Advertisement

Spatial problems of the theory of cracks (review)

1. Fundamental mechanical concepts and mathematical methods in spatial problems of the theory of cracks
  • V. V. Panasyuk
  • A. E. Andreikiv
  • M. M. Stadnik
Article

Keywords

Spatial Problem 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Literature cited

  1. 1.
    A. A. Griffith, “The phenomenon of rupture and flow in solids,” Phil. Trans. Roy. Soc., Ser. A,221, 163–198 (1920).Google Scholar
  2. 2.
    G. R. Irwin, “Analysis of stresses and strain near the end of a crack transversing a plate,” J. Appl. Mech.,24, No. 3, 361–364 (1957).Google Scholar
  3. 3.
    V. V. Panasyuk, Limit Equilibrium of Brittle Bodies with Cracks [in Russian], Naukova Dumka, Kiev (1968).Google Scholar
  4. 4.
    V. V. Panasyuk, A. E. Andreikiv, and S. E. Kovchik, Methods of Evaluating the Crack Resistance of Structural Materials [in Russian], Naukova Dumka, Kiev (1977).Google Scholar
  5. 5.
    G. P. Cherepanov, The Mechanics of Brittle Fracture [in Russian], Nauka, Moscow (1974).Google Scholar
  6. 6.
    G. P. Cherepanov and L. V. Ershov, Fracture Mechanics [in Russian], Mashinostroenie, Moscow (1977).Google Scholar
  7. 7.
    V. Z. Parton and E. M. Morozov, The Mechanics of Elastoplastic Fracture [in Russian], Nauka, Moscow (1974).Google Scholar
  8. 8.
    J. E. Srawley and W. F. Brown, Plane Strain Crack Toughness Testing of High-Strength Metallic Materials, ASTM, Philadelphia (1966).Google Scholar
  9. 9.
    G. S. Vasil'chenko and P. F. Koshelev, Practical Application of Fracture Mechanics in Stress Analysis of Structures [in Russian], Nauka, Moscow (1974).Google Scholar
  10. 10.
    L. M. Kachanov, Fundamentals of Fracture Mechanics [in Russian], Nauka, Moscow (1974).Google Scholar
  11. 11.
    T. Ekobori, The Physics and Mechanics of Fracture and Strength of Solids [in Russian], Metallurgiya, Moscow (1971).Google Scholar
  12. 12.
    F. A. McClintock and A. S. Argon, Mechanical Behavior of Materials, Addison-Wesley (1966).Google Scholar
  13. 13.
    L. I. Sedov, Mechanics of the Continuum: in Two Volumes [in Russian], Vol. 2, Nauka, Moscow (1970).Google Scholar
  14. 14.
    S. V. Serensen, Resistance of Materials to Fatigue and Brittle Fracture [in Russian], Atomizdat, Moscow (1975).Google Scholar
  15. 15.
    V. M. Finkel', The Physics of Fracture [in Russian], Metallurgiya, Moscow (1970).Google Scholar
  16. 16.
    N. A. Makhutov, Resistance of Structural Elements to Brittle Fracture [in Russian], Mashinostroenie, Moscow (1973).Google Scholar
  17. 17.
    E. M. Morozov, Introduction to the Mechanics of Crack Propagation [in Russian], Mosk. Inzh.-Fiz. Inst., Moscow (1977).Google Scholar
  18. 18.
    Liebowitz (editor), Fracture. An Advanced Treatise, Vols. 1–7, Academic Press, New York-London (1968–1972).Google Scholar
  19. 19.
    S. Ya. Yarema, “Determination of the state of stress of a disk weakened by a system of cracks,” Fiz.-Khim. Mekh. Mater.,9, No. 4, 75–81 (1973).Google Scholar
  20. 20.
    P. M. Vitvitski, V. V. Panasyuk, and S. Ya. Yarema, “Plastic deformation around crack and fracture criteria,” Eng. Fract. Mech.,7, No. 2, 305–319 (1975).Google Scholar
  21. 21.
    V. Panasyuk, M. Savruk, and A. Datsyshyn, “A general method of solution of two-dimensional problems in the theory of cracks,” Eng. Fract. Mech.,9, No. 2, 491–497 (1977).Google Scholar
  22. 22.
    M. Ya. Leonov and V. V. Panasyuk, “Rozvitok naidribnishikh trishchin v tverdomu till,” Prikl. Mekhanika,5, No. 4, 391–401 (1959).Google Scholar
  23. 23.
    D. S. Dugdale, “Yielding of steel sheets containing slits,” J. Mech. Phys. Solids,8, No. 2, 100–104 (1960).Google Scholar
  24. 24.
    G. R. Irwin, Fracture, in: Handbuch der Physik, 6, Springer-Verlag, Berlin (1958), pp. 551–590.Google Scholar
  25. 25.
    E. O. Orowan, Trans. Inst. Eng. Shipbuild., Scotland,89, 165 (1945).Google Scholar
  26. 26.
    E. M. Morozov “Energy condition of crack growth in elastoplastic bodies,” Dokl. Akad. Nauk USSR,187, No. 1, 57–60 (1969).Google Scholar
  27. 27.
    E. M. Morozov, “The energy criterion of fracture for elastoplastic bodies,” in: Stress Concentration [in Russian], Issue 3, Naukova Dumka, Kiev (1971), pp. 85–90.Google Scholar
  28. 28.
    G. P. Cherepanov, “Crack propagation in a continuum,” Prikl. Mat. Mekh.,31, No. 3, 476–488 (1967).Google Scholar
  29. 29.
    G. C. Sih and B. C. Cha, “A fracture criterion for three-dimensional crack problem,” Eng. Fract. Mech.,6, No. 3, 699–723 (1974).Google Scholar
  30. 30.
    G. C. Sih and B. Macdonald, “Fracture mechanics applied to engineering problems. Strain energy density fracture criterion,” Eng. Fract Mech.,6, No. 2, 361–386 (1974).Google Scholar
  31. 31.
    V. I. Mossakovskii and M. T. Rybka, “Attempt at constructing a theory of strength of brittle materials based on Griffith's energy concepts,” Prikl. Mat. Mekh.,29, No. 2, 291–296 (1965).Google Scholar
  32. 32.
    A. E. Andreikiv, “Theory of limit equilibrium of quasibrittle bodies acted on by force, temperature, and diffusion,” in: Sixth All-Union Conference on the Physicochemical Mechanics of Structural Materials. Abstracts of Papers [in Russian], Fiz.-Mekh. Inst., AN USSR, Lvov (1974), pp. 22–23.Google Scholar
  33. 33.
