# Spatial problems of the theory of cracks (review)

1. Fundamental mechanical concepts and mathematical methods in spatial problems of the theory of cracks

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- 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.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.V. V. Panasyuk, Limit Equilibrium of Brittle Bodies with Cracks [in Russian], Naukova Dumka, Kiev (1968).Google Scholar
- 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.G. P. Cherepanov, The Mechanics of Brittle Fracture [in Russian], Nauka, Moscow (1974).Google Scholar
- 6.G. P. Cherepanov and L. V. Ershov, Fracture Mechanics [in Russian], Mashinostroenie, Moscow (1977).Google Scholar
- 7.V. Z. Parton and E. M. Morozov, The Mechanics of Elastoplastic Fracture [in Russian], Nauka, Moscow (1974).Google Scholar
- 8.J. E. Srawley and W. F. Brown, Plane Strain Crack Toughness Testing of High-Strength Metallic Materials, ASTM, Philadelphia (1966).Google Scholar
- 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.L. M. Kachanov, Fundamentals of Fracture Mechanics [in Russian], Nauka, Moscow (1974).Google Scholar
- 11.T. Ekobori, The Physics and Mechanics of Fracture and Strength of Solids [in Russian], Metallurgiya, Moscow (1971).Google Scholar
- 12.F. A. McClintock and A. S. Argon, Mechanical Behavior of Materials, Addison-Wesley (1966).Google Scholar
- 13.L. I. Sedov, Mechanics of the Continuum: in Two Volumes [in Russian], Vol. 2, Nauka, Moscow (1970).Google Scholar
- 14.S. V. Serensen, Resistance of Materials to Fatigue and Brittle Fracture [in Russian], Atomizdat, Moscow (1975).Google Scholar
- 15.V. M. Finkel', The Physics of Fracture [in Russian], Metallurgiya, Moscow (1970).Google Scholar
- 16.N. A. Makhutov, Resistance of Structural Elements to Brittle Fracture [in Russian], Mashinostroenie, Moscow (1973).Google Scholar
- 17.E. M. Morozov, Introduction to the Mechanics of Crack Propagation [in Russian], Mosk. Inzh.-Fiz. Inst., Moscow (1977).Google Scholar
- 18.Liebowitz (editor), Fracture. An Advanced Treatise, Vols. 1–7, Academic Press, New York-London (1968–1972).Google Scholar
- 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.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.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.M. Ya. Leonov and V. V. Panasyuk, “Rozvitok naidribnishikh trishchin v tverdomu till,” Prikl. Mekhanika,5, No. 4, 391–401 (1959).Google Scholar
- 23.D. S. Dugdale, “Yielding of steel sheets containing slits,” J. Mech. Phys. Solids,8, No. 2, 100–104 (1960).Google Scholar
- 24.G. R. Irwin, Fracture, in: Handbuch der Physik, 6, Springer-Verlag, Berlin (1958), pp. 551–590.Google Scholar
- 25.E. O. Orowan, Trans. Inst. Eng. Shipbuild., Scotland,89, 165 (1945).Google Scholar
- 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.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.G. P. Cherepanov, “Crack propagation in a continuum,” Prikl. Mat. Mekh.,31, No. 3, 476–488 (1967).Google Scholar
- 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.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.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.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.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.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.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.A. E. Andreikiv, “A certain strain criterion of local fracture,” Fiz.-Khim. Mekh. Mater.,13, No. 4, 23–25 (1977).Google Scholar
- 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.V. V. Novozhilov, “The necessary and sufficient criterion of brittle strength,” Prikl. Mat. Mekh.,33, No. 2, 212–222 (1969).Google Scholar
- 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.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.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.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.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.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.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.E. Macherauch, Bruchmechanik, in: Grundlagen des Festigkeits- und Bruchverhaltens, Dusseldorf (1974), pp. 143–161.Google Scholar
- 47.T. Kanazawa, “Review of Japanese research on brittle fracture,” Pressure Eng.,11, No. 6, 316–339 (1973).Google Scholar
- 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.T. Ekobori, Scientific Foundations of Strength and Fracture of Materials [in Russian], Naukova Dumka, Kiev (1978).Google Scholar
- 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.A. Hotano, “Basic models of brittle fracture,” Bull. Inst At. Energy Kyoto Univ.,49, 1–19 (1976).Google Scholar
- 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.J. F. Knott, “Fracture mechanics,” Met. Sci.,9, No. 9, 445–447 (1975).Google Scholar
- 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.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.L. I. Slepyan and L. V. Troyankina, Theory of Cracks. Basic Concepts and Results [in Russian], Sudostroenie, Leningrad (1976).Google Scholar
- 57.G. M. Boyd, “From Griffith to cod and beyond,” Eng. Fract. Mech.,4, No. 3, 459–482 (1972).Google Scholar
- 58.G. P. Cherepanov, “Some models of fracture mechanics,” in: Aerogasdynamics and Physical Kinetics [in Russian], Novosibirsk (1977), pp. 211–238.Google Scholar
- 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.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.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.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.V. S. Ivanova and V. F. Terent'ev, The Nature of Metal Fatigue [in Russian], Metallurgiya, Moscow (1975).Google Scholar
- 64.M. M. Shkol'nik, Crack Growth Rate and Life of Metals [in Russian], Metallurgiya, Moscow (1973).Google Scholar
- 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.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.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.T. Ekobori, “Methodology of investigating various problems of fracture mechanics,” Sci. Mech.,27, No. 9, 1107–1114 (1975).Google Scholar
