Free-edge effects in composite laminates

Applied Mechanics Reviews

Volumn 60, Issue 1-6, 2007, Pages 217-245

  Mittelstedt, Christian ^a   Becker, Wilfried ^b  

^a AIRBUS OPERATIONS GMBH   (Germany)

^b DARMSTADT UNIVERSITY OF TECHNOLOGY   (Germany)

Author keywords

Composites; Free edge effect; Interlaminar stresses; Laminates; Layered plates; Singularities

Indexed keywords

DISSIMILAR MATERIALS; FIBER REINFORCED PLASTICS; INTERFACES (MATERIALS); LIGHT WEIGHT STRUCTURES; PLATES (STRUCTURAL COMPONENTS); STRESS CONCENTRATION;

FREE EDGE EFFECTS; INTERLAMINAR STRESSES; LAYERED PLATES; SINGULAR STRESS FIELDS;

LAMINATED COMPOSITES;

EID: 42349108779     PISSN: 00036900     EISSN: None     Source Type: Journal    
DOI: 10.1115/1.2777169     Document Type: Review

References (292)

1. Ashton, J. E., and Whitney, J. M., 1970, Theory of Laminated Plates, Technomic, Stamford.
2. Jones, R. M., 1975, Mechanics of Composite Materials, Scripta Book Co., Washington.
3. Bert, C. W., 1975, "Analysis of Plates," Composite Materials, L. J. Broutman and R. H.Krock, eds., Vol. 7, Structural Design and Analysis, C. C. Chamis, ed., Academic, New York, Vol. 1, Pt. I, pp. 150-206.
4. Tsai, S. W., and Hahn, H. T., 1980, Introduction to Composite Materials, Technomic, Lancaster.
5. Herakovich, C. T., 1998, Mechanics of Fibrous Composites, Wiley, New York.
6. Reddy, J. N., 2004, Mechanics of Laminated Composite Plates and Shells, 2nd ed., CRC, Boca Raton, FL.
7. Bogdanovich, A. E., and Sierakowski, R. L., 1999, "Composite Materials and Structures: Science, Technology and Applications," Appl. Mech. Rev., 52, pp. 351-366.
8. Noor, A. K., and Burton, W. S., 1989, "Assessment of Shear Deformation Theories for Multilayered Composite Plates," Appl. Mech. Rev., 42, pp. 1-13.
9. Noor, A. K., and Burton, W. S., 1990, "Assessment of Computational Models for Multilayered Anisotropic Plates," Compos. Struct., 14, pp. 233-265.
10. Pipes, R. B., and Pagano, N. J., 1970, "Interlaminar Stresses in Composite Laminates Under Uniform Axial Extension," J. Compos. Mater., 4, pp. 538-548.
11. Pipes, R. B., and Daniel, I. M., 1971, "Moire Analysis of the Interlaminar Shear Edge Effect in Laminated Composites," J. Compos. Mater., 5, pp. 255-259.
12. Herakovich, C. T., Post, D., Buczek, M. B., and Czarnek, R., 1985, "Free Edge Strain Concentrations in Real Composite Laminates: Experimental-Theoretical Correlation," ASME J. Appl. Mech., 52, pp. 787-793.
13. Herakovich, C. T., 1989, "Free Edge Effects in Laminated Composites," Handbook of Composites, Herakovich, C. T., and Tarnopol'skii, Y. M., eds., Elsevier Science B. V., Amsterdam, Vol. 2, pp. 187-230.
14. Kassapoglou, C., and Lagace, P. A., 1986, "An Efficient Method for the Calculation of Interlaminar Stresses in Composite Materials," ASME J. Appl. Mech., 53, pp. 744-750.
15. Kassapoglou, C., and Lagace, P. A., 1987, "Closed Form Solutions for the Interlaminar Stress Field in Angle-Ply and Cross-Ply Laminates," J. Compos. Mater., 21, pp. 292-308.
16. Hayashi, T., 1967, "Analytical Study of Interlaminar Shear Stresses in a Laminated Composite Plate," Trans. Jpn. Soc. Aeronaut. Space Sci., 10, pp. 43-48.
17. Puppo, A. H., and Evensen, H. A., 1970, "Interlaminar Shear in Laminated Composites Under Generalized Plane Stress," J. Compos. Mater., 4, pp. 204-220.
18. Pagano, N. J., and Pipes, R. B., 1971, "The Influence of Stacking Sequence on Laminate Strength," J. Compos. Mater., 5, pp. 50-57.
19. Pagano, N. J., and Pipes, R. B., 1973, "Some Observations on the Interlaminar Strength of Composite Laminates," Int. J. Mech. Sci., 15, pp. 679-688.
20. Harris, A., and Orringer, O., 1978, "Investigation of Angle-Ply Delamination Specimen for Interlaminar Strength Test," J. Compos. Mater., 12, pp. 285-299.
21. Conti, P., and De Paulis, A., 1985, "A Simple Model to Simulate the Interlaminar Stresses Generated Near the Free Edge of a Composite Laminate," Delamination and Debonding of Materials, ASTM, STP 876, Johnson, W. S., ed., American Society for Testing and Materials, Philadelphia, pp. 35-51.
22. Valisetty, R. R., and Rehfield, L. W., 1985, "A New Ply Model for Interlaminar Stress Analysis," Delamination and Debonding of Materials, ASTM, STP 876, Johnson, W. S., ed., American Society for Testing and Materials, Philadelphia, pp. 52-68.
23. Moore, T. D., and Jarvis, J. L., 2004, "Peeling in Bimaterial Beams: The Peeling Moment and Its Relation to the Differential Rigidity," ASME J. Appl. Mech., 71, pp. 290-292.
24. Pagano, N. J., 1974, "On the Calculation of Interlaminar Normal Stress in Composite Laminate," J. Compos. Mater., 8, pp. 65-81.
25. Whitney, J. M., 1987, Structural Analysis of Laminated Anisotropic Plates, Technomic, Lancaster.
26. Krishna Murty, A. V., and Hari Kumar, H. K., 1989, "Modelling of Symmetric Laminates Under Extension," Compos. Struct., 11, pp. 15-32.
27. Becker, W., 1993, Beiträge zur Analytischen Behandlung Ebener Laminate, VDI, Düsseldorf.
28. Becker, W., 1993, "Closed-Form Solution for the Free-Edge Effect in Cross-Ply Laminates," Compos. Struct., 26, pp. 39-45.
29. S- Winkelverbund," ZAMM, 73, pp. T429-T432.
30. Becker, W., 1994, "Closed-Form Analysis of the Free Edge Effect in Angle-Ply Laminates," ASME J. Appl. Mech., 61, pp. 209-211.
31. Becker, W., 1995, "Free-Edge Stress Concentration in Angle-Ply Laminates," Arch. Appl. Mech., 65, pp. 38-43.
32. Becker, W., and Kress, G., 1994, "Stiffness Reduction in Laminate Coupons Due to the Free-Edge Effect," Compos. Sci. Technol., 52, pp. 109-115.
33. Becker, W., 1995, "Zum Breiteneinfluss von Steifigkeitsmessungen bei Laminat-Zugproben," ZAMM, 75, pp. S143-S144.
34. S- Angle-Ply Laminates," Arch. Appl. Mech., 66, pp. 419-426.
35. Becker, W., 1997, "The Influence of Clamping on Uniaxial Laminate Tensile Tests," ZAMM, 77, pp. S513-S514.
36. Pipes, R. B., and Pagano, N. J., 1974, "Interlaminar Stresses in Composite Laminates: An Approximate Elasticity Solution," ASME J. Appl. Mech., 41, pp. 668-672.