    A. E. Andreikiv, “Determination of the strength of three-dimensional solid bodies weakened by cracks,” Fiz.-Khim. Mekh. Mater.,10, No. 1, 65–70 (1974).Google Scholar
  34. 34.
    V. V. Panasyuk and A. E. Andreikiv, “Effect of temperature fields on crack propagation in a deformed solid body,” Dokl. Akad. Nauk USSR, Ser. A, No. 4, 334–336 (1974).Google Scholar
  35. 35.
    V. V. Panasyuk and A. E. Andreikiv, “Theoretical model of an elastoplastic body with strain-hardening,” Dokl. Akad. Nauk USSR, Ser. A, No. 12, 1094–1098 (1974).Google Scholar
  36. 36.
    A. E. Andreikiv, “A certain strain criterion of local fracture,” Fiz.-Khim. Mekh. Mater.,13, No. 4, 23–25 (1977).Google Scholar
  37. 37.
    A. E. Andreikiv, Fracture of Quasibrittle Bodies with Cracks in a State of Complex Stress [in Russian], Naukova Dumka, Kiev (1979).Google Scholar
  38. 38.
    V. V. Novozhilov, “The necessary and sufficient criterion of brittle strength,” Prikl. Mat. Mekh.,33, No. 2, 212–222 (1969).Google Scholar
  39. 39.
    V. V. Novozhilov, “Foundations of the equilibrium of cracks in brittle bodies,” Prikl. Mat. Mekh.,33, No. 5, 797–812 (1969).Google Scholar
  40. 40.
    A. N. Guz', G. G. Kuliev, and I. A. Tsurpal, “Theory of fracture of thin bodies with cracks,” Prikl. Mekh.,11, No. 5, 32–35 (1975).Google Scholar
  41. 41.
    V. A. Ibragimov and V. D. Klyushnikov, “Effect of strain anisotropy on the state in the vicinity of the crack end,” Prikl. Mat. Mekh.,41, No. 5, 943–948 (1977).Google Scholar
  42. 42.
    V. A. Ibragimov, “One class of solutions of the elastoplastic problem under conditions of antiplane state,” Izv. Akad. Nauk SSSR, Mekh. Tverd. Tela, No. 3, 85–91 (1978).Google Scholar
  43. 43.
    E. M. Morozov and V. T. Sapunov, Subcritical crack growth, in: Materials of Nuclear Engineering [in Russian], Atomizdat, Moscow (1975), pp. 76–82.Google Scholar
  44. 44.
    V. Z. Parton and G. P. Cherepanov, Fracture mechanics, in: 50 Years of Mechanics in the USSR [inRussian], Vol. 3, Nauka, Moscow (1972), pp. 365–467.Google Scholar
  45. 45.
    D. H. Kaelble, “A relationship between the fracture mechanics and surface energetics failure criteria,” J. Appl. Polymer. Sci.,18, No. 6, 1869–1889 (1974).Google Scholar
  46. 46.
    E. Macherauch, Bruchmechanik, in: Grundlagen des Festigkeits- und Bruchverhaltens, Dusseldorf (1974), pp. 143–161.Google Scholar
  47. 47.
    T. Kanazawa, “Review of Japanese research on brittle fracture,” Pressure Eng.,11, No. 6, 316–339 (1973).Google Scholar
  48. 48.
    Yu. N. Rabotnov and A. N. Polilov, Problems of the fracture of materials, in: Mechanics. Periodic Collection of Translations of Foreign Articles, No. 5 (1974), pp. 79–94.Google Scholar
  49. 49.
    T. Ekobori, Scientific Foundations of Strength and Fracture of Materials [in Russian], Naukova Dumka, Kiev (1978).Google Scholar
  50. 50.
    N. A. Makhutov, “Theoretical characteristics of resistance to brittle fracture and methods of determining them (review),” Zavod. Lab.,42, No. 8, 987–995 (1976).Google Scholar
  51. 51.
    A. Hotano, “Basic models of brittle fracture,” Bull. Inst At. Energy Kyoto Univ.,49, 1–19 (1976).Google Scholar
  52. 52.
    E. Smith, “A critical survey of models that account for nonlinearity of material behavior at a crack tip,” in: Prospects Frack Mech., Leuden (1974), pp. 461–476.Google Scholar
  53. 53.
    J. F. Knott, “Fracture mechanics,” Met. Sci.,9, No. 9, 445–447 (1975).Google Scholar
  54. 54.
    D. J. Hayes, “Origins of the stress intensity factor approach to fracture,” J. Strain Anal.,10, No. 4, 198–200 (1975).Google Scholar
  55. 55.
    C. E. Turner and F. M. Burdekin, “Review of current status of yielding fracture mechanics,” At. Energy Rev.,12, No. 3, 439–503 (1974).Google Scholar
  56. 56.
    L. I. Slepyan and L. V. Troyankina, Theory of Cracks. Basic Concepts and Results [in Russian], Sudostroenie, Leningrad (1976).Google Scholar
  57. 57.
    G. M. Boyd, “From Griffith to cod and beyond,” Eng. Fract. Mech.,4, No. 3, 459–482 (1972).Google Scholar
  58. 58.
    G. P. Cherepanov, “Some models of fracture mechanics,” in: Aerogasdynamics and Physical Kinetics [in Russian], Novosibirsk (1977), pp. 211–238.Google Scholar
  59. 59.
    O. N. Romaniv and A. N. Tkach, “Micromechanical modeling of the fracture toughness of materials and alloys,” Fiz.-Khim. Mekh. Mater.,13, No. 5, 3–22 (1977).Google Scholar
  60. 60.
    A. Ya. Krasovskii and V. A. Vainshtok, “Criterion of failure of materials taking the kind of state of stress at the crack tip into account,” Probl. Prochn., No. 5, 64–69 (1978).Google Scholar
  61. 61.
    R. M. Thomson, “The fracture crack as an inperfection in a nearly perfect solid,” Ann. Rev. Mater. Sci., Palo Alto, Calif.,3, 31–51 (1973).Google Scholar
  62. 62.
    S. E. Gurevich and L. D. Edidovich, “Speed of propagation of a crack and threshold values of the stress intensity factor in the process of fatigue loading,” in: Fatigue and Fracture Toughness of Metals [in Russian], Nauka, Moscow (1974), pp. 36–78.Google Scholar
  63. 63.
