8
, 533
–547
.50.
Jones
JP
Whittier
JS
1967
), Waves at a flexibly bonded interface
, ASME J. Appl. Mech.
34
, 905
–909
.51.
Lene
F
Leguillon
D
1982
), Homogenized constitutive law for a partially cohesive composite material
, Int. J. Solids Struct.
18
, 443
–458
.52.
Ying
X
Katz
IN
1987
), A uniform formulation for the calculation of stress singularities in the plane elasticity of a wedge composed of multiple isotropic materials
, Comput. Math. Appl.
14
, 437
–458
.53.
Dundurs
J
1969
), Discussion of “Edge-bonded dissimilar orthogonal elastic wedges under normal and shear loading
,” ASME J. Appl. Mech.
36
, 650
–652
.54.
Bogy
DB
1968
), Edge-bonded dissimilar orthogonal elastic wedges under normal and shear loading
, ASME J. Appl. Mech.
35
, 460
–466
.55.
Zak
AR
Williams
ML
1963
), Crack point stress singularities at a bi-material interface
, ASME J. Appl. Mech.
30
, 142
–143
.56.
Dundurs
J
1967
), Effect of elastic constants on stress in a composite under plane deformation
, J. Compos. Mater.
1
, 310
–322
.57.
Koguchi
H
Inoue
T
Yada
T
1996
), Stress singularity in three-phase bonded structure
, ASME J. Appl. Mech.
63
, 252
–258
.58.
Williams
MI
1959
), The stresses around a fault or crack in dissimilar media
, Bull. Seismol. Soc. Am.
49
, 199
–204
.59.
Bogy
DB
1971
), Two edge-bonded elastic wedges of different materials and wedge angles under surface tractions
, ASME J. Appl. Mech.
38
, 377
–386
.60.
Theocaris
PS
Gdoutos
EE
1977
), Stress singularities in cracked composite full-planes
, Int. J. Fract.
13
, 763
–773
.61.
Ting
TCT
1986
), Explicit solution and invariance of the singularities at an interface crack in anisotropic composites
, Int. J. Solids Struct.
22
, 965
–983
.62.
Ballarini
R
1990
), A rigid line inclusion at a bimaterial interface
, Eng. Fract. Mech.
37
, 1
–5
.63.
Comninou
M
1977
), Interface crack with friction in the contact zone
, ASME J. Appl. Mech.
44
, 780
–781
.64.
Dempsey
JP
Sinclair
GB
1981
), On the singular behavior at the vertex of a bi-material wedge
, J. Elast.
11
, 317
–327
.65.
Comninou
M
1977
), The interface crack
, ASME J. Appl. Mech.
44
, 631
–636
.66.
Comninou
M
1976
), Stress singularity at a sharp edge in contact problems with friction
, Z. Angew. Math. Phys.
27
, 493
–499
.67.
Dundurs
J
Lee
M-S
1972
), Stress concentration at a sharp edge in contact problems
, J. Elast.
2
, 109
–112
.68.
Wu
K-C
1990
), Line inclusions at anisotropic bimaterial interface
, Mech. Mater.
10
, 173
–182
.69.
Chen
YZ
Hasebe
N
1993
), Singularity eigenvalue analysis of a crack along a wedge-shaped interface
, ASME J. Appl. Mech.
60
, 781
–783
.70.
Van Vroonhoven
JCW
1992
), Stress singularities in bi-material wedges with adhesion and delamination
, Fatigue Fract. Eng. Mater. Struct.
15
, 159
–171
.71.
Bogy
DB
Wang
KC
1971
), Stress singularities at interface corners in bonded dissimilar isotropic elastic materials
, Int. J. Solids Struct.
7
, 993
–1005
.72.
Chen
D-H
Nisitani
H
1993
), Singular stress field near the corner of jointed dissimilar materials
, ASME J. Appl. Mech.
60
, 607
–613
.73.
Pageau
SS
Joseph
PF
Biggers
Jr SB
1994
), The order of stress singularities for bonded and disbonded three-material junctions
, Int. J. Solids Struct.