37. Hsu, P. W., and Herakovich, C. T., 1977, "A Perturbation Solution for Interlaminar Stresses in Bidirectional Laminates," Composite Materials: Testing and Design (Fourth Conference), ASTM, STP, 617, American Society for Testing and Materials, Philadelphia, pp. 296-316.
38. Hsu, P. W., and Herakovich, C. T., 1977, "Edge Effects in Angle-Ply Composite Laminates," J. Compos. Mater., 11, pp. 422-428.
39. Wang, J. T. S., and Dickson, J. N., 1978, "Interlaminar Stresses in Symmetric Composite Laminates," J. Compos. Mater., 12, pp. 390-402.
40. Kress, G., and Becker, W., 1995, "Effective Tensile Stiffness of Finite-Width Quasi-Isotropic Laminates," J. Reinf. Plast. Compos., 14, pp. 1043-1053.
41. Zhu, C., and Lam, Y. C., 1998, "A Rayleigh-Ritz Solution for Local Stresses in Composite Laminates," Compos. Sci. Technol., 58, pp. 447-461.
42. Tahani, M., and Nosier, A., 2003, "Free Edge Stress Analysis of General Cross-Ply Composite Laminates Under Extension and Thermal Loading," Compos. Struct., 60, pp. 91-103.
43. Nosier, A., Kapania, R. K., and Reddy, J. N., 1993, "Free Vibration Analysis of Laminated Plates Using a Layerwise Theory," AIAA J., 31, pp. 2335-2346.
44. Flanagan, G., 1994, "An Efficient Stress Function Approximation for the Free-Edge Stresses in Laminates," Int. J. Solids Struct., 31, pp. 941-952.
45. Lekhnitskii, S. G., 1963, Theory of Elasticity of an Anisotropic Body, Holden-Day, San Francisco.
46. Kassapoglou, C., 1989, "The Effect of Combined Loading and Stacking Sequence on the Interlaminar Stress Field at Free Edges of Composite Laminates," 30th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference: A Collection of Technical Papers, Pt. 4, pp. 2089-2097.
47. Webber, J. P. H., and Morton, S. K., 1993, "An Analytical Solution for the Thermal Stresses at the Free Edges of Laminated Plates," Compos. Sci. Technol., 46, pp. 175-185.
48. Morton, S. K., and Webber, J. P. H., 1993, "Interlaminar Failure Due to Mechanical and Thermal Stresses at the Free Edges of Laminated Plates," Compos. Sci. Technol., 47, pp. 1-13.
49. Rose, C. A., and Herakovich, C. T., 1993, "An Approximate Solution for Interlaminar Stresses in Composite Laminates," Composites Eng., 3, pp. 271-285.
50. Lin, C. C., Hsu, C. Y., and Ko, C. C., 1995, "Interlaminar Stresses in General Laminates With Straight Free Edges," AIAA J., 33, pp. 1471-1476.
51. Stiftinger, M. A., 1996, Semi-Analytical Finite Element Formulations for Layered Composite Shells With Consideration of Edge Effects, VDI, Düsseldorf.
52. Amrutharaj, G. S., Lam, K. Y., and Cotterell, B., 1996, "Delaminations at the Free Edge of a Composite Laminate," Composites, Part B, 27B, pp. 475-483.
53. Whitney, J. M., 1973, "Free-Edge Effects in the Characterization of Composite Materials," ASTM, STP 521, American Society for Testing and Materials, Philadelphia, pp. 167-180.
54. Tang, S., 1975, "A Boundary Layer Theory - Part, I: Laminated Composites in Plane Stress," J. Compos. Mater., 9, pp. 33-41.
55. Tang, S., and Levy, A., 1975, "A Boundary Layer Theory - Part II: Extension of Laminated Finite Strip," J. Compos. Mater., 9, pp. 42-52.
56. Pagano, N. J., 1978, "Stress Fields in Composite Laminates," Int. J. Solids Struct., 14, pp. 385-400.
57. Pagano, N. J., 1978, "Free Edge Stress Fields in Composite Laminates," Int. J. Solids Struct., 14, pp. 401-406.
58. Reissner, E., 1950, "On a Variational Theorem in Elasticity," J. Math. Phys., 29, pp. 90-95.
59. Pagano, N. J., and Soni, S. R., 1983, "Global-Local Laminate Variational Model," Int. J. Solids Struct., 3, pp. 207-228.
60. Soni, S. R., and Pagano, N. J., 1983, "Elastic Response of Composite Laminates," Mechanics of Composite Materials: Recent Advances, Hashin, Z., and Herakovich, C. T., eds., Pergamon, New York, pp. 227-242.
61. Pagano, N. J., and Soni, S. R., 1989, "Models for Studying Free-Edge Effects," Interlaminar Response of Composite Materials Composite Materials Series Vol. 5, Pagano, N. J., ed., Elsevier, Amsterdam, pp. 1-68.
62. Whitney, J. M., and Sun, C. T., 1973, "A Higher Order Theory for Extensional Motion of Laminated Composites," J. Sound Vib., 30, pp. 85-97.
63. Soni, S. R., 1982, "Stress and Strength Analysis of Composite Laminates at Delamination," Proceedings of the International Conference on Composite Materials, Tokyo, pp. 251-260.
64. Johnson, E. R., and Kemp, B. L., 1985, "Modeling the Stress Field in Laminated Composite Plates Near Discontinuities," Compos. Struct., 3, pp. 145-166.
65. Diaz Díaz, A., Caron, J. F., and Carreira, R. P., 2002, "Software Application for Evaluating Interfacial Stresses in Inelastic Symmetrical Laminates With Free Edges," Compos. Struct., 58, pp. 195-208.
66. Harrison, P. N., and Johnson, E. R., 1996, "A Mixed Variational Formulation for Interlaminar Stresses in Thickness-Tapered Composite Laminates," Int. J. Solids Struct., 33, pp. 2377-2399.
67. Pagano, N. J., Schoeppner, G. A., Kim, R., and Abrams, F. L., 1998, "Steady-State Cracking and Edge Effects in Thermo-Mechanical Transverse Cracking of Cross-Ply Laminates," Compos. Sci. Technol., 58, pp. 1811-1825.
68. Bar-Yoseph, P., and Pian, T. H. H., 1981, "Calculation of Interlaminar Stress Concentration in Composite Laminates," J. Compos. Mater., 15, pp. 225-239.
69. Bar-Yoseph, P., 1983, "On the Accuracy of Interlaminar Stress Calculation in Laminated Plates," Comput. Methods Appl. Mech. Eng., 36, pp. 309-329.
70. Kassapoglou, C., 1990, "Determination of Interlaminar Stresses in Composite Laminates Under Combined Loads," J. Reinf. Plast. Compos., 9, pp. 33-58.
71. Bhat, A. V., and Lagace, P. A., 1994, "An Analytical Method for the Evaluation of Interlaminar Stresses Due to Material Discontinuities," J. Compos. Mater., 28, pp. 190-210.
72. Yin, W. L., 1994, "Free-Edge Effects in Anisotropic Laminates Under Extension, Bending and Twisting, Part I: A Stress-Function-Based Variational Approach," ASME J. Appl. Mech., 61, pp. 410-415.
73. Yin, W L., 1994, "Free-Edge Effects in Anisotropic Laminates Under Extension, Bending and Twisting, Part II: Eigenfunction Analysis and the Results for Symmetric Laminates," ASME J. Appl. Mech., 61, pp. 416-421.
74. Yin, W. L., 1997, "The Effect of Temperature Gradient on the Free-Edge Interlaminar Stresses in Multi-Layered Structures," J. Compos. Mater., 31, pp. 2460-2477.
