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Three-dimensional boundary-value problems of the theory of elasticity for noncanonical regions

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Literature Cited

  1. B. L. Abramyan and A. Ya. Aleksandrov, “Axisymmetrical problems of the theory of elasticity,” in: Proc. of the Second All-Union Conference on Theoretical and Applied Mechanics. The Mechanics of Solids, [in Russian], Nauka, Moscow (1966), pp. 7–37.

    Google Scholar 

  2. A. Ya. Aleksandrov and Yu. I. Solov'ev, Three-Dimensional Problems of the Theory of Elasticity [in Russian], Nauka, Moscow (1979).

    Google Scholar 

  3. S. A. Ambartsumyan, The Theory of Anisotropic Plates [in Russian], Nauka, Moscow (1967).

    Google Scholar 

  4. S. A. Ambertsumyan, General Theory of Anisotropic Shells [in Russian], Nauka, Moscow (1974).

    Google Scholar 

  5. É. N. Baida, “General solution of the equilibrium equations of anisotropic and isotropic bodies,” Izv. Vyssh. Uchebn. Zaved., Stroit. Arkhitekt., No. 6, 17–27 (1968).

    Google Scholar 

  6. Kh. B. Berkinov, “Functions of the tensor of the stresses of an anisotropic elastic body,” in: Integration of the Equations of Mathematical Physics [in Russian], Nauka, Tashkent (1964), pp. 83–103.

    Google Scholar 

  7. Kh. B. Berkinov and N. M. Saifulaev, “The tensor of the functions of the stresses of an anisotropic body,” Dokl. TadzhSSR,10, No. 11, 13–15 (1967).

    Google Scholar 

  8. G. I. Brankov, “Special characteristics with the investigation of wavy shells,” in: The Mechanics of Continuous Media and Applied Problems of Analysis [in Russian], Nauka, Moscow (1972), pp. 79–88.

    Google Scholar 

  9. A. I. Vaindiner and V. V. Moskvitin, “Singular integral equations of three-dimensional problems of the theory of elasticity; regularization, cubic functions, differential properties, and approximate methods of solution,” Dokl. Akad. Nauk SSSR,228, No. 6, 1310–1313 (1976).

    Google Scholar 

  10. M. Van Dyke, Perturbation Methods in Fluid Mechanics, Academic Press (1964).

  11. G. N. Watson, The Theory of Bessel Functions [Russian translation], Vol. 2, Inostr. Lit. (1949).

  12. Yu. V. Veryuzhskii, The Method of Integral Equations in the Mechanics of Deformable Solids [in Russian], Kiev (1977).

  13. S. D. Volkov, “The potential of anisotropy in the theory of elasticity,” Dokl. Akad. Nauk SSSR,197, No. 3, 547–549 (1971).

    Google Scholar 

  14. I. I. Vorovich, “Mathematical questions of the theory of plates and shells,” in: Proc. of the Second All-Union Conference on Theoretical and Applied Mechanics. The mechanics of Solids [in Russian], Nauka, Moscow (1966), pp. 116–136.

    Google Scholar 

  15. I. I. Vorovich, V. M. Aleksandrov, and V. A. Babeshko, Nonclassical Mixed Problems in the Theory of Elasticity [in Russian], Nauka, Moscow (1974).

    Google Scholar 

  16. I. Kh. Ganev, “Complete solution of the three-dimensional problem of orthotropic continuous media in rectangular coordinates,” in: The Mechanics of Continuous Media. Collection of Papers from an International Conference, Bolg. Akad. Nauk, Sofia (1968), pp. 123–134.

  17. E. W. Hobson, The Theory of Spherical and Ellipsoidal Functions [Russian translation], Inostr. Lit (1952).

  18. V. T. Grinchenko, Equilibrium and Fully Established Vibrations of Elastic Bodies of Finite Dimensions [in Russian], Naukova Dumka, Kiev (1978).

    Google Scholar 

  19. V. G. Gromov, “The method of perturbations in a boundary-value problem of thermoviscoelasticity,” Prikl. Mat. Mekh.,36, No. 3, 506–513 (1972).

    Google Scholar 

  20. V. G. Gromov and V. S. Orlov, “The practical application of the method of perturbations in an inhomogeneous boundary-value problem of thermoviscoelasticity,” Prikl. Mekh.,8, No. 9, 58–63 (1973).

    Google Scholar 

  21. O. M. Guz', “Approximation method for determining the density of strains in curvilinear apertures in shells,” Prikl. Mekh.,8, No. 6, 605–612 (1962).