    V. S. Ivanova and V. F. Terent'ev, The Nature of Metal Fatigue [in Russian], Metallurgiya, Moscow (1975).Google Scholar
  64. 64.
    M. M. Shkol'nik, Crack Growth Rate and Life of Metals [in Russian], Metallurgiya, Moscow (1973).Google Scholar
  65. 65.
    S. Ya. Yarema, “Investigation of fatigue crack growth and kinetic diagrams of fatigue fracture,” Fiz.-Khim. Mekh. Mater.,13, No. 4, 3–22 (1977).Google Scholar
  66. 66.
    S. Ya. Yarema and S. I. Mikitishin, “Analytical description of the diagram of fatigue fracture of materials,” Fiz.-Khim. Mekh. Mater.,11, No. 6, 47–54 (1975).Google Scholar
  67. 67.
    D. W. Hoeppner and W. E. Krupp, “Prediction of component life by application of fatigue crack growth knowledge,” J. Eng. Fract Mech.,6, No. 1, 47–70 (1974).Google Scholar
  68. 68.
    T. Ekobori, “Methodology of investigating various problems of fracture mechanics,” Sci. Mech.,27, No. 9, 1107–1114 (1975).Google Scholar
  69. 69.
    A. I. Zhilyukas, “Microscopic mechanism of fatigue crack propagation,” in: Resistance of Materials [in Russian], Kaunas (1974), pp. 92–97.Google Scholar
  70. 70.
    J. Nemec, “Zakonistosti šiřeni únavových trhlin ve složitých tělesech,” Strojirenstvi,23, No. 9, 553–554 (1973).Google Scholar
  71. 71.
    G. Sanz, “Developments récents dans le domaine de la méchanique de la rupture,” Rev. Met.,74, No. 11, 605–619 (1977).Google Scholar
  72. 72.
    P. S. Baburamani, “Review of crack initiation in fatigue,” Indian Eng.,18, No. 7, 7–15 (1974).Google Scholar
  73. 73.
    T. C. Lindley, C. E. Richards, and R. O. Ritchie, “Mechanics and mechanisms of fatigue crack growth in metals: a review,” Met Metal. Form.,43, No. 9, 268–274 (1976).Google Scholar
  74. 74.
    S. J. Maddox, “The effect of mean stress on fatigue crack propagation. A literature review,” Int. J. Fraet,11, No. 3, 389–408 (1975).Google Scholar
  75. 75.
    P. C. Paris, M. P. Gomez, and W. E. Anderson, “A rational analytic theory of fatigue,” The Trend in Engineering,13, 54–61 (1961).Google Scholar
  76. 76.
    D. N. Lal and V. Weiss, “A notch analysis of fracture approach to fatigue crack propagation,” in: Proc. 2nd Int. Conf. Mech. Behav. Mater., Boston, Mass., 1976, S. 1 (1976), pp. 617–621.Google Scholar
  77. 77.
    B. Cioclov Dragos, “A note on the quantitative assessment of fatigue crack propagation,” Int. J. Fract.,9, No. 2, 237–239 (1973).Google Scholar
  78. 78.
    H. de Leiris and C. Bathias, “La propagation des fissures de fatigue. Connaissances actuelles et récentes applications,” Rev. Met.,20, No. 1, 9–20 (1974).Google Scholar
  79. 79.
    K.-H. Schwalbe, “Approximate calculation on fatigue crack,” Int J. Fract.,9, No. 4, 381–395 (1973).Google Scholar
  80. 80.
    G. P. Cherepanov, V. D. Kuliev, and Kh. Khalmanov, “Crack growth upon cyclic and variable loading,” in: Fatigue and Fracture Toughness of Metals [in Russian], Nauka, Moscow (1974), pp. 200–209.Google Scholar
  81. 81.
    V. M. Radhakrishnau, “Crack propagation and fatigue failure,” Indian J. Technol.,11, No. 8, 338–341 (1973).Google Scholar
  82. 82.
    V. Weiss, “Recent advances in notch analysis of fracture and fatigue,” Ing.-Arch.,45, No. 4, 281–289 (1976).Google Scholar
  83. 83.
    C. Hagendorf Howand, “A new model of fatigue crack propagation using a material flaw growth resistance parameter,” in: Proc. AIAA (ASME) SAE 17th Struct, Dyn. and Mater. Conf., King Prussia, Pa. (1976), pp. 495–521.Google Scholar
  84. 84.
    M. Watanabe, Nadai Kin-ichi, and S. Hioki, “An elastoplastic fracture mechanics approach to fatigue crack propagation,” Bull. ISME,19, No. 132, 571–576 (1976).Google Scholar
  85. 85.
    A. E. Andreikiv, S. E. Kovchik, and V. V. Panasyuk, “On the theory of determining the life of materials and of structural elements,” in: 4th All-Union Congress on Theoretical and Applied Mechanics, Kiev, May 21–28, 1976 [in Russian], Naukova Dumka, Kiev (1976), p. 45.Google Scholar
  86. 86.
    A. E. Andreikiv and V. V. Panasyuk, “Determination of the life of quasibrittie bodies with cracks in cyclic loading,” Fiz.-Khim. Mekh. Mater.,11, No. 5, 35–40 (1975).Google Scholar
  87. 87.
    V. V. Panasyuk and A. E. Andreikiv, “Fatigue crack propagation in a quasibrittie body under cyclic load,” in: Predicting the Strength of Materials and Structural Elements of Powerful Machines [in Russian], Naukova Dumka, Kiev (1977), pp. 169–178.Google Scholar
  88. 88.
    V. V. Panasyuk, A. E. Andreikiv, and M. M. Stadnik, “ Life of a quasibrittle body with internal pennyshaped crack under cyclic load,” Probl. Prochn., No. 5, 19–22 (1977).Google Scholar
  89. 89.
    A. E. Andreikiv, M. M. Stadnik, and I. N. Pan'ko, “Kinetics of the fatigue propagation of an external penny-shaped crack in a circular cylinder,” Fiz.-Khim. Mekh. Mater.,13, No. 3, 15–20 (1977).Google Scholar
  90. 90.
    M. M. Stadnik and A. E. Andreikiv, “Fatigue propagation of an internal penny-shaped crack in a circular cylinder,” Probl. Prochn., No. 4, 53–56 (1979).Google Scholar
  91. 91.