75. Yin, W. L., 1994, "Simple Solutions of the Free-Edge Stresses in Composite Laminates Under Thermal and Mechanical Loads," J. Compos. Mater., 28, pp. 573-586.
76. Kim, T., and Atluri, S. N., 1994, "Interlaminar Stresses in Composite Laminates Under Out-Of-Plane Shear/Bending," AIAA J., 32, pp. 1700-1708.
77. Kim, T., and Atluri, S. N., 1995, "Analysis of Edge Stresses in Composite Laminates Under Combined Thermo-Mechanical Loading, Using a Complementary Energy Approach," Comput. Mech., 16, pp. 83-97.
78. Zhang, C., and Yeh, H. Y., 1998, "A Variational Approach for Straight Edge Effect Stresses in Laminated Composites," Compos. Struct., 43, pp. 243-254.
79. Cho, M., and Kim, H. S., 1998, "Iterative Free Edge Stress Analysis of Composite Laminates Under Extension, Bending, Twisting and Thermal Loadings," Proceedings of the 39th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference, Long Beach, pp. 1545-1555.
80. Cho, M., and Kim, H. S., 2000, "Iterative Free-Edge Stress Analysis of Composite Laminates Under Extension, Bending, Twisting and Thermal Loadings," Int. J. Solids Struct., 37, pp. 435-459.
81. Kim, H. S., Cho, M., and Kim, G. I., 2000, "Free-Edge Strength Analysis in Composite Laminates by the Extended Kantorovich Method," Compos. Struct., 49, pp. 229-235.
82. Whitney, J. M., and Nuismer, R. J., 1974, "Stress Fracture Criteria for Laminated Composites Containing Stress Concentrations," J. Compos. Mater., 8, pp. 253-265.
83. Hein, V L., and Erdogan, F., 1971, "Stress Singularities in a Two-Material Wedge," Int. J. Fract. Mech., 7, pp. 317-330.
84. Bogy, D. B., 1972, "The Plane Solution for Anisotropic Elastic Wedges Under Normal and Shear Loading," ASME J. Appl. Mech., 39, pp. 1103-1109.
85. Kuo, M. C., and Bogy, D. B., 1974, "Plane Solutions for the Displacement and Traction-Displacement Problems for Anisotropic Elastic Wedges," ASME J. Appl. Mech., 41, pp. 197-202.
86. Wang, S. S., and Choi, I., 1980, "Boundary-Layer Hygroscopic Stresses in Angle-Ply Composite Laminates," Proceedings of the 21st AIAA/ASME/ASCE/AHS Structures, Structural Dynamics, and Materials Conference, Seattle, pp. 307-317.
87. Wang, S. S., and Choi, I., 1982, "Boundary-Layer Effects in Composite Laminates, Part 1 : Free-Edge Stress Singularities," ASME J. Appl. Mech., 49, pp. 541-548.
88. Wang, S. S., and Choi, I., 1982, "Boundary-Layer Effects in Composite Laminates, Part 2: Free-Edge Stress Solutions and Basic Characteristics," ASME J. Appl. Mech., 49, pp. 549-560.
89. Wang, S. S., and Choi, I., 1982, "Influence of Fiber Orientation and Ply Thickness on Hygroscopic Boundary-Layer Stresses in Angle-Ply Composite Laminates," J. Compos. Mater., 16, pp. 244-258.
90. Wang, S. S., 1981, "Edge Delaminations in Angle-Ply Composite Laminates," Proceedings of the 22nd AIAA/ASME/ASCE/AHS Structures, Structural Dynamics, and Materials Conference, Atlanta, pp. 473-484.
91. Wang, S. S., 1983, "Elasticity Solutions for a Class of Composite Laminate Problems With Stress Singularities," Mechanics of Composite Materials: Recent Advances, Hashin, Z., and Herakovich, C. T. eds., Pergamon, New York, pp. 259-281.
92. Stroh, A. N., 1962, "Steady State Problems in Anisotropic Elasticity," J. Math. Phys., 41, pp. 77-103.
93. Ting, T. C. T., and Chou, S. C., 1981, "Edge Singularities in Anisotropic Composites," Int. J. Solids Struct., 17, pp. 1057-1068.
94. Zwiers, R. I., Ting, T. C. T., and Spilker, R. L., 1982, "On the Logarithmic Singularity of Free-Edge Stress in Laminated Composites Under Uniform Extension," ASME J. Appl. Mech., 49, pp. 561-569.
95. Dempsey, J. P., and Sinclair, G. B., 1981, "On the Singular Behavior at the Vertex of a Bi-Material Wedge," J. Elast., 11, pp. 317-327.
96. Delale, F., 1984, "Stress Singularities in Bonded Anisotropic Materials," Int. J. Solids Struct., 20, pp. 31-40.
97. Stolarski, H. K., and Chiang, M. Y. M., 1989, "On the Significance of the Logarithmic Term in the Free Edge Stress Singularity of Composite Laminates," Int. J. Solids Struct., 25, pp. 75-93.
98. Yang, Y. Y., 1992, Spannungssingularitäten in Zweistoffverbunden bei Mechanischer und Thermischer Belastung, VDI, Düsseldorf.
99. Ding, S., and Kumosa, M., 1994, "Singular Stress Behaviour at an Adhesive Interface Corner," Eng. Fract. Mech., 47, pp. 503-519.
100. Williams, M. L., 1952, "Stress Singularities Resulting From Various Boundary Conditions in Angular Corners of Plates in Extension," ASME J. Appl. Mech., 19, pp. 526-528.
101. Kim, T. W., and Im, S., 1995, "Boundary Layers in Wedges of Laminated Composite Strips Under Generalized Plane Deformation-Part I: Asymptotic Solutions," Int. J. Solids Struct., 32, pp. 609-628.
102. Kim, T. W., and Im, S., 1995, "Boundary Layers in Wedges of Laminated Composite Strips Under Generalized Plane Deformation-Part II: Complete Numerical Solutions," Int. J. Solids Struct., 32, pp. 629-645.
103. Chaudhuri, R. A., and Xie, M., 2000, "A. Novel Eigenfunction Expansion Solution for Three-Dimensional Crack Problems," Compos. Sci. Technol., 60, pp. 2565-2580.
104. Chaudhuri, R. A., and Xie, M., 1998, "Free-Edge Stress Singularity in a Bimaterial Laminate," Compos. Struct., 40, pp. 129-136.
105. Xie, M., and Chaudhuri, R. A., 1998, "Three-Dimensional Stress Singularity at a Bimaterial Interface Crack Front," Compos. Struct., 40, pp. 137-147.
106. Xie, M., and Chaudhuri, R. A., 2001, "Three-Dimensional Asymptotic Stress Field at the Front of a Bimaterial Wedge of Symmetric Geometry Under Antiplane Shear Loading," Compos. Struct., 54, pp. 509-514.
107. Chiu, J. S. H., and Chaudhuri, R. A., 2002, "Three-Dimensional Asymptotic Stress Field at the Front of an Unsymmetric Bimaterial Pie-Shaped Wedge Under Antiplane Shear Loading," Compos. Struct., 58, pp. 129-137.
108. Müller, A., Hohe, J., and Becker, W., 2002, "A Closed-Form Analysis of Material and Geometry Effects on Stress Singularities at Unsymmetric Bimaterial Notches," Proceedings of the 73rd Annual Meeting of the GAMM - Gesellschaft für Angewandte Mathematik und Mechanik e. V., Augsburg, Germany, 210-211.
109. Müller, A., Hohe, J., and Becker, W., 2002, "Material-Und Geometrieabhängigkeit der Spannungssingularitäten an Bimaterialkerben," DVM-Bericht 234 Fortschritte der Bruch- und Schädigungsmechanik, Deutscher Verband Für Materialforschung und - Prüfung, e. V., Berlin, pp. 109-118.