    Google Scholar 

  22. A. N. Guz', “Solution of two-dimensional and three-dimensional problems of the mechanics of continuous media for multiply connected regions,” Kontsentr. Napryazh., No. 2, 54–58 (1968).

    Google Scholar 

  23. A. N. Guz', “Pro odin metod rozv'yazuvannaya trivirnikh liniinikh zadach mekhaniki sutsil'nogo seredovishcha dlya nekanonichnikh oblastei,” Dov. Akad. Nauk URSR, Ser. A, No. 4 (1970), pp. 352–355.

    Google Scholar 

  24. A. N. Guz', “The diffraction of waves at finite bodies of revolution,” Prikl. Mekh.,9, No. 7, 10–18 (1973).

    Google Scholar 

  25. A. N. Guz', “The propagation and diffraction of waves in bodies with nonround cylindrical boundaries,” Prikl. Mekh.,9, 3–11 (1973).

    Google Scholar 

  26. A. N. Guz' and V. T. Golovchan, Diffraction of Elastic Waves in Multiply Connected Bodies [in Russian], Naukova Dumka, Kiev (1972).

    Google Scholar 

  27. A. N. Guz', Yu. R. Kerimov, and S. Yu. Kerimov, “Diffraction of torsion waves in finite bodies of revolution,” Izv. Akad. Nauk AzSSR, Ser. Fiz.,-Tekh. Mat. Nauk, No. 2, 144–149 (1973).

    Google Scholar 

  28. A. N. Guz', V. D. Kubenko, and M. A. Cherevko, Diffraction of Elastic Waves [in Russian], Naukova Dumka, Kiev (1978).

    Google Scholar 

  29. A. N. Guz', V. D. Kubenko, and M. A. Cherevko, “Diffraction of elastic waves,” Prikl. Mekh.,14, No. 8, 3–15 (1978).

    Google Scholar 

  30. A. N. Guz', P. Z. Lugovoi, and N. A. Shul'ga, Conical Shells, Weakened by Openings [in Russian], Naukova Dumka, Kiev (1976).

    Google Scholar 

  31. A. N. Guz' and I. A. Tsurpal, “The equilibrium of a physically nonlinear thick-walled spherical shell,” in: The Theory of Shells and Plates, Proc. of a Symposium, Kazan', 1971 [in Russian], Nauka, Moscow (1971), pp. 82–84.

    Google Scholar 

  32. A. N. Guz', I. S. Chernyshenko, and K. I. Shnerenko, Spherical Bottoms, Weakened by Openings [in Russian], Naukova Dumka (1970).

  33. A. N. Guz', I. S. Chernyshenko, Val. N. Chekhov, Vik. N. Chekhov, and K. I. Shnerenko, Cylindrical Shells, Weakened by Openings [in Russian], Naukova Dumka, Kiev (1974).

    Google Scholar 

  34. V. I. Gulyaev, V. A. Bazhenov, and P. P. Lizunov, Nonclassical Theory of Shells and Its Application to the Solution of Engineering Problems [in Russian], Vishcha Shkola, L'vov (1978).

    Google Scholar 

  35. V. M. Deev, “Solution of a three-dimensional problem of elasticity for an anisotropic medium,” Dop. Akad. Nauk UkSSR, No. 7, 707–711 (1958).

    Google Scholar 

  36. A. A. Dorodnitsyn, “Use of the method of a small parameter for the solution of the equations of mathematical physics,” in: Numerical Methods for Solution of the Problems of the Mechanics of Continuous Media [in Russian], Vychisl. Tsentr. Akad. Nauk SSSR, Moscow (1969), pp. 85–100.

    Google Scholar 

  37. D. D. Ivlev and L. V. Ershov, The Method of Perturbations in the Theory of an Elastico-plastic Body [in Russian], Nauka, Moscow (1978).

    Google Scholar 

  38. A. A. Il'yushin, Plasticity [in Russian], I. Gostekhizdat, Moscow-Leningrad (1948).

    Google Scholar 

  39. V. N. Ionov and P. M. Ogibalov, Strength of the Three-Dimensional Elements of Constructions [in Russian], Vysshaya Shkola, Moscow (1972).

    Google Scholar 

  40. A. I. Kalandiya, A. I. Lur'e, G. F. Mandzhavidze, V. K. Prokopov, and Ya. S. Uflyand, “The linear theory of elasticity,” in: Mechanics in the USSR for the Last Fifty Years [in Russian]. Vol. 3, Nauka, Moscow (1972), pp. 4–70.