- 69.A. I. Zhilyukas, “Microscopic mechanism of fatigue crack propagation,” in: Resistance of Materials [in Russian], Kaunas (1974), pp. 92–97.Google Scholar
- 70.J. Nemec, “Zakonistosti šiřeni únavových trhlin ve složitých tělesech,” Strojirenstvi,23, No. 9, 553–554 (1973).Google Scholar
- 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.P. S. Baburamani, “Review of crack initiation in fatigue,” Indian Eng.,18, No. 7, 7–15 (1974).Google Scholar
- 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.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.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.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.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.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.K.-H. Schwalbe, “Approximate calculation on fatigue crack,” Int J. Fract.,9, No. 4, 381–395 (1973).Google Scholar
- 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.V. M. Radhakrishnau, “Crack propagation and fatigue failure,” Indian J. Technol.,11, No. 8, 338–341 (1973).Google Scholar
- 82.V. Weiss, “Recent advances in notch analysis of fracture and fatigue,” Ing.-Arch.,45, No. 4, 281–289 (1976).Google Scholar
- 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.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.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.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.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.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.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.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.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.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.A. I. Lur'e, Theory of Elasticity [in Russian], Nauka, Moscow (1970).Google Scholar
- 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.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.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.N. Wiener and E. Hopf, Über eine Klasse singulärer Integralgliechungen, in: Sitzungsber. Akad. Wiss., Berlin (1931), pp. 24–28.Google Scholar
- 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.B. Noble, Methods Based on the Wiener-Hopf Technique, Pergamon (1959).Google Scholar
- 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.L. A. Vainshtein, The Theory of Diffraction and the Method of Factorization [in Russian], Sov. Radio, Moscow (1966).Google Scholar
- 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.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.V. M. Aleksandrov, “Contact problems for an elastic wedge,” Izv. Akad. Nauk SSSR, Mekh. Tverd. Tela, No. 2, 120–131 (1967).Google Scholar
- 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.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.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.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.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.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.B. Noble, “Certain dual integral equations,” J. Math. Phys.,37, No. 2, 128–136 (1958).Google Scholar
- 112.C. J. Tranter, “Dual trigonometrical series,” Proc. Glasgow Math. Soc.,4, No. 2, 49–57 (1959).Google Scholar
- 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.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.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.Ya. S. Uflyand, Integral Transformations in Problems of the Theory of Elasticity [in Russian], Nauka, Moscow-Leningrad (1967).Google Scholar
- 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.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.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.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.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.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.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.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.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.E. C. Titchmarsh, Introduction to the Theory of Fourier Integrals, Oxford Univ. Press (1937).Google Scholar
- 127.Yu. I. Cherskii, “Equations of the type of convolution,” Izv. Akad. Nauk SSSR, Mat.,22, No. 3, 361–378 (1958).Google Scholar
- 128.W. Busbridge, “Dual integral equations,” Proc. London Math. Soc.,2, 44 (1938).Google Scholar
- 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.V. M. Aleksandrov, “Solution of one class of dual equations,” Dokl. Akad. Nauk SSSR,210, No. 1, 55–58 (1973).Google Scholar
- 131.A. A. Babloyan, “Solution of some dual integral equations,” Prikl. Mat. Mekh.,28, No. 6, 1015–1023 (1964).Google Scholar
- 132.A. A. Babloyan, “Solution of some ‘dual’ series,” Dokl. Akad. Nauk ArmSSR,39, No. 3, 149–157 (1964).Google Scholar
- 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.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.B. Noble, “The solution of Bessel function dual integral equations by multiplying factor method,” Proc. Cambridge Philos. Soc.,59, 351 (1965).Google Scholar
- 136.C. J. Tranter, “Some triple integral equations,” Proc. Glasgow Math. Assc.,4, No. 4, 200–203 (1960).Google Scholar
- 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.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.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.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.J. C. Cooke, “Some further triple integral equation solutions,” Proc. Edinburgh Math. Soc.,13, No. 4, 303–316 (1963).Google Scholar
- 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.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.A. E. Andreikiv, “Solution of some problems of thermoelasticity by using harmonic functions,” Prikl. Mekh.,7, No. 9, 13–18 (1971).Google Scholar