110. Müller, A., Hohe, J., Goswami, S., and Becker, W., 2003, "Thermal Effects on Fracture Initiation at Bimaterial Notches," Proceedings of the TS2003-Fifth International Congress on Thermal Stresses and Related Topics, Blacksburg, pp. MA-7-4-1-MA-7-4-4.
111. Muskhelishwili, N. I., 1975, Some Basic Problems of the Mathematical Theory of Elasticity, Noordhoff, Leyden.
112. Barsoum, R. S., 1988, "Theoretical Basis of the Finite Element Iterative Method for the Eigenvalue Problem in Stationary Cracks," Int. J. Numer. Methods Eng., 26, pp. 531-539.
113. Barsoum, R. S., 1990, "Asymptotic Fields at Interfaces Using the Finite Element Iterative Method," Comput. Struct., 35, pp. 285-292.
114. Gu, L., and Belytschko, T., 1994, "A. Numerical Study of Stress Singularities in a Two-Material Wedge," Int. J. Solids Struct., 31, pp. 865-889.
115. Pageau, S. S., Joseph, P. F., and Biggers, S. B., 1995, "Finite Element Analysis of Anisotropic Materials with Singular Inplane Stress Fields," Int. J. Solids Struct., 32, pp. 571-591.
116. Pageau, S. S., and Biggers, S. B., 1996, "A. Finite Element Approach to Three-Dimensional Singular Stress States in Anisotropic Multi-Material Wedges and Junctions," Int. J. Solids Struct., 33, pp. 33-47.
117. Zhang, N., and Joseph, P. F., 1998, "A. Nonlinear Finite Element Eigenanalysis of Singular Plane Stress Fields in Bimaterial Wedges Including Complex Eigenvalues," Int. J. Fract., 90, pp. 175-207.
118. Zhang, N., and Joseph, P. F., 1998, "A. Nonlinear Finite Element Eigenanalysis of Singular Stress Fields in Bimaterial Wedges for Plane Strain," Int. J. Fract., 94, pp. 299-319.
119. Yosibash, Z., and Szabo, B., 1995, "Numerical Analysis of Singularities in Two-Dimensions Part 1 : Computation of Eigenpairs," Int. J. Numer. Methods Eng., 38, pp. 2055-2082.
120. Szabo, B., and Yosibash, Z., 1996, "Numerical Analysis of Singularities in Two-Dimensions Part 2: Computation of Generalized Flux/Stress Intensity Factors," Int. J. Numer. Methods Eng., 39, pp. 409-434.
121. Yosibash, Z., 1997, "Computing Edge Singularities in Elastic Anisotropic Three-Dimensional Domains," Int. J. Fract., 86, pp. 221-245.
122. Yosibash, Z., 1997, "Numerical Analysis of Edge Singularities in Three-Dimensional Elasticity," Int. J. Numer. Methods Eng., 40, pp. 4611-4632.
123. Yosibash, Z., 1997, "On Solutions of Two-Dimensional Linear Elastostatic and Heat-Transfer Problems in the Vicinity of Singular Points," Int. J. Solids Struct., 34, pp. 243-274.
124. Bazant, Z. P., and Estenssoro, L. F., 1979, "Surface Singularity and Crack Propagation," Int. J. Solids Struct., 15, pp. 405-426.
125. Yamada, Y., and Okumara, H., 1981, "Analysis of Local Stress in Composite Materials by the 3D Finite Element," Composite Materials: Proceedings of the Japan-U. S. Conference, Tokyo, pp. 55-64.
126. Yeh, J. R., and Tadjbakhsh, I. G., 1986, "Stress Singularity in Composite Laminates by Finite Element Method," J. Compos. Mater., 20, pp. 347-364.
127. Somaratna, N., and Ting, T. C. T., 1986, "Three-Dimensional Stress Singularities in Anisotropic Materials and Composites," Int. J. Eng. Sci., 24, pp. 1115-1134.
128. Wolf, J. P., and Song, C., 1996, Finite-Element Modelling of Unbounded Media, Wiley, Chichester.
129. Wolf, J. P., and Song, C., 1998, "The Scaled Boundary Finite-Element Method - A Fundamental-Solution-Less Boundary Element Method," Proceedings of the Fourth World Congress on Computational Mechanics, Buenos Aires, Argentina, pp. 1-20.
130. Song, C., and Wolf, J. P., 2002, "Semi-Analytical Representation of Stress Singularities as Occurring in Cracks in Anisotropic Multi-Materials With the Scaled Boundary Finite-Element Method," Comput. Struct., 80, pp. 183-197.
131. Raju, I. S., and Crews, J. H., 1981, "Interlaminar Stress Singularities at a Straight Free Edge in Composite Laminates," Comput. Struct., 14, pp. 21-28.
132. Anquez, L., 1986, "A. Numerical Analysis of Singular Stress Fields at the Free Edge of Layered Composites," Brittle Matrix Composite, Brandt, A. M., and Marshall, I. H., eds., Elsevier Applied Science, London, Vol. 1, pp. 287-303.
133. Dempsey, J. P., and Sinclair, G. B., (1979), "On the Stress Singularities in the Plane Elasticity of the Composite Wedge," J. Elast., 9, pp. 373-391.
134. Davet, J. L., and Destuynder, P., 1986, "Free-Edge Stress Concentration in Composite Laminates: A Boundary Layer Approach," Comput. Methods Appl. Mech. Eng., 59, pp. 129-140.
135. Rösel, R., 1987, "On the Wedge/Notch Eigenvalues," Int. J. Fract., 33, pp. 61-71.
136. Bar-Yoseph, P., and Avrashi, J., 1988, "On the Nature of the Free Edge Stress Singularity in Composite Laminated Plates," Int. J. Numer. Methods Eng., 26, pp. 1507-1523.
137. Reedy, E. D., 1989, "On Free-Edge Interlaminar Stress Distributions," Compos. Sci. Technol., 34, pp. 259-266.
138. Christensen, R. M., and DeTeresa, S. J., 1992, "Elimination/ Minimization of Edge-Induced Stress Singularities in Fiber Composite Laminates," Int. J. Solids Struct., 29, pp. 1221-1231.
139. Akisanya, A. R., and Fleck, N. A., 1997, "Interfacial Cracking From the Free-Edge of a Long Bi-Material Strip," Int. J. Solids Struct., 34, pp. 1645-1665.
140. Tan, M. A., and Meguid, S. A., 1997, "Analysis of Bimaterial Wedges Using a New Singular Finite Element," Int. J. Fract., 88, pp. 373-391.
141. Berger, J. R., Martin, P. A., and Lien, J. P., 1998, "Reduction of Free-Edge Stress Intensities in Anisotropic Bimaterials," Int. J. Fract., 91, pp. 165-177.
142. Chimani, C. M., Böhm, H. J., and Rammerstorfer, F. G., 1998, "On Interface Edge Singularities in Layered Composites," ZAMM, 78, pp. 49-52.
143. Rahman, A., and Lau, A. C. W., 1998, "Singular Stress Fields in Interfacial Notches of Hybrid Metal Matrix Composites," Composites, Part B, 29B, pp. 763-768.
144. Joseph, P. F., and Zhang, N., 1998, "Multiple Root Solutions, Wedge Paradoxes and Singular Stress States That are not Variable-Separable," Compos. Sci. Technol., 58, pp. 1839-1859.
145. Lee, S. S., 1998, "Boundary Element Analysis of the Stress Singularity at the Interface Corner of Viscoelastic Adhesive Layers," Int. J. Solids Struct., 35, pp. 1385-1394.