    Google Scholar 

  41. L. V. Kantorovich and V. I. Krylov, Approximation Methods of Higher Analysis [in Russian], Fizmatgiz, Moscow (1962).

    Google Scholar 

  42. G. Kauderer, Nonlinear Mechanics [Russian translation], Inostr. Lit., Moscow (1961).

    Google Scholar 

  43. Ya. F. Kayuk, “The stress state of hollow shells of revolution with large displacements,” Izv. Akad. Nauk SSSR, Mekh. Tverd. Tela, No. 5, 159–163 (1969).

    Google Scholar 

  44. Ya. F. Kayuk, “Improving the convergence of the method of simple iterations in nonlinear problems of the theory of plates and hollow shells,” Prikl. Mekh., No. 11, 47–55 (1974).

    Google Scholar 

  45. N. A. Kil'chevskii, “Analysis of various methods for reducing three-dimensional problems of the theory of elasticity to two-dimensional and investigation of the statement of boundary-value problems of the theory of shells,” in: The Theory of Plates and Shells. Proc. of the Second All-Union Converence on Plates and Shells [in Russian], Kiev (1962) pp. 58–69.

  46. I. V. Kim, “Elastic equilibrium of an unbounded orthogonal space, weakened by two elliptical openings,” Izv. Akad. Nauk SSSR, Mekh. Tverd. Tela, No. 2, 74–80 (1972).

    Google Scholar 

  47. I. V. Kim and R. Ya. Suncheleev, “A contact problem for an orthogonal half-space,” Prikl. Mekh.,6, No. 7, 40–47 (1970).

    Google Scholar 

  48. A. D. Kovalenko and V. G. Karnaukhov, “An approximation method for solution of threedimensional problems of the theory of elasticity and viscoelasticity,” Prikl. Mekh.,5, No. 8, 1–10 (1969).

    Google Scholar 

  49. A. D. Kovalenko and V. G. Karnaukhov, “An approximation method for calculation of the stress state of thick-walled shells of revolution,” Prikl. Mekh.,6, No. 6, 3–12 (1970).

    Google Scholar 

  50. A. D. Kovalenko and V. G. Karnaukhov, “Approximation method for solving problems in thermoviscoelasticity for thermorheologically simple materials,” Dop. Akad. Nauk URSR, Ser. A, No. 1, 68–71 (1971).

    Google Scholar 

  51. V. V. Kolokol'chikov, “Exact solution of some one-dimensional problems of the physically nonlinear quadratic theory of elasticity,” Prikl. Mekh.,6, No. 9, 95–101 (1970).

    Google Scholar 

  52. G. V. Kolosov, The Use of Complex Diagrams in the Theory of Functions of a Complex Variable in the Theory of Elasticity [in Russian], ONTI, Leningrad-Moscow (1935).

    Google Scholar 

  53. M. A. Koltunov, Yu. N. Vasil'ev, and V. A. Chernykh, Elasticity and Strength of Cylindrical Bodies [in Russian], Vysshaya Shkola, Moscow (1975).

    Google Scholar 

  54. A. S. Kosmodamianskii, Anisotropic Multiply Connected Media [in Russian], Donetsk. Univ., Donetsk (1970).

    Google Scholar 

  55. A. S. Kosmodamianskii, The Plane Problem of the Theory of Elasticity for Plates with Openings, Cuts, and Protrusions [in Russian], Vishcha Shkola, Kiev (1975).

    Google Scholar 

  56. A. S. Kosmodamianskii, The Stress State of Anisotropic Media with Openings and Cavities [in Russian], Vishcha Shkola, Kiev-Donetsk (1976).

    Google Scholar 

  57. A. S. Kosmodamianskii and V. A. Shaldyrvan, Thick Multiply Connected Plates [in Russian], Naukova Dumka, Kiev (1978).

    Google Scholar 

  58. D. Cowle, Perturbation Methods in Applied Mathematics [Russian translation], Mir, Moscow (1972).

    Google Scholar 

  59. V. D. Kupradze, T. G. Gegelia, M. O. Basheleishvili, and T. V. Burchuladze Three-Dimensional Problems of the Mathematical Theory of Elasticity and Thermoelasticity [in Russian], Nauka, Moscow (1976).

    Google Scholar 

  60. G. V. Kutsenko and A. F. Ulitko, “Axisymmetrical deformations of a hollow ellipsoid of revolution,” Tep. Napryazh. Elem. Konstr., No. 11, 37–42 (1971).