31
, 2979
–2997
.74.
Chaudhuri
RA
Xie
M
Garala
HJ
1996
), Stress singularity due to kink band weakening a unidirectional composite under compression
, J. Compos. Mater.
30
, 672
–691
.75.
Khrapkov
AA
1968
), First fundamental problem for a piecewise-homogeneous plane with a slit perpendicular to the line of separation
, J. Appl. Math. Mech.
32
, 666
–678
.76.
Bogy
DB
1971
), On the plane elastostatic problem of a loaded crack terminating at a material interface
, ASME J. Appl. Mech.
38
, 911
–918
.77.
Comninou
M
Dundurs
J
1979
), A closed crack tip terminating at an interface
, ASME J. Appl. Mech.
46
, 97
–100
.78.
Wijeyewickrema
AC
Dundurs
J
Keer
LM
1995
), The singular stress field of a crack terminating at a frictional interface between two materials
, ASME J. Appl. Mech.
62
, 289
–293
.79.
Gharpuray
VM
Dundurs
J
Keer
LM
1991
), A crack terminating at a slipping interface between two materials
, ASME J. Appl. Mech.
58
, 960
–963
.80.
Fenner
DN
1976
), Stress singularities in composite materials with an arbitrarily oriented crack meeting an interface
, Int. J. Fract.
12
, 705
–721
.81.
Yong-Li
W
1992
), Crack tip stress singularities in a bimaterial with an inclined interface
, Int. J. Fract.
54
, R65–R72
R65–R72
.82.
Wang
W-C
Chen
J-T
1994
), Singularities of an arbitrarily inclined semi-infinite crack meeting a bimaterial interface
, Eng. Fract. Mech.
49
, 671
–680
.83.
Tan MA, and Meguid SA (1997), Stress singularities of a sharp notch terminating at a bimaterial interface, Proc of 16th Canadian Congress of Applied Mechanics Vol 1, Laval Univ, Quebec, Canada, 17–18.
84.
Pinsan
C
Zhuping
D
1991
), Singular behavior and asymptotic stress field of a crack terminating at a bimaterial interface
, Acta Mech. Sin.
7
, 344
–350
.85.
Bogy
DB
1970
), On the problem of edge-bonded quarter-planes loaded at the boundary
, Int. J. Solids Struct.
6
, 1287
–1313
.86.
Hein
VL
Erdogan
F
1971
), Stress singularities in a two-material wedge
, Int. J. Fract. Mech.
7
, 317
–330
.87.
Kubo S, Ohji K, and Nakai Y (1991), Free-edge singularities in edge-bonded elastic dissimilar wedges—geometrical conditions for appearance and disappearance of stress singularities, Report of the 61st Meeting of the Committee on Fracture Mechanics, Vol 39, Soc of Materials Science, Japan, 13–17 (this work is summarized in Murakami 95).
88.
Theocaris
PS
Gdoutos
EE
1976
), Stress singularities at equal angle biwedges and two-material composite half planes with rough interfaces
, ASME J. Appl. Mech.
43
, 64
–68
.89.
Theocaris
PS
Gdoutos
EE
1976
), Stress singularities at vertices of composite plates with smooth or rough interfaces
, Arch. Mech. Stosow.
28
, 693
–704
.90.
Aksentian
OK
1967
), Singularities of the stress-strain state of a plate in the neighborhood of an edge
, J. Appl. Math. Mech.
31
, 193
–202
.91.
Avetisian
AG
Chobanian
KS
1972
), On the nature of stresses in the fixed vicinity of the junction surface brink of a composite elastic body loaded in conditions of a plane problem of the elasticity theory (Russian
), Dokl. Akad. Nauk Arm. SSR
25
, 13
–25
.92.
Picu
CR
Gupta
V
1996
), Stress singularities at triple junctions with freely sliding grains
, Int. J. Solids Struct.
33
, 1535
–1541
.93.
Inoue
T
Koguchi
H
1996
), Influence of the intermediate material on the order of stress singularity in three-phase bonded structure
, Int. J. Solids Struct.