146. Yang, Y. Y., 1998, "Asymptotic Description of the Logarithmic Singular Stress Field and Its Application," Int. J. Solids Struct., 35, pp. 3917-3933.
147. Chaudhuri, R. A., and Xie, M., 2000, "A. Tale of Two Saints: St. Venant and 'St. Nick'-Does St. Venants Principle Apply to Bi-Material Straight-Edge and Wedge-Singularity Problems?," Compos. Sci. Technol., 60, pp. 2503-2515.
148. Glushkov, E. V., Glushkova, N. V., Munz, D., and Yang, Y. Y., 2000, "Analytical Solution for Bonded Wedges Under Thermal Stresses," Int. J. Fract., 106, pp. 321-339.
149. Chue, C. H., Tseng, C. H., and Liu, C. I., 2001, "On Stress Singularities in an Anisotropic Wedge for Various Boundary Conditions," Compos. Struct., 54, pp. 87-102.
150. Chue, C. H., Chen, T. H., and Lee, H. T., 2002, "A. General Solution on Stress Singularities in the Junction of Two Anisotropic Materials," Compos. Struct., 55, pp. 81-93.
151. Chue, C. H., and Liu, C. I., 2002, "Disappearance of Free-Edge Stress Singularity in Composite Laminates," Compos. Struct., 56, pp. 111-129.
152. Chue, C. H., and Liu, C. I., 2002, "Stress Singularities in a Bimaterial Anisotropic Wedge With Arbitrary Fiber Orientation," Compos. Struct., 58, pp. 49-56.
153. Chue, C. H., and Weng, S. M., 2002, "Stress Singularities in Anisotropic Three-Material Wedges and Junctions With Applications," Compos. Struct., 58, pp. 443-456.
154. Pipes, R. B., 1972, Solution of Certain Problems in the Theory of Elasticity for Laminated Anisotropic Systems, University of Texas, Arlington.
155. Pipes, R. B., 1980, "Boundary Layer Effects in Composite Laminates," Fibre Sci. Technol., 13, pp. 49-71.
156. Altus, E., Rotem, A., and Shmueli, M., 1980, "Free Edge Effect in Angle Ply Laminates: A New Three Dimensional Finite Difference Solution," J. Compos. Mater., 14, pp. 21-30.
157. Hong, C. S., and Kim, K. S., 1982, "An Analysis of Free-Edge Delamination in Laminated Composite Under Uniform Axial Strain," Progress in Science and Engineering of Composites, Proceedings of the International Conference on Composite Materials, Tokyo, pp. 261-268.
158. Bauld, N. R., Goree, J. G., and Tzeng, L. S., 1985, "A. Comparison of Finite-Difference and Finite-Element Methods for Calculating Free Edge Stresses in Composites," Comput. Struct., 20, pp. 897-914.
159. Isakson, G., and Levy, A., 1971, "Finite-Element Analysis of Interlaminar Shear in Fibrous Composites," J. Compos. Mater., 5, pp. 273-276.
160. Wang, A. S. D., and Crossman, F. W., 1976, "Calculation of Edge Stresses in Multi-Layer Laminates by Sub-Structuring," J. Compos. Mater., 12, pp. 76-83.
161. Wang, A. S. D., and Crossman, F. W., 1977, "Some New Results on Edge Effect in Symmetric Composite Laminates," J. Compos. Mater., 11, pp. 92-106.
162. Wang, A. S. D., and Crossman, F. W., 1977, "Edge Effects on Thermally Induced Stresses in Composite Laminates," J. Compos. Mater., 11, pp. 300-312.
163. Crossman, F. W., and Wang, A. S. D., 1978, "Stress Field Induced by Transient Moisture Sorption in Finite-Width Composite Laminates," J. Compos. Mater., 12, pp. 2-18.
164. Whitcomb, J. D., Raju, I. S., and Goree, J. G., 1982, "Reliability of the Finite Element Method for Calculating Free Edge Stresses in Composite Laminates," Comput. Struct., 15, pp. 23-37.
165. Rohwer, K., 1982, "On the Determination of Edge Stresses in Layered Composites," Nucl. Eng. Des., 70, pp. 57-65.
166. Rohwer, K., 1982, Stresses and Deformations in Laminated Test Specimens of Carbon Fiber Reinforced Composites, DFVLR, Institut für Strukturmechanik, Braunschweig.
167. Rohwer, K., 1985, "Einsatz Von Finiten Elementen zur Berechnung von Faserverbundstrukturen," Leichtbau mit Kohlenstofffaserverstärkten Kunststoffen, G. Niederstadt, J. Block, B. Geier, K. Rohwer, and R. Weiß, eds., Expert, Sindelfingen, 160-210.
168. Whitcomb, J. D., and Raju, I. S., (1983), "Superposition Method for Analysis of Free-Edge Stresses," J. Compos. Mater., 17, pp. 492-507.
169. Wu, C. M. L., 1987, "Nonlinear Analysis of Edge Effects in Angle-Ply Laminates," Comput. Struct., 25, pp. 787-798.
170. Wu, C. M. L., 1990, "Nonlinear Thermal and Mechanical Analysis of Edge Effects in Angle-Ply Laminates," Comput. Struct., 35, pp. 705-717.
171. Wu, C. M. L., 1992, "Elasto-Plastic Analysis of Edge Effects in Metal Matrix Angle-Ply Laminates," Comput. Struct., 45, pp. 273-280.
172. Ye, L., 1990, "Some Characteristics of Distributions of Free-Edge Interlaminar Stresses in Composite Laminates," Int. J. Solids Struct., 26, pp. 331-351.
173. Frick, A., and Klamser, H., 1990, Untersuchung der Verschlebungs- und Spannungsverteilungen an Unbelasteten Rändern Multidirektionaler Laminate, VDI, Düsseldorf.
174. Hwang, S. J., and Gibson, R. F., 1991, "The Effects of Three-Dimensional States of Stress on Damping of Laminated Composites," Compos. Sci. Technol., 41, pp. 379-393.
175. Yi, S., 1993, "Thermoviscoelastic Analysis of Delamination Onset and Free Edge Response in Laminated Composites," AIAA J., 31, pp. 2320-2328.
176. Lessard, L. B., Schmidt, A. S., and Shokrieh, M. M., 1996, "Three-Dimensional Stress Analysis of Free-Edge Effects in a Simple Composite Cross-Ply Plate," Int. J. Solids Struct., 33, pp. 2243-2259.
177. Lindemann, J., and Becker, W., 2000, Optimierung von Verbundwerkstoffen unter Berücksichtigung des Laminatrandeffekts, Universität Siegen, Siegen.
178. Lindemann, J., and Becker, W., 2001, "Optimization of Composite Laminates Under Uniaxial Tension With Respect to the Free-Edge Effect," ZAMM, 81, pp. S683-S684.
179. Lindemann, J., and Becker, W., 2002, "The Tendency for Free-Edge Delamination in Laminates and Its Minimization," Compos. Sci. Technol., 62, pp. 233-242.
180. Weikl, S., 2002, Quantitative Delaminationsbestimmang an Geschichteten Verbundwerkstoffen, Karlsruhe University, Institute of Solid Mechanics, Karlsruhe.
181. Artel, J., and Becker, W., 2005, "Coupled and Uncoupled Analysis of Piezoelectric Free-Edge Effect in Laminated Plates," Compos. Struct., 69(3), pp. 329-335.
182. Hirai, T., Semba, T., and Tarui, M., 1982, "Three-Dimensional Interlaminar Stress Distribution in Symmetric Composite Laminate," Progress in Science and Engineering of Composites, Proceedings of the International Conference on Composite Materials, Tokyo, pp. 243-250.