    S. Kusumoto, Y. Ito, H. Miyata, and S. Usami, “Improving the methods of assessing critical states in fracture mechanics,” Pressure Eng.,13, No. 6, 231–238 (1975).Google Scholar
  92. 92.
    P. G. Bergan and B. Aamodt, “Finite element analysis of propagation in three-dimensional solids under cyclic loading,” Nucl. Eng. Des.,29, No. 2, 180–188 (1974).Google Scholar
  93. 93.
    A. I. Lur'e, Theory of Elasticity [in Russian], Nauka, Moscow (1970).Google Scholar
  94. 94.
    A. E. Andreikiv, “Three-dimensional problems of the theory of cracks for quasibrittie bodies,” Fiz.-Khim. Mekh. Mater.,12, No. 3, 54–60 (1976).Google Scholar
  95. 95.
    A. E. Andreikiv and Ya. Yu. Morozov, “Elastic equilibrium of polyhedrons weakened by plane cracks,” in: 14th Scientific Conference on Thermal Stresses in Structural Elements: Abstracts of Papers [in Russian], Naukova Dumka, Kiev (1977), pp. 5–6.Google Scholar
  96. 96.
    G. S. Kit and M. V. Khai, “Integral' ni rivnyannya prostorovykh zadach termopruzhnosti dlya til z trishchinami,” DAN URSR, S. A, No. 12, 1105–1109 (1975).Google Scholar
  97. 97.
    N. Wiener and E. Hopf, Über eine Klasse singulärer Integralgliechungen, in: Sitzungsber. Akad. Wiss., Berlin (1931), pp. 24–28.Google Scholar
  98. 98.
    M. G. Krein, “Integral equations on a half-line with kernel depending on the difference of the arguments,” Usp. Mat Nauk,13, No. 5, 83–88 (1958).Google Scholar
  99. 99.
    B. Noble, Methods Based on the Wiener-Hopf Technique, Pergamon (1959).Google Scholar
  100. 100.
    V. A. Fok, “Expansion of an arbitrary function into an integral with respect to Legendre functions with complex index,” Dokl. Akad. Nauk SSSR,39, No. 7, 279–283 (1943).Google Scholar
  101. 101.
    L. A. Vainshtein, The Theory of Diffraction and the Method of Factorization [in Russian], Sov. Radio, Moscow (1966).Google Scholar
  102. 102.
    W. T. Koiter, “Approximate solution Wiener-Hopf type integral equations with applications, Pts. I-III,” Proc. Kon. Ned. Akad. Wet. B. 57, No. 5, 558–579 (1954).Google Scholar
  103. 103.
    V. M. Aleksandrov, “Asymptotic methods in contact problems of the theory of elasticity,” Prikl. Mat. Mekh.32, No. 4, 672–683 (1968).Google Scholar
  104. 104.
    V. M. Aleksandrov, “Contact problems for an elastic wedge,” Izv. Akad. Nauk SSSR, Mekh. Tverd. Tela, No. 2, 120–131 (1967).Google Scholar
  105. 105.
    V. M. Aleksandrov, “Approximate solution of some integral equations of the theory of elasticity and mathematical physics,” Prikl. Mat. Mekh.,31, No. 6, 1117–1131 (1967).Google Scholar
  106. 106.
    V. M. Aleksandrov and A. V. Belokon', “Asymptotic solution of one class of integral equations and its application to contact problem for cylindrical elastic bodies,” Prikl. Mat Mekh.,31, No. 4, 704–710 (1967).Google Scholar
  107. 107.
    O. I. Cherskii, “Two theorems of assessing the error and some of its applications,” Dokl. Akad. Nauk SSSR,150, No. 2, 271–274 (1963).Google Scholar
  108. 108.
    V. A. Babeshko, “Integral equations of convolution of the first kind in a system of intercepts originating in the theory of elasticity and mathematical physics,” Prikl. Mat Mekh.,35, No. 1, 88–99 (1971).Google Scholar
  109. 109.
    G. Ya. Popov, “Method of orthogonal polynomials in contact problems of the theory of elasticity,” Prikl. Mat Mekh.,33, No. 3, 518–531 (1969).Google Scholar
  110. 110.
    G. Ya. Popov, “Application of the Wiener-Hopf method and of orthogonal polynomials to contact problems,” in: Contact Problems and Their Engineering Applications [in Russian], Nauchno-Issled. Inst Mashinostr., Moscow (1969), pp. 7–14.Google Scholar
  111. 111.
    B. Noble, “Certain dual integral equations,” J. Math. Phys.,37, No. 2, 128–136 (1958).Google Scholar
  112. 112.
    C. J. Tranter, “Dual trigonometrical series,” Proc. Glasgow Math. Soc.,4, No. 2, 49–57 (1959).Google Scholar
  113. 113.
    N. N. Lebedev, “Distribution of electricity over a thin parabolic segment,” Dokl. Akad. Nauk SSSR,114, No. 3, 513–516 (1957).Google Scholar
  114. 114.
    N. N. Lebedev and Ya. S. Uflyand, “Axisymmetric contact problem for an elastic layer,” Prikl. Mat Mekh.,22, No. 3, 320–326 (1958).Google Scholar
  115. 115.
    J. C. Cooke, “A solution of Tranters dual integral equation problem,” Quart. J. Mech Appl. Math.,9, No. 1, 103–110 (1956).Google Scholar
  116. 116.
    Ya. S. Uflyand, Integral Transformations in Problems of the Theory of Elasticity [in Russian], Nauka, Moscow-Leningrad (1967).Google Scholar
  117. 117.
    Ya. S. Uflyand, “Some mixed problems of the theory of elasticity solved with the aid of dual integral equations,” in: 4th All-Union Congress on Theoretical and Applied Mechanics, Kiev, May 21–28, 1976 [in Russian], Naukova Dumka, Kiev (1976), p. 108.Google Scholar
  118. 118.
    A. N. Rukhovets and Ya. S. Uflyand, “One class of dual integral equations and their application to the theory of elasticity,” Prikl. Mat. Mekh.,30, No. 2, 271–278 (1966).Google Scholar
  119. 119.
    V. G. Grinchenko and A. F. Ulitko, “Extension of an elastic space weakened by a circular crack,” Prikl. Mekh.,1, No. 10, 61–64 (1965).Google Scholar
  120. 120.
    V. G. Grinchenko and A. F. Ulitko, “One mixed boundary problem of thermal conductivity for a half-space,” Inzh.-Fiz. Zh.,6, No. 10, 67–71 (1963).Google Scholar
  121. 121.