33
, 399
–417
.1.
Pageau
SS
Gadi
KS
Biggers
Jr SB
Joseph
PF
1996
), Standardized complex and logarithmic eigensolutions for n-material wedges and junctions
, Int. J. Fract.
77
, 51
–76
2.
Pageau SS, Gadi KS, Biggers Jr SB, and Joseph PF (See also:Int. J. Fract. IJFRAP80, 97).
1.
Murakami Y (1992), Stress singularity for notch at bimaterial interface, Stress Intensity Factors Handbook Vol 3, Y Murakami et al (eds), Pergamon Press, Oxford, UK, 963–1062.
2.
Chen
D-H
1996
), Logarithmic singular stress field in a semi-infinite plate consisting of two edge-bonded wedges subjected to surface tractions
, Int. J. Fract.
75
, 352
–378
.3.
Courant R and Hilbert D (1953), Methods of Mathematical Physics, 1st English Edition, Vol I, Interscience Publ, New York, NY.
4.
de Saint-Venant
B
1878
), On the torsion of prisms with bases made of circular arcs and radial lines, and on a singularity which can be found in certain uses of the logarithmic cylindrical coordinate system of Lame´ (French
), Acad. Sci., Paris, C. R.
87
, 849
–854
.5.
Sinclair
GB
1980
), On the singular eigenfunctions for plane harmonic problems in composite regions
, ASME J. Appl. Mech.
47
, 87
–92
.6.
Thomson W, and Tait PG (1867), A Treatise on Natural Philosophy, Cambridge Univ Press, Cambridge, UK (This book is also available in two parts as Principles of Mechanics and Dynamics, Dover Publ, New York, NY).
7.
de Saint-Venant
B
1878
), Sample calculations for the torsion of prisms with bases made of circular arcs and radial lines (French
), Acad. Sci., Paris, C. R.
87
, 893
–899
.8.
Irwin GR, and Kies JA (1957), Fracture, Proc of ONR Symp, Washington DC, 563–571.
9.
Wasow
W
1957
), Asymptotic development of the solution of Dirichlet’s Problem at analytic corners
, Duke Math. J.
24
, 47
–56
.10.
Ting
TCT
1985
), Elastic wedge subjected to antiplane shear tractions—A paradox explained
, Q. J. Mech. Appl. Math.
38
, 245
–255
.11.
Sinclair
GB
1999
), A note on the removal of further breakdowns in classical solutions of Laplace’s equation on sectorial regions
, J. Elast.
56
, 247
–252
.12.
Ma
C-C
Hour
B-L
1989
), Analysis of dissimilar anisotropic wedges subjected to antiplane shear deformation
, Int. J. Solids Struct.
25
, 1295
–1309
.13.
Sinclair GB (2000), Logarithmic stress singularities in two-dimensional and three-dimensional elasticity, Proc of 20th Southeastern Conf of Theoretical and Applied Mechanics, Callaway Gardens, GA, SM94.1–8.
14.
Barnett
DM
1967
), The effect of shear modulus on the stress distribution produced by a planar array of screw dislocations near a bi-metallic interface
, Acta Metall.
15
, 589
–594
.15.
Sendeckyj GP (1973), Analysis of cracks in heterogeneous solids, Fracture Mechanics of Ceramics, Vol 1, RC Bradt, DPH Hasselman, and FF Lang (eds), Plenum Press, New York, NY, 269–282.
16.
Pageau
SS
Joseph
PF
Biggers
Jr SB
1995
), Singular antiplane stress fields for bonded and disbonded three-material junctions
, Eng. Fract. Mech.
52
, 821
–832
.17.
Keer
LM
Freeman
NJ
1970
), Load transfer problem for an embedded shaft in torsion
, ASME J. Appl. Mech.
37
, 959
–964
.18.
Love AEH (1944), A Treatise on the Mathematical Theory of Elasticity, 4th Edition, Dover Publ, New York, NY.
19.
Kirchhoff
G
1850
), On the equilibrium and deflection of an elastic plate (German
), J. Reine Angew. Math.
40
, 51
–88
.20.