183. Whitcomb, J. D., and Raju, I. S., 1985, "Analysis of Interlaminar Stresses in Thick Composite Laminates With and Without Edge Delamination," Delamination and Debonding of Materials, ASTM STP 876, Johnson, W. S., ed., American Society for Testing and Materials, Philadelphia, 69-94.
184. Sun, C. T., and Liao, W. C., (1990), "Analysis of Thick Section Composite Laminates Using Effective Moduli," J. Compos. Mater., 24, pp. 977-993.
185. Joo, J. W., and Sun, C. T., 1992, "A. Failure Criterion for Laminates Governed by Free Edge Interlaminar Shear Stress," J. Compos. Mater., 26, pp. 1510-1522.
186. Kress, G. R., 1993, Analytische und Experimentelle Untersuchung zu Versagensvorgängen in Faserverbundwerkstoffen mit Besonderer Berücksichtigung der Randeffekte, VDI, Düsseldorf.
187. Yang, H. T. Y., and He, C. C., 1994, "Three-Dimensional Finite Element Analysis of Free Edge Stresses and Delamination of Composite Laminates," J. Compos. Mater., 28, pp. 1394-1412.
188. Schipperen, J. H. A., and Lingen, F. J., 1999, "Validation of Two-Dimensional Calculations of Free Edge Delamination in Laminated Composites," Compos. Struct., 45, pp. 233-240.
189. Tong, P., and Pian, T. H. H., 1973, "On the Convergence of the Finite Element Method for Problems Wim Singularity," Int. J. Solids Struct., 9, pp. 313-321.
190. Rybicki, E. F., 1971, "Approximate Three-Dimensional Solutions for Symmetric Laminates Under Inplane Loading," J. Compos. Mater., 5, pp. 354-360.
191. Spilker, R. L., 1980, "A Traction-Free-Edge Hybrid-Stress Element for the Analysis of Edge Effects in Cross-Ply Laminates," Comput. Struct., 12, pp. 167-179.
192. Spilker, R. L., and Chou, S. C., 1980, "Edge Effects in Symmetric Composite Laminates: Importance of Satisfying the Traction Free Edge Condition," J. Compos. Mater., 14, pp. 2-20.
193. Wang, S. S., and Yuan, F. G., 1983, "A Singular Hybrid Finite Element Analysis of Boundary-Layer Stresses in Composite Laminates," Int. J. Solids Struct., 19, pp. 825-837.
194. Wang, S. S., and Yuan, F. G., 1983, "A Hybrid Finite Element Approach to Composite Laminate Elasticity Problems With Singularities," ASME J. Appl. Mech., 50, pp. 835-844.
195. Bar-Yoseph, P., and Avrashi, J., 1986, "New Variational-Asymptotic Formulations for Interlaminar Stress Analysis in Laminated Plates," ZAMP, 37, pp. 305-321.
196. Bar-Yoseph, P., and Ben-David, D., 1995, "Free-Edge Effects in Unsymmetrically Laminated Composite Plates," Compos. Struct., 30, pp. 13-23.
197. Chang, C. C., Sandhu, R. S., Sierakowski, R. L., and Wolfe, W. E., 1988,
198. Wörtler, M., 1989, Interlaminare Spannungskonzentrationen in Faserverbundwerkstoffen, VDI, Düsseldorf.
199. Gruttmann, F., and Wagner, W., 1994, "On the Numerical Analysis of Local Effects in Composite Structures," Compos. Struct., 29, pp. 1-12.
200. Icardi, U., and Bertetto, A. M., 1995, "An Evaluation of the Influence of Geometry and of Material Properties at Free Edges and at Corners of Composite Laminates," Comput. Struct., 57, pp. 555-571.
201. Robbins, D. H., and Reddy, J. N., 1996, "Variable Kinematic Modelling of Laminated Composite Plates," Int. J. Numer. Methods Eng., 39, pp. 2283-2317.
202. Gaudenzi, P., Mannini, A., and Carbonaro, R., 1998, "Multi-Layer Higher-Order Finite Elements for the Analysis of Free-Edge Stresses in Composite Laminates," Int. J. Numer. Methods Eng., 41, pp. 851-873.
203. Yi, S., Ahmad, M. F., and Hilton, H. H., 1998, "Nonlinear Viscoelastic Stress Singularities Near Free Edges of Unsymmetrically Laminated Composites," Int. J. Solids Struct., 35, pp. 3221-3237.
204. Phillips, E. A., Herakovich, C. T., and Graham, L. L., 2001, "Damage Development in Composites With Large Stress Gradients," Compos. Sci. Technol., 61, pp. 2169-2182.
205. Mannini, A., and Gaudenzi, P., 2003, "Multi-Layer Higher-Order Finite Elements for the Analysis of Free-Edge Stresses in Piezoelectric Actuated Laminates," Compos. Struct., 61, pp. 271-278.
206. Wolf, J. P., and Song, C., 2000, "The Scaled Boundary Finite-Element Method-A Primer: Derivations," Comput. Struct., 78, pp. 191-210.
207. Song, C., and Wolf, J. P., 2000, "The Scaled Boundary Finite-Element Method-A Primer: Solution Procedures," Comput. Struct., 78, pp. 211-225.
208. Wolf, J. P., 2003, The Scaled Boundary Finite Element Method, Wiley, Chichester.
209. Lindemann, J., and Becker, W., 2000, "Analysis of the Free-Edge Effect in Composite Laminates by the Boundary Finite Element Method," Mech. Compos. Mater., 36, pp. 355-366.
210. Lindemann, J., and Becker, W., 2001, "The Boundary Finite Element Method for Stress Concentration Problems in Composite Laminates," Proceedings of the 72nd Annual Meeting of the GAMM-Gesellschaft für Angewandte Mathematik und Mechanik e. V, Zürich, pp. 1-2.
211. Lindemann, J., and Becker. W., 2001, "Investigation of Stress-Concentration Problems in Composite Laminates by the Boundary Finite Element Method," Proceedings of the Third International Conference Tools for Mathematical Modelling Saint-Petersburg, pp. 49-58.
212. Lindemann, J., and Becker, W., 2002, "Free-Edge Stresses Around Holes in Laminates by the Boundary Finite-Element Method," Mech. Compos. Mater., 38, pp. 407-416.
213. Müller, A., Wenck, J., Goswami, S., Lindemann, J., Hohe, J., and Becker, W., 2005, "The Boundary Finite Element Method for Predicting Directions of Cracks Emerging From Notches at Bimaterial Junctions," Eng. Fract. Mech., 72(3), pp. 373-386.
214. Öry, H., Reimerdes, H. G., and Dieker, S., 1984, "Berechnung von Interlaminaren Spannungen in Mehrschichtigen Faserverbundwerkstoffen mit Hilfe von Übertragungsmatrizen," Z. Flugwiss. Weltraumforsch., 8, pp. 392-404.
215. Davi, G., 1996, "Stress Fields in General Composite Laminates," AIAA J., 34, pp. 2604-2608.
216. Vanderplaats, G. N., 1984, Numerical Optimization Techniques for Engineering Design, 3rd ed., McGraw-Hill, New York.
217. Kim, D. M., and Hong, C. S., 1992, "A Simple Sublaminate Approach to the Design of Thick Composite Laminates for Suppression of Free-Edge Delamination," Compos. Sci. Technol., 43, pp. 147-158.
218. Kim, T., and Atluri, S. N., 1995, "Optimal Through-Thickness Temperature Gradients for Control of Interlaminar Stresses in Composites," AIAA J., 33, pp. 730-738.
