A review of SIF evaluation and modelling of singularities in BEM

Computational Mechanics

Volumn 25, Issue 4, 2000, Pages 358-375

  Mukhopadhyay, N K ^a   Maiti, S K ^b   Kakodkar, A ^a  

^a BHABHA ATOMIC RESEARCH CENTRE   (India)

^b INDIAN INSTITUTE OF TECHNOLOGY BOMBAY   (India)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0000748036     PISSN: 01787675     EISSN: None     Source Type: Journal    
DOI: 10.1007/s004660050483     Document Type: Review

References (130)

1. Aliabadi MH, Rooke DP, Cartwright DJ (1987) An improved boundary element formulation for calculating stress intensity factors: application to aerospace structures. J. Strain Anal. 22:203-207
2. Atluri SN (1997) Structural Integrity & Durability, Tech. Science Press
3. Aliabadi MH, Rooke DP, Cartwright DJ (1989) Fracture-mechanics weight-functions by the removal of singular fields using boundary element analysis. Int. J. Fract. 40:271-284
4. Ang WT (1986) A boundary integral solution for the problem of multiple interacting cracks in an elastic material. Int. J. Fract. 31:259-270
5. Ang HE, Torrance JE, Tan CL (1996) Boundary element analysis of orthotropic delamination specimens with interface cracks. Eng. Fract. Mech. 54:601-615
6. Atluri SN, Kobayashi AS, Nakagaki M (1975) An assumed hybrid finite element model for linear fracture mechanics. Int. J. Fract. 11:257
7. Badri Narayan K, George S, Duttaguru B, Ramamurthy TS, Vijaykumar K (1994) Modified crack closure integral (MCCI) for 3-d problems using 20-noded brick elements. Fatigue Fract. Eng. Mater. Struct. 2:145-1557
8. Bakr AA, Fenner RT (1985) Axisymmetric fracture mechanics analysis by the boundary element method. Int. J. Pres. Ves. Piping 18:55-75
9. Balas J, Sladek J, Sladek V (1989) Stress Analysis by Boundary Element Method, Elsevier, Amsterdam
10. Barsoum RS (1977) Triangular quarter point elements as elastic and perfectly plastic crack tip elements. Int. J. Num. Meth. Eng. 11:85-98
11. Blandford GE, Ingraffea AR, Liggett JA (1981) Two-dimensional stress intensity factor computations using the boundary element method. Int. J. Num. Meth. Eng. 17:387-404
12. Chan SK, Tuba IS, Wilson WK (1970) On the finite element method in linear fracture mechanics, Eng. Fract. Mech. 2:1-17
13. Chandra A, Huang Y, Wei X, Hu KX (1995) A hybrid micro-macro BEM formulation for micro-crack clusters in elastic components. Int. J. Num. Meth. Eng. 38:1215-1236
14. Chao CK, Chang RC (1992) Crack trajectories influenced by mechanical and thermal disturbance in anisotropic material. Theo. Appl. Fract. Mech. 17:177-187
15. Choa WT, Atluri SN (1995) Finite element calculation of stress intensity factors for an interfacial crack, using the virtual crack closure integral. Comput. Mech. 16:417-425
16. Choa WT, Beom HG, Atluri SN (1995) Calculation of stress intensity factors for an interfacial crack between dissimilar anisotropic media, using a hybrid element method and the mutual integral. Comput. Mech. 16:546-557
17. Chen WH, Chen TC (1995) An efficient dual boundary element technique for a two-dimensional fracture problem with multiple cracks. Int. J. Num. Meth. Eng. 38:1739-1756
18. Chen YZ (1995) Hypersingular integral equation approach for the multiple crack problem in an infinite plate. Acta Mechanica 108:121-131
19. Chen YZ (1997) Numerical solution of multiple crack problem by using hypersingular integral equation. Int. J. Fract. 88:L9-L14
20. Chen YZ, Hasebe N (1995) Solution of multiple-edge crack problem of elastic half-plane by singular equation approach. Commun. Num. Meth. Eng. 11:607-617
21. Chen YZ, Hasebe N (1997) Novel weight function approach for plane elasticity crack problem, Int. J. Eng. Sci. 35:4234-4355
22. Chirino F, Dominguez J (1989) Dynamic analysis of cracks using boundary element method. Eng. Fract. Mech. 34:1051-1061
23. Chudnovsky A, Kachanov M (1983) Interaction of a crack with a field of microcracks, Int. J. Eng. Sci. 21:1009-1018