- 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.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.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.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.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.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.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.G. Szefer, “Solution of a set of dual integral equations,” Arch. Mech. Stosow.,17, No. 4, 537–545 (1965).Google Scholar
- 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.C. Weber, “Achsensymmetrische Deformation von Umdrehungskörpern,” Z. Angew. Math. Mech.,5, No. 6, 464–468 (1925).Google Scholar
- 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.T. H. Pöschl, “Zur Theorie des Druckversuchs für zylindrische Kürper,” Z. Angew. Math. Mech.,7, No. 6, 424–425 (1927).Google Scholar
- 157.K. Marquerre, “Ebenes und achsensymmetrisches Problem der Elastizitäts-theorie,” Z. Angew. Math. Mech.,13, No. 6, 437–438 (1933).Google Scholar
- 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.A. Foppl and L. Foppl, Force and Deformation. Applied Theory of Elasticity [Russian translation], Vol. 2, ONTI, Moscow-Leningrad (1936).Google Scholar
- 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.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.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.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.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.A. Ya. Aleksandrov and Yu. I. Solov'ev, Spatial Problems of the Theory of Elasticity fin Russian], Nauka, Moscow (1978).Google Scholar
- 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.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.M. Ya. Belen'kii, “Some axisymmetric problems of the theory of elasticity,” Prikl. Mat Mekh.,24, No. 3, 582–584 (1960).Google Scholar
- 169.M. D. Martynenko, “Druga kraiova zadacha teorii pruzhnosti dlya oblastei z shchilinami,” DAN URSR, No. 6, 707–711 (1964).Google Scholar
- 170.M. D. Martynenko, “Osnovni kraiovi zadachi prostorovoi teorii pruzhnosti dlya oblastei z shchilinami,” DAN URSR, No. 6, 695–698 (1965).Google Scholar
- 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.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.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.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.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.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.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.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.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.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.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.J. Weaver, “Three-dimensional crack analysis,” Int. J. Solids Struct.,13, No. 4, 321–330 (1977).Google Scholar
- 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.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.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.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.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.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.V. D. Kupradze, Methods of Potential in the Theory of Elasticity [in Russian], Fizmatgiz, Moscow (1963).Google Scholar
- 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.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.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.D. V. Grilits'kii, “Kruchennya dvosharovogo pruzhnogoseredovishcha,” Prikl. Mekh.,7, No. 1, 87–94 (1961).Google Scholar
- 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.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.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.D. M. Tracey, “Finite elements for three-dimensional elastic crack analysis,” Nucl. Eng. Des.,26, No. 2, 282–290 (1974).Google Scholar
- 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.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.A. Holston, “A mixed mode crack tip finite element,” Int. J. Fract,12, No. 6, 887–899 (1976).Google Scholar
- 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.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.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.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.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.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.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.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.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.V. Horak, “Inverse variational principles in fracture mechanics of solids,” Acta techn CSAV,15, No. 6, 639–651 (1970).Google Scholar
- 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.E. S. Folias, “On the three-dimensional theory of cracked plates,” Trans. ASME, E. 42, No. 3, 663–674 (1975).Google Scholar
- 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.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.J. P. Benthem and W. T. Koiter, “Asymptotic approximations to crack problems,” Mech. Fract., Leuden,1, 131–178 (1973).Google Scholar
- 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.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.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.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.D. D. Ivlev, “Theory of cracks of quasibrittle fracture,” Zh. Prikl. Mekh. Tekh. Fiz., No. 6, 88–128 (1967).Google Scholar
- 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.Development of the Theory of Contact Problems in the USSR [in Russian], Nauka, Moscow (1976).Google Scholar
- 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.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.D. J. Cartwright and D. P. Rooke, “Evaluation of stress intensity factors,” J. Strain Anal.,10, No. 4, 217–224 (1975).Google Scholar
- 226.Y. Ueda and T. Yao, “Methods of calculating stress intensity factors,” J. Jap. Weld. Soc.,42, 934–950 (1973).Google Scholar
- 227.J. N. Sneddon, “Integral transform methods,” Mech. Fract., Leuden,1, 315–367 (1973).Google Scholar
- 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.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

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