    V. G. Grinchenko and A. F. Ulitko, “Contact problem of the theory of elasticity for a system of annular punches,” Mat. Fiz., Resp. Mezhved. Nauch.-Tekh. Sb., No. 5, 54–57 (1968).Google Scholar
  122. 122.
    A. F. Ulitko, “Extension of an elastic space weakened by two circular cracks lying in one plane,” in: Stress Concentration [in Russian], Issue 2, Naukova Dumka, Kiev (1968), pp. 201–208.Google Scholar
  123. 123.
    Z. S. Agranovich, V. A. Marchenko, and V. P. Shestipalov, “Diffraction of electromagnetic waves on flat metal screens,” Zh. Tekh. Fiz.,32, No. 4, 381–394 (1962).Google Scholar
  124. 124.
    A. M. Danileves'kyi, “Pro rozpodil strumu v tsylindrychnim elektrodi,” Zap. Naukovo-Doslidn. Inst. Mat Mekh. Khark. Derzh. Univ., Her. 4,13, 83–91 (1936).Google Scholar
  125. 125.
    V. I. Mossakovskii, “Pressure of a circular punch on an elastic half-space whose modulus of elasticity is an exponential function of depth,” Prikl. Mat. Mekh.,22, No. 1, 123–125 (1958).Google Scholar
  126. 126.
    E. C. Titchmarsh, Introduction to the Theory of Fourier Integrals, Oxford Univ. Press (1937).Google Scholar
  127. 127.
    Yu. I. Cherskii, “Equations of the type of convolution,” Izv. Akad. Nauk SSSR, Mat.,22, No. 3, 361–378 (1958).Google Scholar
  128. 128.
    W. Busbridge, “Dual integral equations,” Proc. London Math. Soc.,2, 44 (1938).Google Scholar
  129. 129.
    V. M. Aleksandrov, “One contact problem for an elastic wedge,” Izv, Akad. Nauk ArmSSR, Mekh.,20, No. 1, 3–14 (1967).Google Scholar
  130. 130.
    V. M. Aleksandrov, “Solution of one class of dual equations,” Dokl. Akad. Nauk SSSR,210, No. 1, 55–58 (1973).Google Scholar
  131. 131.
    A. A. Babloyan, “Solution of some dual integral equations,” Prikl. Mat. Mekh.,28, No. 6, 1015–1023 (1964).Google Scholar
  132. 132.
    A. A. Babloyan, “Solution of some ‘dual’ series,” Dokl. Akad. Nauk ArmSSR,39, No. 3, 149–157 (1964).Google Scholar
  133. 133.
    S. M. Mkhitaryan, “Some full orthogonal systems of functions and their applications to the solution of two types of dual series of equations,” Izv. Akad. Nauk ArmSSR, Mekh.,23, No. 2, 5–21 (1970).Google Scholar
  134. 134.
    A. I. Tseitlin, “Method of dual integral equations and dual series and its application to problems of mechanics,” Prikl. Mat Mekh.,20, No. 2, 259–270 (1966).Google Scholar
  135. 135.
    B. Noble, “The solution of Bessel function dual integral equations by multiplying factor method,” Proc. Cambridge Philos. Soc.,59, 351 (1965).Google Scholar
  136. 136.
    C. J. Tranter, “Some triple integral equations,” Proc. Glasgow Math. Assc.,4, No. 4, 200–203 (1960).Google Scholar
  137. 137.
    R. Schmeltzer and M. Lewin, “Function theoretic solution to a class of dual integral equations and applications to diffraction theory,” Quart. Appl. Math.,21, No. 4, 269–283 (1964).Google Scholar
  138. 138.
    I. I. Vorovich and Yu. A. Ustinov, “Pressure of a punch on a layer of finite thickness,” Prikl. Mat. Mekh.,23, No. 3, 445–455 (1959).Google Scholar
  139. 139.
    A. E. Andreikiv and V. V. Panasyuk, “Elastic equilibrium of an unbounded body weakened by a system of concentric cracks,” Prikl. Mekh.,6, No. 4, 124–128 (1970).Google Scholar
  140. 140.
    W. D. Collins, “Some axially symmetric stress distributions in elastic solids containing penny-shaped cracks. II. Cracks in solids under torsion,” Mathematics,9, No. 17, 25–37 (1962).Google Scholar
  141. 141.
    J. C. Cooke, “Some further triple integral equation solutions,” Proc. Edinburgh Math. Soc.,13, No. 4, 303–316 (1963).Google Scholar
  142. 142.
    J. C. Cooke, “The solution of triple integral equations in operational form,” Quart. J. Mech. Appl. Math.,18, No. 1, 57–72 (1965).Google Scholar
  143. 143.
    A. E. Andreikiv, “Solution of the problem of thermoelasticity for a half-space with circular boundary lines of the boundary conditions,” in: Thermal Stresses in Structural Elements [in Russian], No. 12, Naukova Dumka, Kiev (1972), pp. 95–101.Google Scholar
  144. 144.
    A. E. Andreikiv, “Solution of some problems of thermoelasticity by using harmonic functions,” Prikl. Mekh.,7, No. 9, 13–18 (1971).Google Scholar
  145. 145.
    A. E. Andreikiv and V. V. Panasyuk, “Pressure of a system of circular punches on an elastic half-space,” Dokl. Akad. Nauk USSR, Ser. A, No. 6, 534–536 (1971).Google Scholar
  146. 146.
    A. E. Andreikiv and V. V. Panasyuk, “Elastic equilibrium of a body weakened by a system of circular cracks arranged along one plane,” Dokl. Akad. Nauk SSSR,197, No. 2, 312–314 (1971).Google Scholar
  147. 147.
    A. E. Andreikiv and V. V. Panasyuk, “Mixed problem of the theory of elasticity for a half-space with circular boundary lines of the boundary conditions,” Izv. Akad. Nauk SSSR, Mekh. Tverd. Tela, No. 3, 26–32 (1972).Google Scholar
  148. 148.
    A. E. Andreikiv, “Pressing a system of punches into an elastic half-space,” Izv. Akad. Nauk. SSSR, Mekh. Tverd. Tela, No. 2, 125–131 (1975).Google Scholar
  149. 149.
    A. E. Andreikiv and V. V. Panasyuk, “Limit equilibrium of a brittle body weakened by a system of axisymmetric external cracks,” Fiz.-Khim. Mekh. Mater.,5, No. 3, 338–344 (1969).Google Scholar
  150. 150.