    Google Scholar 

  61. S. G. Lekhnitskii, Anisotropic Plates [in Russian], Gostekhteorizdat, Moscow-Leningrad (1947).

    Google Scholar 

  62. S. G. Lekhnitskii Torsion of Anisotropic and Inhomogeneous Rods [in Russian], Nauka, Moscow (1971).

    Google Scholar 

  63. S. G. Lekhnitskii, The Theory of Elasticity of an Anisotropic body [in Russian], Nauka, Moscow (1971).

    Google Scholar 

  64. V. A. Lomakin, “Deformation of microinhomogeneous elastic bodies,” Prikl. Mat. Mekh.,29, No. 5, 18–25 (1965).

    Google Scholar 

  65. V. A. Lomakin, “Concentration of stresses around a surface with rapidly oscillating roughnesses,” Prikl. Mekh.,4, No. 2, 1–8 (1968).

    Google Scholar 

  66. V. A. Lomakin, Statistical Problems of the Mechanics of Deformable Solids [in Russian], Nauka, Moscow (1970).

    Google Scholar 

  67. V. A. Lomakin, The Theory of Elasticity of Inhomogeneous Bodies [in Russian], Mosk. Univ., Moscow (1976).

    Google Scholar 

  68. A. I. Lur'e, Three-Dimensional Problems of the Theory of Elasticity [in Russian], Gostekhizdat, Moscow (1955).

    Google Scholar 

  69. D. F. Lyalyuk and Yu. N. Nemish, “Approximation method for investigation of the stress state of thick-walled noncanonical shells of revolution,” in: Proc. of the Ninth All-Union Conference on the Theory of Shells and Plates, Leningrad, 1973, Sudostroenie, Leningrad (1975), pp. 280–282.

    Google Scholar 

  70. G. I. Marchuk, The Method of Computational Mathematics [in Russian], Nauka, Moscow (1977).

    Google Scholar 

  71. P. M. Morse and H. Fishbach, Methods of Theoretical Physics, Vol. 2, McGraw-Hill (1953).

  72. S. Mossakovskaya, “Functions of the stresses for elastic bodies having triaxial orthotropy,” Byull. Polsk. Akad. Nauk, Otd. 4,3, No. 1, 3–6 (1955).

    Google Scholar 

  73. S. Mossakovskaya, “Functions of the stresses for elastic bodies having triaxial orthotropy,” Arch. Mech. Stosowanej,7, No. 1, 87–96 (1955).

    Google Scholar 

  74. N. I. Muskhelishvili, Basic Problems of the Mathematical Theory of Elasticity [in Russian], Nauka, Moscow (1966).

    Google Scholar 

  75. A. H. Nayfeh, Perturbation Methods, Wiley (1973).

  76. G. Neiber, Stress Concentration [Russian translation], Gostekhizdat, Moscow-Leningrad (1947).

    Google Scholar 

  77. G. Neiber and G. Kahn, “Problems of stress concentration in science and technology,” in: Mechanics [in Russian], No. 3, (1967), pp. 109–131.

  78. V. N. Nemish, “Three-dimensional deformation of an isotropic medium with noncanonical inclusions,” Mat. Fiz., No. 19, 104–109 (1976).

    Google Scholar 

  79. V. N. Nemish, “Stress distribution around closed axisymmetric cavities and inclusions with torsion,” Prikl. Mekh.,13, No. 11, 32–44 (1977).

    Google Scholar 

  80. Yu. N. Nemish, “Approximate solution of three-dimensional problems of the theory of elasticity for a transversely isotropic medium,” Prikl. Mekh.,5, No. 8, 26–34 (1969).

    Google Scholar 

  81. Yu. N. Nemish, “The stress state of a thick-walled surface of revolution,” Dop. Akad. Nauk URSR, Ser. A, No. 6, 542–547 (1970).

    Google Scholar 

  82. Yu. N. Nemish, “Approximate solution of three-dimensional, physically nonlinear problems of the theory of elasticity,” Prikl. Mekh.,6, No. 7, 53–57 (1970).

    Google Scholar 

  83. Yu. M. Nemish, “One method of investigating the stress state of physically nonlineci bodies of revolution,” Dop. Akad. Nauk URSR, Ser. A., No. 11, 1015–1019 (1970).