Timoshenko SP, and Woinowsky-Krieger S (1959), Theory of Plates and Shells, 2nd Edition, McGraw-Hill, New York, NY.
21.
Williams ML (1951), Surface stress singularities resulting from various boundary conditions in angular corners of plates under bending, Proc of 1st US Nat Congress of Applied Mechanics, Illinois Inst of Tech, Chicago, IL, 325–329.
22.
Southwell
RV
1950
), On the analogues relating flexure and extension of flat plates
, Q. J. Mech. Appl. Math.
3
, 257
–271
.23.
Dixon
AC
1934
), The problem of the rectangular plate
, J. Lond. Math. Soc.
9
, 61
–74
.24.
Carrier GF and Shaw FS (1949), Some problems in the bending of thin plates, Proc of 3rd Symp in Applied Mathematics of the Am Mathematical Soc, Vol 3, Univ of Michigan, Ann Arbor, MI, 125–128.
25.
Morley
LSD
1964
), Bending of clamped rectilinear plates
, Q. J. Mech. Appl. Math.
17
, 293
–317
.26.
Hrudey
TM
Hrabok
MM
1986
), Singularity finite elements for plate bending
, J. Eng. Mech.
112
, 666
–681
.27.
Leissa
AW
McGee
OG
Huang
CS
1993
), Vibrations of sectorial plates having corner stress singularities
, ASME J. Appl. Mech.
60
, 134
–140
.28.
Gregory
RD
Chonghua
G
Wan
FYM
1996
), The cantilever strip under torsion, bending or flexure at infinity
, J. Elast.
43
, 109
–136
.29.
Williams
ML
1961
), The bending stress distribution at the base of a stationary crack
, ASME J. Appl. Mech.
28
, 78
–82
.30.
Williams
ML
1957
), On the stress distribution at the base of a stationary crack
, ASME J. Appl. Mech.
24
, 109
–114
.31.
Irwin
GR
1957
), Analysis of stresses and strains near the end of a crack traversing a plate
, ASME J. Appl. Mech.
24
, 361
–364
.32.
Sinclair
GB
2000
), Logarithmic stress singularities resulting from various boundary conditions in angular corners of plates under bending
, ASME J. Appl. Mech.
67
, 219
–223
.33.
Na´dai A (1925), The Elastic Plate (German), Julius Springer Publ, Berlin, Germany.
34.
Sih
GC
Rice
JR
1964
), The bending of plates of dissimilar materials with cracks
, ASME J. Appl. Mech.
31
, 477
–482
.35.
Huang
CS
2002
), Corner singularities in bi-material Mindlin plates
, Compos. Struct.
56
, 315
–327
.36.
Reissner
E
1945
), The effect of transverse shear deformation on the bending of elastic plates
, ASME J. Appl. Mech.
12
, A-69–A-77
A-69–A-77
.37.
Hencky
H
1947
), On the treatment of shear rotations in flat plates (German
), Oesterr. Ing.-Arch.
16
, 72
–76
.38.
Burton
WS
Sinclair
GB
1986
), On the singularities in Reissner’s theory for the bending of elastic plates
, ASME J. Appl. Mech.
53
, 220
–222
.39.
Yen
DHY
Zhou
M
1989
), On the corner singularities in Reissner’s theory for the bending of elastic plates
, ASME J. Appl. Mech.
56
, 726
–729
.40.
Huang
CS
McGee
OG
Leissa
AW
1994
), Exact analytical solutions for free vibrations of thick sectional plates with simply supported radial edges
, Int. J. Solids Struct.
31
, 1609
–1631
.41.
Knowles
JK
Wang
N-M
1960
), On the bending of an elastic plate containing a crack
, Z. Agnew Math. Phys.
39
, 223
–236
.42.
Hartranft
RJ
Sih
GC
1968
), Effect of plate thickness on the bending stress distribution around through cracks
, Z Agnew Math. Phys.
47
, 276
–291
.43.
Wang
N-M
1968
), Effects of plate thickness on the bending of an elastic plate containing a crack
, Z Agnew Math. Phys.