    Yu. N. Kuz'min and Ya. S. Uflyand, “Axisymmetric problem of the theory of elasticity for a half-space weakened by a flat circular slit,” Prikl. Mat. Mekh.,29, No. 6, 1132–1137 (1965).Google Scholar
  151. 151.
    Yu. N. Kuz'min and Ya. S. Uflyand, “Contact problem of the compression of an elastic layer by two punches,” Prikl. Mat. Mekh.,31, No. 4, 711–715 (1967).Google Scholar
  152. 152.
    G. Szefer, “Solution of a set of dual integral equations,” Arch. Mech. Stosow.,17, No. 4, 537–545 (1965).Google Scholar
  153. 153.
    V. V. Panasyuk and O. E. Andreikiv, “Granichna rivnovaga krikhkogo tila, oslablenogo dyoma zovnishnimi trischinami,” DAN URSR, S. A, No. 9, 823–827 (1969).Google Scholar
  154. 154.
    C. Weber, “Achsensymmetrische Deformation von Umdrehungskörpern,” Z. Angew. Math. Mech.,5, No. 6, 464–468 (1925).Google Scholar
  155. 155.
    C. Weber, “Zur Umwandlung von rotationssymmetrischen Problemen in zweidimensionale und umgekehrt,” Z. Angew. Math. Mech.,20, No. 2, 117–118 (1940).Google Scholar
  156. 156.
    T. H. Pöschl, “Zur Theorie des Druckversuchs für zylindrische Kürper,” Z. Angew. Math. Mech.,7, No. 6, 424–425 (1927).Google Scholar
  157. 157.
    K. Marquerre, “Ebenes und achsensymmetrisches Problem der Elastizitäts-theorie,” Z. Angew. Math. Mech.,13, No. 6, 437–438 (1933).Google Scholar
  158. 158.
    V. I. Smirnov and S. L. Sobolev, “Application of a new method of studying elastic oscillations in a space with axial symmetry,” Tr. Seismolog. Inst AN SSSR, No. 29, 48 (1933).Google Scholar
  159. 159.
    A. Foppl and L. Foppl, Force and Deformation. Applied Theory of Elasticity [Russian translation], Vol. 2, ONTI, Moscow-Leningrad (1936).Google Scholar
  160. 160.
    P. F. Papkovich, “Analogy between the plane problem of the theory of elasticity and the problem of defor mation symmetric about axis,” Prikl. Mat. Mekh.,3, No. 3, 45–66 (1939).Google Scholar
  161. 161.
    V. I. Mossakovskii, “Principal mixed problem of the theory of elasticity for a half-space with a circular boundary line of the boundary conditions,” Prikl. Mat, Mekh.,16, No. 2, 187–196 (1954).Google Scholar
  162. 162.
    J. Golecki, “Analogy between boundary value problems for regions bounded by concentric circles and axially symmetrical boundary value problems for regions bounded by concentric spherical surfaces,” Bull. Akad. Pol. Sci.,4, 5, No. 6, 327–333 (1957).Google Scholar
  163. 163.
    G. M. Polozhii, “Pro odne integral'ne peretvorennya uzagal'nenikh analitichnikh funktsii,” Visnik Kiiv. Univ. Ser. Astron., Mat. Mekh.,1, No. 2, 19–29 (1959).Google Scholar
  164. 164.
    G. N. Polozhii, “One theory of axisymmetric potential and a system of a circular and an annular punch,” Prikl. Mekh.,3, No. 12, 16–27 (1967).Google Scholar
  165. 165.
    A. Ya. Aleksandrov and Yu. I. Solov'ev, Spatial Problems of the Theory of Elasticity fin Russian], Nauka, Moscow (1978).Google Scholar
  166. 166.
    A. Ya. Aleksandrov, “Solution of a spatial axisymmetric elastic problem with spatial forces or thermal stresses with the aid of analytical functions,” Izv. Akad. Nauk SSSR, OTN, Mekh. Mashinostr., No. 4, 130–133 (1962).Google Scholar
  167. 167.
    A. Ya. Aleksandrov, “Some correlations between the solutions of plane and axisymmetric problems of the theory of elasticity for an infinite plate,” Dokl, Akad. Nauk SSSR,128, No. 1, 57–60 (1959).Google Scholar
  168. 168.
    M. Ya. Belen'kii, “Some axisymmetric problems of the theory of elasticity,” Prikl. Mat Mekh.,24, No. 3, 582–584 (1960).Google Scholar
  169. 169.
    M. D. Martynenko, “Druga kraiova zadacha teorii pruzhnosti dlya oblastei z shchilinami,” DAN URSR, No. 6, 707–711 (1964).Google Scholar
  170. 170.
    M. D. Martynenko, “Osnovni kraiovi zadachi prostorovoi teorii pruzhnosti dlya oblastei z shchilinami,” DAN URSR, No. 6, 695–698 (1965).Google Scholar
  171. 171.
    M. D. Martynenko, “Some spatial problems of the equilibrium of an elastic body weakeded by a crack,” Prikl. Mekh.,6, No. 10, 84–88 (1970).Google Scholar
  172. 172.
    A. Ya. Aleksandrov, “Solution of basic three-dimensional problems of the theory of elasticity for bodies of arbitrary shape by numerical realization of the method of integral equations,” Dokl. Akad. Nauk SSSR,208, No. 2, 291–294 (1973).Google Scholar
  173. 173.
    A. Ya. Aleksandrov, “Solution of basic problems of the theory of elasticity by numerical realization of the method of integral equations,” in: Achievements of the Mechanics of Deformed Media [in Russian], Nauka, Moscow (1975), pp. 3–24.Google Scholar
  174. 174.
    A. Ya. Aleksandrov, “Solution of mixed three-dimensional problems of the theory of elasticity for bodies of arbitrary shape,” in: 4th All-Union Congress on Theoretical and Applied Mechanics, Kiev, May 21–28, 1976 [in Russian], Naukova Dumka, Kiev (1976), p. 77.Google Scholar
  175. 175.
    B. M. Zinov'ev, “One approximate method of calculating bodies with slits,” Tr. Novosib. Inst. Inzh. Zhelezmo-Dorozhn. Transporta, No. 137, 105–125 (1972).Google Scholar
  176. 176.