    Google Scholar 

  84. Yu. N. Nemish, “The stress state of nonlinearly elastic bodies,” Izv. Akad. Nauk SSSR, Mekh. Tverd. Tela, No. 4, 81–89 (1971).

    Google Scholar 

  85. Yu. N. Nemish, “Axisymmetric problem of the stress state of orthogonal elastic bodies,” Prikl. Mekh.,7, No. 6, 17–24 (1971).

    Google Scholar 

  86. Yu. N. Nemish, “Investigation of the thermal stress state of a medium taking account of physical nonlinearity,” Tepl. Napryazh. Elem. Konstr., No. 11, 81–85 (1971).

    Google Scholar 

  87. Yu. N. Nemish, “Small-parameter method in spatially axisymmetric problems for cylindrically isotropic bodies,” Dop. Akad. Nauk URSR, Ser. A, No. 3, 247–249 (1972).

    Google Scholar 

  88. Yu. N. Nemish, “Approximation method for investigation of the symmetrical deformation of orthotropic bodies,” Izv. Akad. Nauk SSSR, Mekh. Tverd. Tela, No. 5, 81–87 (1972).

    Google Scholar 

  89. Yu. N. Nemish, “Approximation method for solution of boundary-value problems of the mathematical theory of elasticity of anisotropic media,” Mat. Fiz., No. 11, 98–104 (1972).

    Google Scholar 

  90. Yu. M. Nemish, “Elastic equilibrium of deformed cylinders of varying thickness,” Dop. Akad. Nauk URSR, Ser. A, No. 2, 155–158 (1973).

    Google Scholar 

  91. Yu. N. Nemish, “Elastic equilibrium of three-dimensional deformable bodies bounded by nonround cylindrical surfaces,” Izv. Akad. Nauk SSSR, Mekh. Tverd. Tela, No. 2, 77–86 (1973).

    Google Scholar 

  92. Yu. N. Nemish, “Generalization of three-dimensional harmonic functions,” Diff. Uravn., No. 5, 967–968 (1973).

    Google Scholar 

  93. Yu. N. Nemish, “Recurrence relations of the perturbation method in three-dimensional relationships of the theory of elasticity,” Prikl. Mekh.,9, No. 9, 64–70 (1973).

    Google Scholar 

  94. Yu. N. Nemish, “Three-dimensional problems for an elastic medium bounded by cylindrical surfaces,” Mat. Fiz., No. 13, 73–78 (1973).

    Google Scholar 

  95. Yu. N. Nemish, “Limit problems in the theory of elasticity for multiply connected noncanonical regions in space,” Dop. Akad. Nauk URSR, Ser. A, No. 8, 743–747 (1974).

    Google Scholar 

  96. Yu. N. Nemish, “Construction of one class of three-dimensional polyharmonic functions,” Mat. Fiz., No. 15, 123–128 (1974).

    Google Scholar 

  97. Yu. N. Nemish, “The method of ‘perturbation of the form of the boundary’ in three-dimensional problems of the mechanics of deformable media” Izv. Akad. Nauk SSSR, Mekh. Tela, No. 1, 17–26 (1975).

    Google Scholar 

  98. Yu. N. Nemish, “Method for investigation of the stress state of corrugated thick-walled shells,” in: Material from the First All-Union School on the Theory and Numerical Methods for Calculation of Shells and Plates, Gegechkori, GruzSSR, 1974 [in Russian], Tbilis. Univ., Tbilisi (1975), pp. 381–393.

    Google Scholar 

  99. Yu. N. Nemish, “Method for solution of three-dimensional problems of the mechanics of deformable bodies bounded by arbitrary surfaces,” Dokl. Akad. Nauk UkrSSR, Ser. A, No. 1, 48–52 (1976).

    Google Scholar 

  100. Yu. N. Nemish, “Substantiation of the method of perturbations in problems of the mechanics of deformable media,” Prikl. Mekh.,13, No. 12, 25–33 (1977).

    Google Scholar 

  101. Yu. N. Nemish, “Three-dimensional mixed boundary-value problems of the mechanics of deformable bodies for noncanonical surfaces,” in: Mixed Problems of the Mechanics of a Deformable Body. Summaries of Papers from an All-Union Scientific-Conference, Rostov [in Russian], Part 1 (1977), p. 41.

  102. Yu. N. Nemish, “Approximation method for solution of three-dimensional problems of the theory of the elasticity of a curvilinear orthogonal body for noncanonical regions,” Prikl. Mekh.,14, No. 7, 10–17 (1978).