24. Cook TS, Erdogan F (1972) Stresses in bonded material with a crack perpendicular to the interface. Int. J. Eng. Sci. 10:677-697
25. Cotterell B, Rice JR (1980) Slightly curved or kinked cracks. Int. J. Fract. 16:155-169
26. Crouch LS, Starfield AM (1983) Boundary Element Methods in Solid Mechanics, George Allen & Unwin, London
27. Cruse TA (1969) Numerical solutions in three dimensional elastostatics. Int. J. Solids Struct. 5:1259-1274
28. Cruse TA, Buren W Van (1971) Three-dimensional elastic stress analysis of a fracture specimen with an edge crack. Int. J. Fract. Mech. 7:1-16
29. Cruse TA (1972) Numerical evaluation of elastic stress intensity factors by the boundary integral equation method. In: Swedlow JL (ed.) The Surface Crack: Physical Problems and Computational Solutions ASME, New York 153-170
30. Cruse TA (1978) Two-dimensional BIE fracture mechanics analysis. Appl. Math. Modelling 2:287-293
31. Cruse TA, Wilson RB (1978) Advanced applications of boundary-integral equation methods. Nucl. Eng. Des. 46:223-234
32. Cruse TA (1988) Boundary Element Analysis in Computational Fracture Mechanics, Kluwer, Dordrecht
33. Cruse TA, Raveendra ST (1988) A general solution procedure for fracture mechanics weight function evaluation based on the boundary element method. Comput. Mech. 3:157-166
34. Cruse TA, Novati G (1992) Traction BIE formulations and applications too non-planar and multiple cracks. In: Atluri SN, Newman Jr JC, Raju IS, Epstein JS (Eds.) Fracture Mechanics: Twenty-Second Symposium, Vol II, ASTM STP 1131, American Society for Testing and Materials, Philadelphia, 314-332
35. Cruse TA (1996) BIE fracture mechanics analysis: 25 years of developments. Comput. Mech. 18:1-11
36. Dominguez J, Gallego R (1992) Time domain boundary element method for dynamic stress intensity factor computations. Int. J. Num. Meth. Eng. 33:635-647
37. Dutta BK, Maiti SK, Kakodkar A (1990) On the use of one point and two points singularity elements in the analysis of kinked cracks. Int. J. Num. Meth. Eng. 29:1487-1499
38. Emery AF, Neighbors PK, Kobayashi AS, Love WJ (1977) Stress intensity factors in edge-cracked plates subjected to transient thermal singularities. J. Pres. Ves. Tech. 99:100-105
39. Farris TN, Liu M (1993) Boundary element crack closure calculation of three-dimensional stress intensity factors. Int. J. Fract. 60:33-47
40. Fedelinski P, Aliabadi MH, Rooke DP (1995) A single-region time domain BEM for dynamic crack problems. Int. J. Solids and Struct. 32:3555-3571
41. Gangming L, Yongyuan Z (1988) Application of boundary element method with singular and isoparametric elements in three dimensional crack problems. Eng. Fract. Mech. 29:97-106
42. Gangming L, Yongyuan Z (1988) Improvement of stress singular element for crack problems in three dimensional boundary element method. Eng. Fract. Mech. 31:993-999
43. Gerstle WH, Ingraffea AR, Perucchio R (1988) Three-dimensional fatigue crack propagation analysis using the boundary element method. Int. J. Fatigue 10:189-192
44. Gray LJ, Martha JF, Ingraffea AR (1990) Hypersingular integrals in boundary element fracture analysis. Int. J. Num. Meth. Eng. 29:1135-1158
45. Gray LJ, Paulino GH (1997) Symmetric Galerkin boundary integral fracture analysis for plane orthotropic elasticity. Comput. Mech. 20:26-33
46. Guimaraes S, Telles JCF (1994) On the hyper-singular boundary-element formulation for fracture-mechanics applications. Eng. Anal. Bound. Ele. 13 :353-363
47. Hensell RD, Shaw KG (1975) Crack tip elements are unnecessary. Int. J. Num. Meth. Eng. 9:495-507
48. Hori M, Nemat-Nasser S (1987) Interacting micro-cracks near the tip in the process zone of a macro-crack. J. Mech. Phys. Solids 35:601-629
49. Hucker SA, Farris TN (1993) Modified crack closure method using boundary elements. Eng. Fract. Mech. 46:763-772
50. Irwin GR (1958) In: Flugge S (Ed.) Fracture I, Hanbuch der physik VI Springer, Berlin 558-590