219. Cho, M., and Rhee, S. Y., 2003, "Layup Optimization Considering Free-Edge Strength and Bounded Uncertainty of Material Properties," AIAA J., 41, pp. 2274-2282.
220. Whitney, J. M., and Browning, C. E., 1972, "Free-Edge Delamination of Tensile Coupons," J. Compos. Mater., 6, pp. 300-303.
221. Pipes, R. B., Kaminski, B. E., and Pagano, N. J., 1973, "Influence of the Free Edge Upon the Strength of Angle-Ply Laminates," Analysis of the Test Methods for High Modulus Fibers and Composites, ASTM STP 521, American Society for Testing and Materials, Philadelphia, pp. 218-228.
222. Herakovich, C. T., 1989, "Failure Modes and Damage Accumulation in Laminated Composites With Free Edges," Compos. Sci. Technol., 36, pp. 105-119.
223. Wang, A. S. D., 1989, "Fracture Analysis of Interlaminar Cracking," Interlaminar Response of Composite Materials, Composite Materials Series Vol. 5, Pagano, N., J., ed., Elsevier, Amsterdam, pp. 69-109.
224. Kim, R. Y., 1989, "Experimental Observations of Free-Edge Delamination," Interlaminar Response of Composite Materials, Composite Materials Series Vol. 5 Pagano, N. J., ed., Elsevier, Amsterdam pp. 111-160.
225. Whitney, J. M., 1989, "Experimental Characterization of Delamination Fracture," Interlaminar Response of Composite Materials, Composite Materials Series Vol. 5, Pagano, N. J., ed., Elsevier, Amsterdam pp. 161-250.
226. Lee, S. M., 1990, "Failure Mechanisms of Edge Delamination of Composites," J. Compos. Mater., 24, pp. 1200-1212.
227. Sun, C. T., and Chu, G. D., 1991, "Reducing Free Edge Effect on Laminate Strength by Edge Modification," J. Compos. Mater., 25, pp. 142-161.
228. Lee, S., Pan, H. M., and Wolfenstine, J., 1992, "Thermal Effective Stress Concentration Problems in Metal Composites," Compos. Sci. Technol., 44, pp. 71-76.
229. Leguillon, D., 1999, "A Method Based on Singularity Theory to Predict Edge Delamination of Laminates," Int. J. Fract., 100, pp. 105-120.
230. Leguillon, D., Marion, G., Harry, R., and Lecuyer, F., 2001, "The Onset of Delamination at Stress-Free Edges in Angle-Ply Laminates-Analysis of Two Criteria," Compos. Sci. Technol., 61, pp. 377-382.
231. Whitney, J. M., 1986, "Stress Analysis of a Mode I Edge Delamination Specimen for Composite Materials," AIAA J., 24, pp. 1163-1168.
232. Armanios, E. A., Badir, A., and Sriram, P., 1989, "Sublaminate Analysis of Mode I Edge Delamination in Laminated Composites," 30th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference: A Collection of Technical Papers, Pt. 4, pp. 2109-2116.
233. Armanios, E. A., and Badir, A. M., 1990, "Hygrothermal Influence on Mode I Edge Delamination in Composites," Compos. Struct., 15, pp. 323-342.
234. Harikumar, H. K., and Krishna Murty, A. V., 1991, "On Modelling of Laminates Containing Free-Edge Delaminations," Compos. Sci. Technol., 42, pp. 393-411.
235. Daniewicz, D., and Frantziskonis, G., 1992, "Edge Delamination in Laminated Composites," Compos. Struct., 21, pp. 141-153.
236. Davidson, B. D., 1994, "Energy Release Rate Determination for Edge Delamination Under Combined In-Plane, Bending and Hygrothermal Loading. Part I-Delamination at a Single Interface," J. Compos. Mater., 28, pp. 1009-1031.
237. Miravete, A., and Jimenez, M. A., 2002, "Application of the Finite Element Method to Prediction of Onset of Delamination Growth," Appl. Mech. Rev., 55, pp. 89-106.
238. Tay, T., 2003, "Characterization and Analysis of Delamination Fracture in Composites: An Overview of Developments From 1990 to 2001," Appl. Mech. Rev., 56, pp. 1-32.
239. Berthelot, J. M., 2003, "Transverse Cracking and Delamination in Cross-Ply Glass-Fiber and Carbon-Fiber Reinforced Plastic Laminates: Static and Fatigue Loading," Appl. Mech. Rev., 56, pp. 111-147.
240. Savin, G. N., 1961, Stress Concentrations Around Holes, Pergamon, New York.
241. Barker, R. M., Dana, J. R., and Pryor, C. W., 1974, "Stress Concentrations Near Holes in Laminates," J. Engrg. Mech. Div., 100, pp. 477-488.
242. Rybicki, E. F., and Schmueser, D. W., 1978, "The Comparison of LPT and Three-Dimensional Stress Distributions for a Laminated Plate Containing a Hole," Proceedings of the Second International Conference on Composite Materials, Toronto, pp. 376-384.
243. Rybicki, E. F., and Schmueser, D. W., 1978, "Effect of Stacking Sequence and Lay-Up Angle on Free Edge Stresses Around a Hole in a Laminated Plate Under Tension," J. Compos. Mater., 12, pp. 300-313.
244. Nishioka, T., and Atluri, S. N., 1982, "Stress Analysis of Holes in Angle-Ply Laminates: An Efficient Assumed Stress 'Special-Hole-Element' Approach and a Simple Estimation Method," Comput. Struct., 15, pp. 135-147.
245. Lee, J. D., 1982, "Three Dimensional Finite Element Analysis of Damage Accumulation in Composite Laminate," Comput. Struct., 15, pp. 335-350.
246. Carlsson, L., 1983, "Interlaminar Stresses at a Hole in a Composite Member Subjected to In-Plane Loading," J. Compos. Mater., 17, pp. 238-249.
247. s Composite Laminates With Circular Holes," J. Compos. Mater., 17, pp. 188-198.
248. s Laminate With a Circular Hole," J. Compos. Mater., 18, pp. 495-506.
249. Reimerdes, H. G., 1984, Zur Berechnung Interlaminarer Spannungen am Rand Kreisrunder Löcher in Mehrschichtigen Laminaten, Aachen University, Aachen.
250. Bar-Yoseph, P., and Avrashi, J., 1985, "Interlaminar Stress Analysis for Laminated Plates Containing a Curvilinear Hole," Comput. Struct., 21, pp. 917-932.
251. Hwang, W. C., and Sun, C. T., 1988, "Analysis of Interlaminar Stresses Near Curved Free-Edges of Laminated Composites Using Iterative Finite Element Method," Comput. Struct., 28, pp. 461-467.
252. Gaudenzi, P., Barboni, R., and Mannini, A., 1995, "A Finite Element Evaluation of Single-Layer and Multi-Layer Theories for the Analysis of Laminated Plates," Compos. Struct., 30, pp. 427-440.
253. Barboni, R., Carbonaro, R., and Gaudenzi, P., 1995, "On the Use of a Multilayer Higher-Order Theory for the Stress Analysis Around a Circular Hole of Laminates Under Tension," Compos. Struct., 32, pp. 649-658.
254. Hu, F. Z., Soutis, C., and Edge, E. C., 1997, "Interlaminar Stresses in Composite Laminates With a Circular Hole," Compos. Struct., 37, pp. 223-232.
255. Yang, B., 2002, "Examination of Free-Edge Crack Nucleation Around an Open Hole in Composite Laminates," Int. J. Fract., 115, pp. 173-191.
256. Tang, S., 1977, "Interlaminar Stresses Around Circular Cutouts in Composite Plates Under Tension," AIAA J., 15, pp. 1631-1637.