    Google Scholar 

  103. Yu. N. Nemish, “Three-dimensional problems of the theory of elasticity for noncanonical regions,” Author's Abstract of Candidate's Dissertation, Kiev (1979).

  104. Yu. N. Nemish and D. F. Lyalyuk, “The convergence of the method of perturbation and the exactness of satisfaction of boundary conditions at noncanonical surfaces,” Prikl. Mekh.,14, No. 4, 41–49 (1978).

    Google Scholar 

  105. Yu. N. Nemish and V. N. Nemish, “Torsion of orthotropic bodies of revolution with noncanonical cavities and inclusions,” Izv. Akad. Nauk SSSR, Mekh. Tverd. Tela, No. 6, 101–111 (1976).

    Google Scholar 

  106. Yu. N. Nemish and V. N. Nemish, “Solution of three-dimensional problems of the theory of elasticity of a transversely isotropic medium for noncanonical regions,” Prikl. Mekh.,12, No. 12, 73–82 (1976).

    Google Scholar 

  107. Yu. N. Nemish and V. N. Nemish, “The stress state of a transversely isotropic medium, weakened by a closed conical cavity,” Mat. Fiz., No. 26, 110–113 (1979).

    Google Scholar 

  108. Yu. N. Nemish, V. N. Nemish, and P. F. Yarema, “Stress distribution around noncanonical surfaces,” Prikl. Mekh.,7, No. 12, 41–50 (1971).

    Google Scholar 

  109. Yu. N. Nemish and D. I. Chernopiskii, “Thermal stress state of a nonlinearly elastic hollow sphere with aerodynamic heating,” Prikl. Mekh.,10, No. 6, 15–26 (1974).

    Google Scholar 

  110. Yu. N. Nemish and D. I. Chernopiskii, “Axisymmetrical stress state of deformed cylinders of variable thickness,” Prikl. Mekh.,11, No. 10, 9–18 (1975).

    Google Scholar 

  111. Yu. N. Nemish and D. I. Chernopiskii, “Convergence, of the method of successive approximations in physically nonlinear boundary-value problems,” Mat. Fiz., No. 18, 125–130 (1975).

    Google Scholar 

  112. Yu. N. Nemish and D. I. Chernopiskii, “Asymtotic method for calculation of thick-walled shells bounded by noncoordinate surfaces,” in: Proc. of the Tenth All-Union Conference on the Theory of Shells and Plates, Kutais, 1975 [in Russian], Vol. I, Metsniereba, Tbilisi (1975), pp. 235–243.

    Google Scholar 

  113. Yu. N. Nemish and D. I. Chernopiskii, “Axisymmetrical boundary-value problems of the statics of transversely corrugated, multiply connected cylinders,” Prikl. Mekh.,13, No. 6, 38–46 (1977).

    Google Scholar 

  114. Yu. N. Nemish and D. I. Chernopiskii, “Three-dimensional boundary-value problems for longitudinally corrugated thick-walled cylinders,” Prikl. Mekh.,14, No. 3, 34–44 (1978).

    Google Scholar 

  115. V. V. Novozhilov, L. A. Tolokoninikov, and K. F. Chernykh, “The, nonlinear theory of elasticity,” in: Mechanics in the USSR in the Least Fifty Years [in Russian], Vol. 3, Nauka, Moscow (1972), pp. 71–78.

    Google Scholar 

  116. V. A. Pal'mov, “Stress concentration around the roughness of the boundary of an elastic body,” Izv. Akad. Nauk SSSR, Mekh. Mashinostr., No. 3, 104–108 (1963).

    Google Scholar 

  117. V. A. Pal'mov, “An elastic plane with an opening of random form,” in: Proc. of Leningrad Polytechnic Institute [in Russian], No. 235 (1964), pp. 35–40.

  118. V. Z. Parton and P. I. Perlin, “Integral equations of the principal three-dimensional and plane problems of elastic equilibrium,” in: The Mechanics of Solid Deformable Bodies [in Russian], Vol. 8 (Summaries of Science and Technology. VINITI Akad. Nauk SSSR), Moscow (1975), pp. 5–84.

  119. V. Z. Parton and P. I. Perlin, Integral Equations of the Theory of Elasticity [in Russian], Nauka, Moscow (1977).

    Google Scholar 

  120. Yu. N. Podil'chuk, “Approximation method for solution of boundary-value problems of the theory of elasticity for figures close to an ellipsoid of revolution,” Prikl. Mekh.,6, No. 9, 23–30 (1970).