47
, 371
–390
.44.
Hartranft RJ (1966), On some problems involving singularities in Reissner’s theory of plate bending, Doctoral dissertation, Lehigh Univ, Bethlehem, PA.
45.
Abramowitz M, and Stegun IA (1965), Handbook of Mathematical Functions, Dover Publ, New York, NY.
46.
Bazˇant
ZP
Keer
LM
1974
), Singularities of elastic stresses and of harmonic functions at conical notches or inclusions
, Int. J. Solids Struct.
10
, 957
–964
.47.
Thomson
TR
Little
RW
1970
), End effects in a truncated semi-infinite cone
, Q. J. Mech. Appl. Math.
23
, 185
–195
.48.
Beagles
AE
Sa¨ndig
A-M
1991
), Singularities of rotationally symmetric solutions of boundary value problems for the Lame´ equations
, Z. Angew. Math. Mech.
71
, 423
–431
.49.
Love
AEH
1939
), Boussinesq’s problem for a rigid cone
, Q. J. Math.
10
, 161
–175
.50.
Hanson
MT
1993
), The elastic field for a sliding conical punch on an isotropic half-space
, ASME J. Appl. Mech.
60
, 557
–559
.51.
Keer
LM
Parihar
KS
1978
), Elastic stress singularity at conical inclusions
, Int. J. Solids Struct.
14
, 261
–263
.52.
Reissner
E
Sagoci
HF
1944
), Forced torsional oscillations of an elastic half-space: I
, J. Appl. Phys.
15
, 652
–654
.53.
Tsuji
T
Noda
N
Shibuya
T
Koizumi
T
1990
), Stress singularity at the bottom of a V-notch in the inner surface of a circular pipe under torsion
, Int. J. Pressure Vessels Piping
42
, 135
–155
.54.
Freeman
NJ
Keer
LM
1967
), Torsion of a cylindrical rod welded to an elastic half space
, ASME J. Appl. Mech.
34
, 687
–692
.55.
Westmann
RA
1968
), Discussion of “Torsion of a cylindrical rod welded to an elastic half space
,” ASME J. Appl. Mech.
35
, 197
–198
.56.
Keer
LM
Freeman
NJ
1969
), Torsion of a finite elastic cylindrical rod partially bonded to an elastic half space
, Q. Appl. Math.
26
, 567
–573
.57.
Barton
MV
1941
), The circular cylinder with a band of uniform pressure on a finite length of the surface
, ASME J. Appl. Mech.
8
, A-97–A-104
A-97–A-104
.58.
Zate
AR
1964
), Stresses in the vicinity of boundary discontinuities in bodies of revolution
, ASME J. Appl. Mech.
31
, 150
–152
.59.
Sneddon
IN
1946
), The distribution of stress in the neighborhood of a crack in an elastic solid
, Proc. R. Soc. London, Ser. A
A187
, 229
–260
.60.
Harding
JW
Sneddon
IN
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
, 16
–26
.61.
Benthem
JP
Minderhoud
P
1972
), The problem of the solid cylinder compressed between rough rigid stamps
, Int. J. Solids Struct.
8
, 1027
–1042
.62.
Agarwal
VK
1978
), Axisymmetric solution of the end-problem for semi-infinite elastic circular cylinder and its application to joined dissimilar cylinders under uniform tension
, Int. J. Eng. Sci.
16
, 985
–998
.63.
Hartranft
RJ
Sih
GC
1977
), Stress singularity for a crack with an arbitrarily curved front
, Eng. Fract. Mech.
9
, 705
–718
.64.
Sadowsky
MA
Sternberg
E
1949
), Stress concentration around a triaxial ellipsoidal cavity
, ASME J. Appl. Mech.
16
, 149
–157
.65.
Green
AE
Sneddon
IN
1950
), The distribution of stress in the neighborhood of a flat elliptical crack in an elastic solid
, Proc. Cambridge Philos. Soc.
46
, 159
–164
.66.
Kassir
MK
Sih
GC
1966
), Three-dimensional stress distribution around an elliptical crack under arbitrary loadings
, ASME J. Appl. Mech.