51. Isida M, Cheng D, Nisatani H (1984) Plane problems of an arbitrary array of cracks emanating from the edge ol an elliptical hole. Trans. Japan Sc. Mech. Engrs. 50(no. 451):330-340
52. Jawson MA (1963) Integral equation methods in potential theory-I, Proc. Roy. Soc. Lond. A 275:23-32
53. Kachanov M (1986) On crack-microcrack interaction. Int. J. Fract. 30:R65-R72
54. Karami G, Fenner RT (1986) Analysis of mixed mode fracture and crack closure using the boundary integral equation method. Int. J. Fract. 30:13-29
55. Katsareas DE, Anifantis NK (1995) On the computation of mode I and II thermal shock stress intensity factors using a boundary-only element method. Int. J. Num. Meth. Eng. 38:4157-4169
56. Katsareas DE, Kanarios VI, Anifantis NK (1998) Performance of traction-singular boundary elements in analysing fracture process in transient quasistatic environments. Comput. Meth. Appl. Mech. Eng. 163:261-270
57. Kebir H, Relandt JM, Foulquier J (1999) A new singular boundary element for crack problems Applications to bolted joints. Eng. Fract. Mech. 62:497-510
58. Krishnamurthy T, Raniamurthy TS, Vijayakumar K, Duttaguru B (1985) Modified crack closure integral method for higher order finite elements. In: Kant T (Ed.) Proc. Int. Conf. Finite Elements in Computational Mechanics, Bombay, 891-900
59. Lachat JC, Watson JO (1976) Effective numerical treatment of boundary integral equations: a formulation for three-dimensional elastoplastics. Int. J. Num. Meth. Eng. 10:991-1005
60. Lam KY, Phua SP (1991) Multiple crack interaction and its effect on stress intensity factor. Eng. Fract. Mech. 40:585-592
61. Lee KY, Cho YH (1990) Boundary element analysis of thermal stress intensity factors for CUSP cracks. Eng. Fract. Mech. 37:787-798
62. Li R, Chudnovsky A (1994) The stress intensity factor Green's function for a crack interacting with a circular inclusion. Int. J. Fract. 67:169-177
63. Liu SB, Tan CL (1992) Two-dimensional boundary element contact mechanics analysis of angled crack problems. Eng. Fract. Mech. 42:273-288
64. Lo KK (1978) Analysis of branched cracks. J. Appl. Mech. 4555:797-802
65. Lynn PP, Ingraffea AR (1978) Transition elements to be used with quarter-point crack tip elements. Int. J. Num. Meth. Eng. 12:1031-1036
66. Maiti SK (1990) Finite element computation of the strain energy release rate for a kinking of a crack. Int. J. Fract. 43:161-174
67. Maiti SK (1992a) A multicorner variable order singularity triangle to model neighbouring singularities. Int. J. Num. Meth. Eng. 35:391-408
68. Maiti SK (1992b) Finite element computation of crack closure integrals and stress intensity factors. Eng. Fract. Mech. 41:339-348
69. Maiti SK (1992c) A finite element for variable order singularities based on the displacement formulation. Int. J. Num. Meth. Eng. 33:1955-1974
70. Martinez J, Dominguez J (1984) On the use of quarter-point boundary elements for stress intensity factor computations. Int. J. Num. Meth. Eng. 20:1941-1950
71. Melnikov YA (1995) Green's functions in Applied Mechanics, Computational Mechanics Publications, Southampton, UK
72. Mogilevskaya SG (1997) Numerical modelling of 2-D smooth crack growth. Int. J. Fract. 87:389-405
73. Mukhopadhyay NK, Maiti SK, Kakodkar A (1998a) Further considerations in modified crack closure integral based computation of stress intensity factor in BEM. Eng. Fract. Mech. 59:269-279
74. Mukhopadhyay NK, Maiti SK, Kakodkar A (1998b) BEM based evaluation of SIFs using modified crack closure integral technique under remote and/or crack edge loading. Eng. Fract. Mech. 61:655-671
75. Mukhopadhyay NK, Maiti SK, Kakodkar A (1999a) Modified crack closure integral based computation of SIFs for 2-D thermoelastic problems through BEM. Nucl. Eng. Des. 187:277-290
76. Mukhopadhyay NK, Maiti SK, Kakodkar A (199b) Effect of modelling of traction and thermal singularities on accuracy of SIFs computation through modified crack closure integral in BEM. Eng. Fract. Mech. 64:141-159