257. Delale, F., 1984, "Stress Analysis of Multilayered Plates Around Circular Holes," Int. J. Eng. Sci., 22, pp. 57-75.
258. Shalev, D., and Reifsnider, K. L., 1989, "Influence of Relative Ply Orientations on the Nature of the Edge Effect Singularities for a Circular Hole in a Composite Laminate," Int. J. Solids Struct., 25, pp. 1115-1132.
259. Ko, C. C., and Lin, C. C., 1992, "Method for Calculating the Interlaminar Stresses in Symmetric Laminates Containing a Circular Hole," AIAA J., 30, pp. 197-204.
260. larve, E. V., 1996, "Spline Variational Three Dimensional Stress Analysis of Laminated Composite Plates With Open Holes," Int. J. Solids Struct., 33, pp. 2095-2118.
261. Herrmann, K. P., and Linnenbrock, K., 2002, "Three-dimensional Thermal Crack Growth in Self-stressed Bimaterial Joints: Analysis and Experiment," Int. J. Fract., 114, pp. 133-151.
262. Becker, W., Jin, P. P., and Neuser, P., 1999, "Interlaminar Stresses at the Free Corners of a Laminate," Compos. Struct., 45, pp. 155-162.
263. Becker, W., Jin, P. P., and Lindemann, J., 2000, "Thermally Induced Interlaminar Stress Concentrations at Laminate Corners," ZAMM, 80, pp. S375-S376.
264. Becker, W., Jin, P. P., and Lindemann, J., 2001, "The 'Free-Corner Effect' in Thermally Loaded Laminates," Compos. Struct., 52, pp. 97-102.
265. Mittelstedt, C., and Becker, W., 2003, "Three-Dimensional Closed-Form Analysis of die Stress Field at Rectangular Corners of Layered Plates," Arch. Appl. Mech., 73, pp. 63-74.
266. Mittelstedt, C., and Becker, W., 2004, "Interlaminar Stress Concentrations in Layered Structures-Part II: Closed-Form Analysis of Stresses at Laminated Rectangular Wedges With Arbitrary Non-Orthotropic Layup," J. Compos. Mater., 38, pp. 1063-1090.
267. Mittelstedt, C., and Becker, W., 2003, "Free-Corner Effects in Cross-Ply Laminates: An Approximate Higher-Order Theory Solution," J. Compos. Mater., 37, pp. 2043-2068.
268. Mittelstedt, C., and Becker, W., 2004, "A Variational Finite Layer Technique for the Analytical Investigation of Free-Corner Effects in Composite Structures," J. Therm. Stresses, 27, pp. 953-981.
269. Mittelstedt, C., and Becker, W., 2004, "Thermoelastic Fields in Boundary Layers of Isotropic Laminates," J. Appl. Mech., 72, pp. 86-101.
270. Reddy, J. N., 1987, "A Generalization of Two-Dimensional Theories of Laminated Composite Plates," Commun. Appl. Numer. Methods, 3, pp. 173-180.
271. Griffin, O. H., 1988, "Three-Dimensional Thermal Stresses in Angle-Ply Composite Laminates," J. Compos. Mater., 22, pp. 53-70.
272. Koguchi, H., 1997, "Stress Singularity Analysis in Three-Dimensional Bonded Structure," Int. J. Solids Struct., 34, pp. 461-480.
273. Labossiere, P. E. W., and Dunn, M. L., 2001, "Fracture Initiation at ThreeDimensional Bimaterial Interface Corners," J. Mech. Phys. Solids, 49, pp. 609-634.
274. Nied, H. F., and Ayhan, A. O., 2001, "Analysis of Three-Dimensional Interface Cracking in Electronic Packages," Proceedings Advances in Fracture Research/ICF 10, K. K. Ravi-Chander, B. L. Kariloo, T. Kishi, R. O. Ritchie, A. T. Yokobori, Jr., and T. Yokobori, eds., Elsevier Science, CD ROM, Paper No. ICF100832OR.
275. Dimitrov, A., Andrae, H., and Schnack, E., 2001, "Efficient Computation of Order and Mode of Corner Singularities in 3D-Elasticity," Int. J. Numer. Methods Eng., 51, pp. 1-24.
276. Dimitrov, A., Andrae, H., and Schnack, E., 2002, "Singularities Near ThreeDimensional Corners in Composite Laminates," Int. J. Fract., 115, pp. 361-375.
277. Dimitrov, A., and Schnack, E., 2002, "Asymptotical Expansion In Non-Lipschitzian Domains-A Numerical Approach," Numer. Linear Algebra Appl., 9, 467-492.
278. Dimitrov, A., Buchholz, F. C., and Schnack, E., 2002, Free-Surface Effects in Crack Propagation: A Theoretical-Numerical-Experimental Correlation, Karlsruhe University, Institute of Solid Mechanics, Karlsruhe.
279. Dimitrov, A., Buchholz, F. C., and Schnack, E., 2002, "3D-Corner Effects in Crack Propagation," Proceedings of the WCCMV-Fifth World Congress on Computational Mechanics, H. A. Mang, F. G. Rammerstorfer, and J. Eberhardsteiner, eds., Vienna, pp. 1-10.
280. Dimitrov, A., 2002, Eckensingularitäten bei Räumlichen Problemen der Elastizitätstheorie: Numerische Berechnung und Anwendungen, Karlsruhe University, Institute of Solid Mechanics, Karlsruhe.
281. Mittelstedt, C., Lindemann, J., and Becker, W., 2004, "A Boundary Finite Element Method Formulation for Stress Concentration Problems in Composite Laminates," Proceedings of the WCCM VI-Sixth World Congress on Computational Mechanics, Beijing.
282. Mittelstedt, C., and Becker, W., 2004, "Semi-Analytical Computation of 3D Stress Singularities in Linear Elasticity," Commun. Numer. Methods Eng., 21, pp. 247-257.
283. Mittelstedt, C., and Becker, W., 2004, "Asymptotic Analysis of Stress Singularities in Composite Laminates by the Boundary Finite Element Method," Int. J. Solids Struct., 43, pp. 2868-2903.
284. Salamon, N. J., 1980, "An Assessment of the Interlaminar Stress Problem in Laminated Composites," J. Compos. Mater., 14, pp. 177-194.
285. Reddy, J. N., 1985, "Finite-Element Modeling of Layered, Anisotropic Composite Plates and Shells: A Review of Recent Research," Shock Vib. Dig., 17, pp. 3-12.
286. Pagano, N. J., 1989, Interlaminar Response of Composite Materials, Composite Materials Series Vol. 5, Elsevier, Amsterdam.
287. Reddy, J. N., and Robbins, D. H., 1994, "Theories and Computational Models for Composite Laminates," Appl. Mech. Rev., 47, pp. 147-169.
288. Rohwer, K., 1996, Modelle und Methoden zur Berechnung von Laminaten aus Unidirektionalen Faserverbunden, VDI, Düsseldorf.
289. Kant, T., and Swaminathan, K., 2000, "Estimation of Transverse/Interlaminar Stresses in Laminated Composites: A Selective Review and Survey of Current Developments," Compos. Struct., 49, pp. 65-75.
290. Yang, Y. Y., 2003, Solutions of Dissimilar Material Singularity and Contact Problems, Forschungszentrum Karlsruhe, Karlsruhe.
291. Altenbach, H., and Becker, W., 2003, Modern Trends in Composite Laminates Mechanics, Springer, Wien.
292. Mittelstedt, C., and Becker, W., 2004, "Interlaminar Stress Concentrations in Layered Structures-Part, 1: A Selective Literature Survey on the Free-Edge Effect Since 1967," J. Compos. Mater., 38, pp. 1037-1062.