33
, 601
–611
.67.
Galin
LA
1948
), Determination of displacements in three-dimensional contact problems of the theory of elasticity (Russian
), Prikl. Mat. Mekh.
12
, 241
–250
.68.
Mindlin
RD
1949
), Compliance of elastic bodies in contact
, ASME J. Appl. Mech.
16
, 259
–268
.69.
Hughes WF, and Gaylord EW (1964), Basic Equations of Engineering Science, Schaum Publ Co, New York, NY.
70.
Love
AEH
1929
), The stress produced in a semi-infinite solid by pressure on part of the boundary
, Philos. Trans. R. Soc. London, Ser. A
A228
, 397
–420
.71.
Turteltaub
MJ
Wheeler
LT
1976
), Line integral representations for the traction problem of the elastic halfspace and their application to a study of the singular effects of load jumps
, J. Elast.
6
, 161
–178
.72.
Michell
JH
1902
), The inversion of plane stress
, Proc. London Math. Soc.
34
, 134
–142
.73.
Green AE, and Zerna W (1968), Theoretical Elasticity, 2nd Edition, Oxford at Clarendon Press, UK.
74.
Smith
FW
Alavi
MJ
1971
), Stress intensity factors for a penny shaped crack in a half space
, Eng. Fract. Mech.
3
, 241
–254
.75.
Shah
RC
Kobayashi
AS
1973
), Stress intensity factors for an elliptical crack approaching the surface of a semi-infinite solid
, Int. J. Fract.
9
, 133
–146
.76.
Liao
CY
Atluri
SN
1989
), Stress intensity factor variation along a semicircular surface flaw in a finite-thickness plate
, Eng. Fract. Mech.
34
, 957
–976
.77.
Galin LA (1947), Pressure of a stamp with a flat base in the form of an infinite wedge on an elastic half-space (Russian), Dokl. Akad. Nauk SSSR 58(2).
78.
Rvachev
VL
1959
), The pressure on an elastic half-space of a stamp with a wedge-shaped planform
, J. Appl. Math. Mech.
23
, 229
–233
.79.
Noble B (1959), The potential and charge distribution near the tip of a flat angular sector, Report NYU EM-135, New York Univ, New York, NY.
80.
Aleksandrov
VM
Babeshko
VA
1972
), On the pressure on an elastic half-space of a wedge-shaped stamp
, J. Appl. Math. Mech.
36
, 78
–83
.81.
Bazˇant
ZP
1974
), Three-dimensional harmonic functions near termination or intersection of gradient intersection lines: A general numerical method
, Int. J. Eng. Sci.
12
, 221
–243
.82.
Walden H (1974), Solution of an eigenvalue problem for the Laplace operator on a spherical surface, Report X-582-74-41, Goddard Space Flight Center, Greenbelt, MD.
83.
Morrison
JA
Lewis
JA
1976
), Charge singularity at the corner of a flat plate
, SIAM (Soc. Ind. Appl. Math.) J. Appl. Math.
31
, 233
–250
.84.
Brothers PW (1976), The rigid rectangular punch on the elastic half-space, Masters thesis, Univ of Auckland, Auckland, New Zealand.
85.
Keer
LM
Parihar
KS
1978
), A note on the singularity at the corner of a wedge-shaped punch or crack
, SIAM (Soc. Ind. Appl. Math.) J. Appl. Math.
34
, 297
–302
.86.
Ioakimidis
NI
1985
), Determination of the order of singularity at the apex of a wedge-shaped crack
, Eng. Fract. Mech.
22
, 369
–373
.87.
Takakuda
K
1985
), Stress singularities near crack front edges
, Bull. Japan Soc. Mech. Engineers
28
, 225
–231
.88.
Xu
L
Kundu
T
1995
), Stress singularities at crack corners
, J. Elast.
39
, 1
–16
.89.
Glushkov
E
Glushkova
N
Lapina
O
1999
), 3D elastic stress singularity at polyhedral corner points
, Int. J. Solids Struct.