    Google Scholar 

  121. Yu. N. Podil'chuk, Three-Dimensional Problems of the Theory of Elasticity [in Russian], Naukova Dumka, Kiev (1979).

    Google Scholar 

  122. Yu. N. Podil'chuk and A. M. Kirichenko, “An approximation method for solution of boundary-value problems of the theory of elasticity for figures close to an elliposid of revolution,” Dokl. Akad. Nauk USSR, Ser A, No. 7, 650–655 (1970).

    Google Scholar 

  123. Yu. N. Podil'chuk and L. A. Neznakina, “Stress distribution in the neighborhood of a short fiber, welded into a matrix,” Prikl. Mekh.,13, No. 5, 3–10 (1977).

    Google Scholar 

  124. Yu. N. Podil'chuk and L. A. Neznakina, “An approximation method for solution of three-dimensional problems of the theory of elasticity,” Prikl. Mekh.,13, No. 10, 100–107 (1977).

    Google Scholar 

  125. G. N. Polozhii, The Theory and Application of p-Analytic and (p, q)-Analytic Functions [in Russian], Naukova Dumka, Kiev (1973).

    Google Scholar 

  126. V. K. Prokopov, “Review of work on homogenous solutions in the theory of elasticity and their application,” in: Proceedings of Leningrad Polytechnic Institute [in Russian], No. 279 (1967), pp. 31–46.

  127. A. Ya. Ishlinskii (editor), The Development of Mechanics in the USSR [in Russian], Nauka, Moscow (1967).

    Google Scholar 

  128. V. L. Rvachev, Geometrical Application of the Algebra of Logic [in Russian], Tekhnika, Kiev (1967).

    Google Scholar 

  129. V. L. Rvachev, “Investigations of Ukrainian scientists in the field of contact problems in the theory of elasticity,” Prikl. Mekh.,3, No. 10, 109–116 (1967).

    Google Scholar 

  130. V. L. Rvachev, Methods of the Algebra of Logic in Mathematical Physics [in Russian], Naukova Dumka (1974).

  131. V. L. Rvachev and V. S. Protsenko, Contact Problems of the Theory of Elasticity for Nonclassical Regions [in Russian], Naukova Dumka, Kiev (1977).

    Google Scholar 

  132. G. N. Savin, Distribution of Stresses Around Openings [in Russian], Naukova Dumka, Kiev (1968).

    Google Scholar 

  133. G. N. Savin and Yu. N. Nemish, “The method of perturbation of elastic properties in the mechanics of solid deformable bodies,” Dokl. Akad. Nauk SSSR,216, No. 1, 53–55 (1974).

    Google Scholar 

  134. V. S. Sarkisyan, New Problems in the Theory of Elasticity of an Anisotropic Body [in Russian], Erevan Univ., Erevan (1970).

    Google Scholar 

  135. I. V. Svirskii, Methods of the Bubnov-Galerkin Type in Successive Approximations [in Russian], Nauka, Moscow (1968).

    Google Scholar 

  136. Collected Works of Academician A. N. Krylov [in Russian], Vol. 10, Akad. Nauk SSSR, Moscow (1948).

  137. K. V. Solyanik-Krassa, The Torsion of Shafts of Variable Cross Section [in Russian], Gostekhizdat, Leningrad-Moscow (1949).

    Google Scholar 

  138. G. S. Taras'ev, “Equations of the nonlinear theory of elasticity at displacements,” Prikl. Mekh.,7, No. 2, 26–33 (1971).

    Google Scholar 

  139. A. F. Ulitko, “The method of vector eigenfunctions in three-dimensional problems of the theory of elasticity,” Prikl. Mekh.,3, No. 9, 1–11 (1967).

    Google Scholar 

  140. A. F. Ulitko, The Method, of Eigenvector Functions in Three-Dimensional Problems of the Theory of Elasticity [in Russian], Naukova Dumka, Kiev (1979).

    Google Scholar 

  141. Yu. A. Ustinov and M. A. Shlenev, “Trends in the development of the asymptotic method in the theory of slabs and shells,” in: Calculation of Shells and Plates [in Russian], Rostov-on-Don (1976), pp. 3–27.

  142. A. P. Khusu, Yu. R. Vitenberg, and V. A. Pal'mov, Roughness of Surfaces: Theoretical-Probability Approach [in Russian], Nauka, Moscow (1975).

    Google Scholar 

  143. I. A. Tsurpal, Calculation of the Elements of Construction from Nonlinearly Elastic Materials [in Russian], Tekhnika, Kiev (1976).