77. Mukhopadhyay NK, Maiti SK, Kakodkar A (1999c) Variable order singularity boundary element and its applications in computation of SIFs. Comput. Struct. (In Press)
78. Mukhopadhyay NK, Maiti SK, Kakodkar A (1999d) Two end variable singularity boundary elements and their applications in crack-crack interaction problems. Int. J. Num. Meth. Eng. (In Press)
79. Murakami Y (1987) Stress intensity factors handbook. Pergamon Press
80. Nadiri F, Tan CL, Fenner RT (1982) Three-dimensional analyses of surface cracks in pressurised thick walled cylinders. Int. J. Pres. Ves. Piping 10:159-167
81. Nishimura N, Guo QC, Kobayashi S (1988) In: Crust TA, Tanaka M (Eds.) Elastodynamic crack analysis by BIEM, Proc. Boundary Element Methods in Applied Mechanics, Pergamon Press, 245-254
82. Nishioka T, Atluri SN (1983) Path-independent integrals, energy release rates, and general solutions of near-tip fields in mixed-mode dynamic fracture mechanics. Eng. Fract. Mech 18:1-22
83. Parks DM (1974) A stiffness derivative finite element technique for determination of crack tip stress intensity factors. Int. J. Fract. 10:487-502
84. Perucchio R, Ingraffea AR (1985) An integrated boundary element analysis system with interactive computer graphics for three-dimensional linear elastic fracture mechanics. Comput. Struct. 20:157-171
85. Pian THH, Tong P, Luk CH (1971) Elastic crack analysis by a finite element hybrid methd, Proceedings of the Third International Conference on Matrix method in Structural Mechanics, Wright-Patterson Air Force Base, Ohio, November
86. Polch EZ, Cruse TA, Huang CJ (1987) Traction BIE solutions for flat cracks. Comput. Mech. 2:253-267
87. Portela A, Aliabadi MH (1992a) The dual boundary element method: effective implementation for crack problems. Int. J. Num. Meth. Eng. 33:1269-1287
88. Portela A, Aliabadi MH, Rooke DP (1992b) Dual boundary element analysis of cracked plates: singularity subtraction technique. Int. J. Fract. 55:17-28
89. Prasad NNV, Aliabadi MH, Rooke DP (1994) The dual boundary element method for thermoelastic crack problems. Int. J. Fract. 66:255-272
90. Prasad NNV, Aliabadi MH, Rooke DP (1996) Effect of thermal singularities on stress intensity factors: edge crack in rectangular and circular plate. Theo. Appl. Fract. Mech. 24:203-215
91. Raju IS (1987) Calculation of strain energy release rates with higher order and singular finite elements. Eng. Fract. Mech. 28:251-264
92. Ramamurthy TS, Krishnamurthy T, Badri Narayan K, Vijaykumar K, Duttaguru B (1986) Modified crack closure integral methods with quarter point elements. Mech. Res. Commun. 13:179-186
93. Raveendra ST, Banerjee PK (1992) Boundary element analysis of cracks in thermally stressed planar structures. Int. J. Solids Struct. 29:2301-2317
94. Raveendra ST, Banerjee PK, Dargush GF (1993) Three-dimensional analysis of thermally loaded cracks. Int. J. Num. Meth. Eng. 36:1909-1926
95. Rice JR (1968) A path independent integral and the approximate analysis of strain concentration by notches and cracks. J. Appl. Mech., Trans. ASME 33:379-386
96. Richardson D, Cruse TA (1998) Nonsingular BEM for fracture modeling. Comput. Struct. 66:695-703
97. Rizzo FJ (1967) An integral equation approach to boundary value problems of classical elastostatics. Q. Appl. Math. 25:83-95
98. Rizzo FJ, Shippy DJ (1977) An advanced boundary integral equation method for three-dimensional thermoelasticity. Int. J. Num. Meth. Eng. 11:1753-1768
99. Rooke DP, Cartwright DJ (1976) Compendium of Stress intensity factors. Her Majesty's Stationery Office, London
100. Rubeinstein AA, Choi HC (1988) Macrocrack interaction with transverse array of microcracks. Int. J. Fract. 36:15-26
101. Rudolphi TJ, Koo LS (1985) Boundary element solutions of multiple, interacting crack problems in plane elastic media. Eng. Anal. 2:211-216
102. Rybicki EF, Kanninen MF (1977) A finite element calculation of stress intensity factors by a modified crack closure integral. Eng. Fract. Mech. 9:931-938