36
, 1105
–1128
.90.
Parihar
KS
Keer
LM
1978
), Stress singularity at the corner of a wedge-shaped crack or inclusion
, ASME J. Appl. Mech.
45
, 791
–796
.91.
Parihar
KS
Keer
LM
1979
), The singularity at the apex of a bonded wedge-shaped stamp
, ASME J. Appl. Mech.
46
, 577
–580
.92.
Abramov
BM
1937
), The problem of contact of an elastic infinite half-plane with an absolutely rigid rough foundation
, C. R. (Dokl.) Acad. Sci. URSS
17
, 173
–178
.93.
Abdel-Messieh
YS
Thatcher
RW
1990
), Estimating the form of some three-dimensional singularities
, Commun. Appl. Numer. Methods
6
, 333
–341
.94.
Schmitz
H
Volk
K
Wendland
W
1993
), Three-dimensional singularities of elastic fields near vertices
, Numer. Methods Partial Differ. Equ.
9
, 323
–337
.95.
Panasyuk
VV
Andrejkiv
AE
Stadnik
MM
1980
), Basic mechanical concepts and mathematical techniques in application to three-dimensional crack problems: A review
, Eng. Fract. Mech.
13
, 925
–937
.96.
Panasyuk
VV
Andrejkiv
AE
Stadnik
MM
1981
), Three-dimensional static crack problems solution (A review
), Eng. Fract. Mech.
14
, 245
–260
.97.
Sih
GC
1971
), A review of the three-dimensional stress problem for a cracked plate
, Int. J. Fract. Mech.
7
, 39
–61
.98.
Folias
ES
1975
), On the three-dimensional theory of cracked plates
, ASME J. Appl. Mech.
42
, 663
–674
.99.
Kawai T, Fujitani Y, and Kumagai K (1977), Analysis of singularity at the root of the surface crack problem, Proc of Int Conf on Fracture Mechanics and Technology, Hong Kong, 1157–1163.
100.
Benthem
JP
1977
), State of stress at the vertex of a quarter-infinite crack in a half-space
, Int. J. Solids Struct.
13
, 479
–492
.101.
Bazˇant ZP and Estenssoro LF (1977), General numerical method for three-dimensional singularities in cracked or notched elastic solids, Proc of 4th Int Conf on Fracture, Vol 3, Waterloo, Ontario, 371–383.
102.
Bazˇant ZP, and Estenssoro LF (1977), Stress singularity and propagation of cracks at their intersection with surfaces, Structural Engineering Report 77-12/480, Dept of Civil Eng, Northwestern Univ, Evanston, IL.
1.
Bazˇant
ZP
Estenssoro
LF
1979
), Surface singularity and crack propagation
, Int. J. Solids Struct.
15
, 405
–426
2.
(See also: (
Addendum
1980
), 16
, 479
–481
, 3.
and Erratum (
1983
), 19
, 661
661
).1.
Sinclair GB (1979), Asymptotic singular eigenfunctions for the three-dimensional crack, Proc of 7th Canadian Congress of Applied Mechanics, Sherbrooke, Quebec, 295–296.
2.
Benthem
JP
1980
), The quarter-infinite crack in a half-space: Alternative and additional solutions
, Int. J. Solids Struct.
16
, 119
–130
.3.
Yamada Y, and Okumura H (1981), Analysis of local stress in composite materials by the 3D finite element, Proc of Japan-US Conf on Composite Materials, Tokyo, Japan, 55–84.
4.
Burton
WS
Sinclair
GB
Solecki
JS
Swedlow
JL
1984
), On the implications for LEFM of the three-dimensional aspects in some crack-surface intersection problems
, Int. J. Fract.
25
, 3
–32
.5.
Shaofu
W
Xing
Z
Qingzhi
H
1988
), Functional variable displacement method in analysis of singularity near the corner point in a three-dimensional cracked solid
, Eng. Fract. Mech.
31
, 191
–200
.6.
Shivakumar
KN
Raju
IS
1990
), Treatment of singularities in cracked bodies
, Int. J. Fract.