    Google Scholar 

  144. I. A. Tsurpal and G. G. Kuliev, “Problems of stress concentration taking account of physical nonlinearity of the material,” Prikl. Mekh.,10, No. 7, 3–22 (1974).

    Google Scholar 

  145. V. T. Shen, “Problems for elastic materials with spherical isotropy,” Proc. ASME, Appl. Mech.,33, No. 3, 71–79 (1966).

    Google Scholar 

  146. D. I. Chernopiskii, “Special characteristics of the calculation of deformed cylinders in modified Bessel functions,” Prikl. Mekh.,14, No. 6, 45–51 (1978).

    Google Scholar 

  147. D. I. Chernopiskii, “The stress state of thick-walled corrugated spherical shells,” Prikl. Mekh.,15, No. 10, 128–133 (1978).

    Google Scholar 

  148. G. S. Shapiro, “Axisymmetric deformations of an ellipsoid of revolution,” Dokl. Akad. Nauk SSSR,58, No. 7, 1309–1312 (1947).

    Google Scholar 

  149. R. N. Shvets and V. I. Eleiko, “The stochastic problem of thermal conductivity and thermoelasticity for a deformable body with a rough surface,” Dokl. Akad. Nauk USSR, Ser. A, No. 11, 1021–1024 (1977).

    Google Scholar 

  150. R. N. Shvets and V. I. Eleiko, “Stochastic temperature stresses in a cylinder with a rough surface,” Prikl. Mekh.,13, No. 12, 39–45 (1977).

    Google Scholar 

  151. V. I. Sheinin, “Distribution of stresses in the neighborhood of endfaces taking account of unevenesses of the contour,” Osn. Fundam. Mekh. Gruntov, No. 4, 21–23 (1965).

    Google Scholar 

  152. M. O. Shul'ga, “Method of solving plasticity problems in the theory of strain for noncanonical regions,” Dop. Akad. Nauk UkrSSR, No. 3, 261–264 (1972).

    Google Scholar 

  153. C. I. Bors, Theory of Elasticity of Anisotropic Bodies [in Russian], R. S. Romanta, Bucharest (1970).

    Google Scholar 

  154. S. K. Datta, “Rectilinear oscillations of a rigid inclusion in an infinite elastic medium,” Int. J. Eng. Sci.,9, No. 10, 947–957 (1971).

    Google Scholar 

  155. A. H. Elliot, “Three-dimensional stress distribution in hexagonal aeolotropic crystals,” Proc. Cambridge Phil. Soc.,44, 621–630 (1948).

    Google Scholar 

  156. H. Grüters, “Iterative Lösung von Lestspannungs problemen in anisotropen Korpern,” Z. Angew. Math. Mech.,54, No. 4, 79–80 (1974).

    Google Scholar 

  157. Z. Kaczkowski, “Strain in an anisotropic body [in Polish],” Arch. Mech. Stosowanej,7, No. 1, 52–86 (1955).

    Google Scholar 

  158. M. Misicu, “Theory of elastic mobility [in Rummanian],” Editurs Akademie R. S. Romania, Bucharest (1972).

    Google Scholar 

  159. H. Miyamoto, “Review on the three-dimensional theory of elasticity,” J. Jpn. Soc. Mech. Eng.,60, No. 460, 477–490 (1957).

    Google Scholar 

  160. G. N. Sawin, A. N. Guz', and A. N. Kosmodamianskij, “Problems of the mechanics of stretched media in noncanonical regions,” Mech. Teor. Stosowana,8, No. 1, 3–18 (1970).

    Google Scholar 

  161. E. Sternberg, “On some recent developments in the linear theory of elasticity,” Struct. Mech., 48–72 (1960).

  162. C. K. Youngdahl, “On the completeness of a set of stress functions appropriate to the solution of elasticity problems in general cylindrical coordinates,” Int J. Eng. Sci.,7, No. 1, 61–79 (1969).

    Google Scholar 

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  1. Yu. N. Nemish
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Institute of Mechanics, Academy of Sciences of the Ukrainian SSR, Kiev. Translated from Prikladnaya Mekhanika, Vol. 16, No. 2, pp. 3–39, February, 1980.

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Nemish, Y.N. Three-dimensional boundary-value problems of the theory of elasticity for noncanonical regions. Soviet Applied Mechanics 16, 85–116 (1980). https://doi.org/10.1007/BF00885101

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