103. Saez A, Gallego R, Domingeuz J (1995) Hypersingular quarter-point boundary elements for crack problems. Int. J. Num. Meth. Eng. 38:1681-1701
104. Selcuk S, Hurd DS, Crouch SL, Gerberich WW (1994) Prediction of interfacial crack path: a direct boundary integral approach and experimental study. Int. J. Fract. 67:1-20
105. Sethuraman R, Maiti SK (1988) Finite element based computation of strain energy release rate by modified crack closure integral. Eng. Fract. Mech. 30:227-231
106. Singh R, Carter BJ, Wawrzynek PA, Ingraffea AR (1998) Universal crack closure integral for SIF estimation. Eng. Fract. Mech. 60:133-146
107. Sladek V, Sladek J, Balas J (1986) Boundary integral formulation of crack problems. ZAMM 66:83-94
108. Sladek J, Sladek V (1986) Dynamic stress intensity factors studied by boundary integro-differential equations. Int. J. Num. Meth. Eng. 23:919-928
109. Sladek V, Sladek J (1993) Boundary integral representation of stress intensity factors in thermoelasticity. Eng. Anal. with Boundary Elements 12:127-135
110. Sladek J, Sladek V (1997) Computation of thermoelastoplastic stresses in crack problems by the BEM. Int. J. Fract. 83:359-378
111. Stern M (1979) Families of consistent conforming elements with singular fields. Int. J. Num. Meth. Eng. 14:409-421
112. Sumi N, Katayama T (1980) Thermal stress singularities at tips of a Griffith crack in a finite rectangular plate. Nucl. Eng. Des. 60:389-394
113. Symm GT (1963) Integral equation methods in potential theory-I, Proc. Roy. Soc. Lond. A275:33-46
114. Synder MD, Cruse TA (1975) Boundary-integral equation analysis of cracked anisotropic plates. Int. J. Fract. Mech. 11:315-328
115. Takakuda K, Korzumi T, Shibuya T (1985a) On integral equation methods for crack problems. Bull. JSME 28:217-224
116. Takakuda K (1985b) Stress singularities near crack front edges. Bull. JSME 28:225-231
117. Tan CL, Fenner RT (1978) Three-dimensional stress analysis by the boundary integral equation method. J. Strain Anal. 13:231-237
118. Tan CL, Fenner RT (1979) Elastic fracture mechanics analysis by the boundary integral equation method. Proc. Roy. Soc. Lond. A369:243-260
119. Tracey DM, Cook TS (1977) Analysis of power type singularities using finite elements. Int. J. Num. Meth. Eng. 11:1225-1233
120. Wang YB, Chau KT (1997) A new boundary element for plane elastic problems involving cracks and holes. Int. J. Fract. 87:1-20
121. Watson JO (1995) Singular boundary elements for the analysis of cracks in plane strain. Int. J. Num. Meth. Eng. 38:2389-2411
122. Watwood VB (1969) The finite element method for prediction of crack behaviour. Nucl. Eng. Des. 11:323-332
123. Weaver J (1977) Three-dimensional crack analysis. Int. J. Solids Struct. 13:321-330
124. Weeen F van der (1983) Mixed mode fracture analysis of rectilinear anisotropic plates using singular boundary elements. Comput. Struct. 17:469-474
125. Wen PH, Aliabadi MH, Rooke DP (1998) Cracks in three dimensions: A dynamic dual boundary element analysis. Comput. Meth. Appl. Mech. Eng. 167:139-151
126. Williams ML (1952) Stress singularities resulting from various boundary conditions in angular ends of plates in extension. J. Appl. Mech. ASME 19:526-528
127. Xanthis LS, Bernai MJM, Atkinson C (1981) The treatment of singularities in the calculation of stress intensity factors using the boundary integral equation method. Comput. Meth. Appl. Mech. Eng. 26:285-304
128. Yuuki R, Xu J-Q (1994) Boundary element method and its applications to the analyses of dissimilar materials and interface cracks. In: Nisatani H (Ed.) Computational and Experimental Fracture Mechanics Computational Mechanics Publications 61-90
129. Zang WL, Gudmundson P (1990) Contact problems of kinked cracks modelled by a boundary integral method. Int. J. Num. Meth. Eng. 29:847-860
130. Zeng Z-J, Dai S-H, Yang Y-M (1993) Analysis of surface cracks using line-spring boundary element method and the virtual crack extension technique. Int. J. Fract. 60:157-167