    A. Ya. Aleksandrov and B. M. Zinov'ev, “Approximate method of solving plane and spatial problems of the theory of elasticity for bodies with reinforced elements and slits,” in: Mechanics of Deformed Bodies and Structures [in Russian], Mashinostroenie, Moscow (1975), pp. 15–25.Google Scholar
  177. 177.
    A. Ya. Aleksandrov and B. M. Zinov'ev, “Numerical solution of problems of the theory of elasticity for bodies with slits,” Izv. Akad. Nauk SSSR, Mekh. Tverd. Tela, No. 5, 89–97 (1978).Google Scholar
  178. 178.
    P. I. Perlin and V. N. Samarov, “Application of the theory of generalized potential to the solution of spatial problems of the theory of elasticity for bodies with slits and the assessment of brittle fracture of structures with complex shape,” Izv. Akad. Nauk KazSSR, Ser. Fiz.-Mat., No. 5, 72–74 (1974).Google Scholar
  179. 179.
    P. I. Perlin and V. N. Samarov, “Application of the theory of potential to the solution of spatial problems of the theory of elasticity for bodies with slits,” in: Applied Problems of Strength and Plasticity [in Russian], No. 6 (1977), pp. 42–46.Google Scholar
  180. 180.
    P. I. Perlin, “Generalization of one method of solving basic plane problems of the theory of potential and the theory of elasticity to the spatial case,” Dokl. Akad. Nauk SSSR,153, No. 5, 1033–1036 (1963).Google Scholar
  181. 181.
    H. D. Bui, “An integral equations method for solving the problem of a plane crack of arbitrary shape,” J. Mech, Phys. Solids,25, 29–39 (1977).Google Scholar
  182. 182.
    J. Weaver, “Three-dimensional crack analysis,” Int. J. Solids Struct.,13, No. 4, 321–330 (1977).Google Scholar
  183. 183.
    V. V. Panasyuk, O. É. Andreikiv, and M. M. Stadnik, “Viznachennya granichnoi rivnovagi krihkogo tila, oslablenogo systemoyu trishchin, bliz'kikh u plani do krugovikh,” DAN URSR, S. A, No. 6, 541–544 (1973).Google Scholar
  184. 184.
    A. E. Andreikiv, V. V. Panasyuk, and M. M. Stadnik, “Fracture of brittle bodies weakened by systems of cracks,” Izv. Akad. Nauk SSSR, Mekh. Tverd. Tela, No. 3, 54–58 (1975).Google Scholar
  185. 185.
    A. E. Andreikiv and M. M. Stadnik, “Propagation of a plane crack with piecewise smooth contour,” Prikl. Mekh.,No. 10, 50–56 (1974).Google Scholar
  186. 186.
    A. P. Datsyshin and M. P. Savruk, “A system of arbitrarily oriented cracks in elastic bodies,” Prikl. Mat. Mekh.,37, No. 2, 326–332 (1973).Google Scholar
  187. 187.
    R. V. Gol'dshtein, I. S. Klein, and G. I. Éskin, Variational-difference Method of Solving Some Integral and Integro-differential Equations of Three-dimensional Problems of the Theory of Elasticity [in Russian], Preprint No. 33, Institut Probl. Mekh. AN SSSR, Moscow (1973).Google Scholar
  188. 188.
    A. E. Andreikiv, “Shear of an unbounded elastic space weakened by a plane crack,” Dokl. Akad. Nauk USSR, S. A, No. 7, 601–603 (1977).Google Scholar
  189. 189.
    V. D. Kupradze, Methods of Potential in the Theory of Elasticity [in Russian], Fizmatgiz, Moscow (1963).Google Scholar
  190. 190.
    V. D. Kupradze, T. G. Gegelia, M. O. Basheleishvili, and T. V. Burchuladze, Three-dimensional Problems of the Mathematical Theory of Elasticity [in Russian], Izd. Tbilissk. Univ., Tbilisi (1968).Google Scholar
  191. 191.
    V. D. Kupradze, T. G. Gegelia, M. O. Basheleishvili, and T. V. Burchuiadze, Three-dimensional Problems of the Mathematical Theory of Elasticity and Thermoelasticity [in Russian], Nauka, Moscow (1976).Google Scholar
  192. 192.
    V. M. Aleksandrov and I. I. Vorovich, “Action of a punch on an elastic layer of a finite crack,” Prikl. Mat Mekh.,24, No. 2, 323–334 (1960).Google Scholar
  193. 193.
    D. V. Grilits'kii, “Kruchennya dvosharovogo pruzhnogoseredovishcha,” Prikl. Mekh.,7, No. 1, 87–94 (1961).Google Scholar
  194. 194.
    D. V. Grilitskii and Ya. M. Kizyma, “Axisymmetric contact problem for a transversely Isotropic layer resting on a rigid base,” Izv. Akad. Nauk SSSR, OTN, Mekh. Mashinostr., No. 3, 134–140 (1962).Google Scholar
  195. 195.
    V. M. Aleksandrov, “Solution of some contact problems of the theory of elasticity,” Prikl. Mat. Mekh.,27, No. 5, 970–972 (1963).Google Scholar
  196. 196.
    V. T. Koiter, “Solution of some problems of the theory of elasticity of asymptotic methods,” in: Application of the Theory of Functions in the Mechanics of the Continuum [in Russian], Vol. 1, Nauka, Moscow (1965), pp. 15–31.Google Scholar
  197. 197.
    D. M. Tracey, “Finite elements for three-dimensional elastic crack analysis,” Nucl. Eng. Des.,26, No. 2, 282–290 (1974).Google Scholar
  198. 198.
    S. M. Atluri, K. Kathiresan, and A. S. Kobayashi, “Three-dimensional linear fracture mechanics analysis by a displacement hybrid finite-element model,” in: 3rd Int. Conf. Struct. Mech React. Technol., Vol. 5, Part L, London (1975); Amsterdam e.a. (1975), L. 7.3/1-L. 7.3/13.Google Scholar
  199. 199.
    W. M. Browning and F. W. Smith, “An analysis technique for complex three-dimensional crack problems,” Dev. Theor. Appl. Mech.,8, 141–150, S. 1, s.a.Google Scholar
  200. 200.
    A. Holston, “A mixed mode crack tip finite element,” Int. J. Fract,12, No. 6, 887–899 (1976).Google Scholar
  201. 201.
    J. Deverall La Mar and G. H. Lindsey, “A comparison of numerical methods for determining stress intensity factors,” Trans. ASME, D 94, No. 2, 508–509 (1972).Google Scholar
  202. 202.