45
, 159
–178
.7.
Zhu
WX
1990
), Singular stress field of three-dimensional crack
, Eng. Fract. Mech.
36
, 239
–244
.8.
Barsoum
RS
Chen
T-K
1991
), Three-dimensional surface singularity of an interface crack
, Int. J. Fract.
50
, 221
–237
.9.
Ghahremani
F
1991
), A numerical variational method for extracting 3D singularities
, Int. J. Solids Struct.
27
, 1371
–1386
.10.
Leung
AYT
Su
RKL
1996
), Order of the singular stress field of through-thickness cracks
, Int. J. Fract.
75
, 85
–93
.11.
Leung
AYT
Su
RKL
1996
), Analytical solution for mode I crack orthogonal to free surface
, Int. J. Fract.
76
, 79
–85
.12.
Su
XM
Sun
CT
1996
), On singular stress of the crack tip of a thick plate under in-plane loading
, Int. J. Fract.
82
, 237
–252
.13.
Lur’e AI (1964), Three-Dimensional Problems of the Theory of Elasticity, Interscience Publ, John Wiley and Sons, New York, NY.
14.
Benthem
JP
Koiter
WT
1976
), Discussion of “On the three-dimensional theory of cracked plates
,” ASME J. Appl. Mech.
43
, 374
374
.15.
Folias
ES
1976
), Authors closure to discussion of “On the three-dimensional theory of cracked plates
,” ASME J. Appl. Mech.
43
, 374
–375
.16.
Folias
ES
1980
), Method of solution of a class of three-dimensional elastostatic problems under mode I loading
, Int. J. Fract.
16
, 335
–348
.17.
Meda
G
Messner
TW
Sinclair
GB
Solecki
JS
1998
), Path-independent H integrals for three-dimensional fracture mechanics
, Int. J. Fract.
94
, 217
–234
.18.
Ghahremani
F
Shih
CF
1992
), Corner singularities of three-dimensional planar interface cracks
, ASME J. Appl. Mech.
59
, 61
–68
.19.
Sagochi
HF
1944
), Forced torsional oscillations of an elastic half-space: II
, J. Appl. Phys.
15
, 655
–662
.20.
Leissa
AW
2001
), Singularity considerations in membrane, plate and shell behaviors
, Int. J. Solids Struct.
38
, 3341
–3353
.21.
Achenbach
JD
Bazˇant
ZP
1975
), Elastodynamic near-tip stress and displacement fields for rapidly propagating cracks in orthotropic materials
, ASME J. Appl. Mech.
42
, 183
–189
.22.
Nowacki W (1968), Thermoelasticity, 2nd Edition, Pergamon Press, Oxford, UK.
23.
Yan
G
Ting
TCT
1993
), The r−1/2(ln r) singularities at interface cracks in monoclinic and isotropic bimaterials due to heat flow
, ASME J. Appl. Mech.
60
, 432
–437
.24.
Yang
YY
Munz
D
1995
), Stress intensity factor and stress distribution in a joint with an interface corner under thermal and mechanical loading
, Comput. Struct.
57
, 467
–476
.25.
Lee
EH
1955
), Stress analysis in visco-elastic bodies
, Q. Appl. Math.
13
, 183
–190
.26.
Williams ML (1962), The fracture of viscoelastic materials, Fracture of Solids, Proc of an Int Conf, Maple Valley, WA, 157–188.
27.
Ting TCT (1986), Anisotropic Elasticity, Oxford Univ Press, New York, NY.
28.
Ting TCT (1998), The remarkable nature of cylindrically uniform anisotropic elastic materials, Proc of 13th US Natl Congress of Applied Mechanics, TA7.
29.
Muki
R
Sternberg
E
1965
), The influence of couple-stresses on singular stress concentrations in elastic solids
, Z. Angew. Math. Phys.
16
, 611
–648
.30.
Sternberg
E
Muki
R
1967
), The effect of couple-stresses on the stress concentration around a crack
, Int. J. Solids Struct.
3
, 69
–95
. Copyright © 2004
by ASME
You do not currently have access to this content.