    M. Higuchi, K. Kondo, and M. Kawahara, “Calculation of the stress intensity factor with the aid of the substructure of model of the finite element method,” J. Soc. Nav. Archit. Jap.,135, 327–335 (1974).Google Scholar
  203. 203.
    G. H. Rowe, “Matrix displacement methods in fracture mechanics analysis of reactor vessels,” Nucl. Eng. Des.,20, No. 1, 251–263 (1972).Google Scholar
  204. 204.
    Y. Yamato, N. Tokuda, and Y. Sumi, “Finite element treatment of singularities of boundary value problems and its application to analysis of stress intensity factors,” in: Theory and Pract Finite Element Struct. Anal., Tokyo (1973), pp. 75–90.Google Scholar
  205. 205.
    B. Aamodt, “Application of the finite element method to problems in linear and nonlinear fracture mechanics,” Rept. Inst. Static. NTH. Univ. Trondheim,11, No. 1, 183 (1974).Google Scholar
  206. 206.
    A. E. Andreikiv, V. V. Panasyuk, and M. M. Stadnik, “Determination of the stress intensity factors in three-dimensional bodies with cracks,” Probl. Prochn., No. 3, 45–50 (1974).Google Scholar
  207. 207.
    B. Budiansky and R. J. O'Connell, “Elastic moduli of a cracked solid,” Int. J. Solids Struct,12, No. 2, 81–97 (1976).Google Scholar
  208. 208.
    T. Kawai and Y. Fujitanl, “Analysis of three-dimensional surface crack problems by boundary integral methods,” Mon. J. Inst Ind. Sci., Univ. Tokyo,28, No. 2, 70–73 (1976).Google Scholar
  209. 209.
    T. Kawai, “Singular solution of a general surface crack problem,” Mon. J. Inst Ind. Sci., Univ. Tokyo,28, No. 2, 74–77 (1976).Google Scholar
  210. 210.
    V. Horak, “Inverse variational principles in fracture mechanics of solids,” Acta techn CSAV,15, No. 6, 639–651 (1970).Google Scholar
  211. 211.
    R. Badaliance and G. C. Sih, “An approximate three-dimensional theory of layered plates containing through thickness cracks,” Eng. Fract. Mech.,7, No. 1, 1–22 (1975).Google Scholar
  212. 212.
    E. S. Folias, “On the three-dimensional theory of cracked plates,” Trans. ASME, E. 42, No. 3, 663–674 (1975).Google Scholar
  213. 213.
    P. M. Besuner, “The influence function method for fracture mechanics and residual fatigue life analysis of cracked components under complex stress fields,” Nucl. Eng. Des.,43, No. 1, 115–154 (1977).Google Scholar
  214. 214.
    J. P. Gyekengesi and A. Mendelson, “Stress analysis and stress intensity factors for finite geometry solids containing rectangular surface cracks,” Trans. ASME, E. 44, No. 3, 442–448 (1977).Google Scholar
  215. 215.
    J. P. Benthem and W. T. Koiter, “Asymptotic approximations to crack problems,” Mech. Fract., Leuden,1, 131–178 (1973).Google Scholar
  216. 216.
    Z. Bažant, “Three-dimensional harmonic functions near termination or intersection of gradient singularity lines: a general numerical method,” Int. J. Eng. Sci.,12, 221–243 (1974).Google Scholar
  217. 217.
    S. K. Kanaun, Random crack field in an elastic continuum, in: Investigations of Elasticity and Plasticity [in Russian], Issue 10, Izd. Leningradsk. Univ. Leningrad (1974), pp. 66–83.Google Scholar
  218. 218.
    T. Crusse, “Application of the boundary integral equation method to three-dimensional stress analysis,” Comput Struct,3, No. 3, 509–527 (1973).Google Scholar
  219. 219.
    A. H. England and R. Shail, “Orthogonal polynomial solution to some mixed boundary-value problems in elasticity. II,” Quart J. Mech. Appl. Math.,30, No. 4, 397–414 (1977).Google Scholar
  220. 220.
    D. D. Ivlev, “Theory of cracks of quasibrittle fracture,” Zh. Prikl. Mekh. Tekh. Fiz., No. 6, 88–128 (1967).Google Scholar
  221. 221.
    V. Z. Parton and P. I. Perlin, “Integral equations of basic spatial and plane problems of elastic equilibrium,” in: Mechanics of Solid Deformed Bodies,8, (1975).Google Scholar
  222. 222.
    Development of the Theory of Contact Problems in the USSR [in Russian], Nauka, Moscow (1976).Google Scholar
  223. 223.
    R. J. Hartranft and G. C. Sih, “Alternating method applied to end and surface crack problems,” Mech. Fracture, Leyden,1, 179–283 (1973).Google Scholar
  224. 224.
    I. I. Vorovich, V. M. Aleksandrov, and V. A. Babeshko, Nonclassical Mixed Problems of the Theory of Elasticity [in Russian], Nauka, Moscow (1974).Google Scholar
  225. 225.
    D. J. Cartwright and D. P. Rooke, “Evaluation of stress intensity factors,” J. Strain Anal.,10, No. 4, 217–224 (1975).Google Scholar
  226. 226.
    Y. Ueda and T. Yao, “Methods of calculating stress intensity factors,” J. Jap. Weld. Soc.,42, 934–950 (1973).Google Scholar
  227. 227.
    J. N. Sneddon, “Integral transform methods,” Mech. Fract., Leuden,1, 315–367 (1973).Google Scholar
  228. 228.
    Yu. D. Kopeikin, “Direct solution of two- and three-dimensional boundary problems of the theory of elasticity and plasticity with the aid of singular integral equations of the method of potential,” in: Numerical Methods of the Mechanics of the Continuum [in Russian], Vol. 5, No. 2, Novosibirsk (1974), pp. 46–56.Google Scholar
  229. 229.
    S. E. Benzley and D. M. Parks, “Fracture mechanics,” in: Struct Mech, Comput Programs Surv. Assessments and Availability, Charlotteville (1974), pp. 81–102.Google Scholar

Copyright information

© Plenum Publishing Corporation 1980

Authors and Affiliations

  • V. V. Panasyuk
    • 1
  • A. E. Andreikiv
    • 1
  • M. M. Stadnik
    • 1
  1. 1.Physicomechanical InstituteAcademy of Sciences of the Ukrainian SSRRussia

Personalised recommendations