Skip to main content
SpringerLink
Log in

Perturbation of boundary shape in continuum mechanics (review)

  • Published:
Soviet Applied Mechanics Aims and scope

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Literature Cited

  1. A. S. Avetisyan, “Stress concentration near a rhombic aperture for a physically nonlinear material,” Prikl. Mekh.,2, No. 10, 128–133 (1966).

    Google Scholar 

  2. A. S. Avetisyan, “Stress concentration near a rhombic aperture in an isotropic, physically nonlinear plate under pure shear,” Prikl. Mekh.,5, No. 3, 120–124 (1969).

    Google Scholar 

  3. A. S. Avetisyan, “Study of the stress concentration near curved apertures in physically nonlinear plates,” Author's Abstract of Candidate's Dissertation, Physicomathematical Sciences, Erevan (1970).

  4. A. S. Avetisyan, M. A. Babaev, and I. A. Tsurpal, “Effect of physical nonlinearity, contour curvature, and rigidity of the support on the stress in a massif with noncircular horizontal shafts,” in: Mechanics Problems of Rocks [in Russian], Nauka, Moscow (1971), pp. 192–190.

    Google Scholar 

  5. S. D. Akbarov, “On the stress in a general curved boundary between two elastic media (plane deformation),” Trans. of Math. and Mechanics Students, for the 60th Anniversary of the USSR, Baku (1983), pp. 15–19.

  6. S. D. Akbarov, “On the stress in an infinite viscoelastic body fortified by a curved layer of sealant,” Trans. 10th Conf. of Stud. of the Inst. of Mechanics, Academy of Sciences of the Ukrainian SSR, Ch. 1, pp. 2–7, Kiev (1984); in: VINITI, July 30, 1984, No. 5535-84.

  7. S. D. Akbarov, “On a method of solving problems in the mechanics of composite materials with distorted viscoelastic layers,” Prikl. Mekh.,21, No. 3, 14–19 (1985).

    Google Scholar 

  8. S. D. Akbarov, “On the normal stress in a fibrous composite material with structural distortions having a small concentration of sealant,” Prikl. Mekh.,21, No. 11, 50–55 (1985).

    Google Scholar 

  9. S. D. Akbarov, “On the stress in a fibrous viscoelastic composite material with structural distortions containing a small concentration of fibers,” Prikl. Mekh.,22, No. 6, 13–21 (1986).

    Google Scholar 

  10. S. D. Akbarov and A. N. Guz', “On a method of solving problems in the mechanics of composite materials with distorted layers,” Prikl. Mekh.,20, No. 4, 3–9 (1984).

    Google Scholar 

  11. S. D. Akbarov and A. N. Guz', “On a method of solving problems in the mechanics of fibrous materials with structural distortions,” Prikl. Mekh.,20, No. 9, 3–12 (1984).

    Google Scholar 

  12. S. D. Akbarov and A. N. Guz', “On the stress in a composite material with distorted layers and a small concentration of sealant,” Mekh. Kompozitn. Mater., No. 6, 990–996 (1984).

    Google Scholar 

  13. S. D. Akbarov and A. N. Guz', “Model of a piecewise-homogeneous body in the mechanics of layered composite materials with small-scale distortions,” Prikl. Mekh.,21, No. 4, 5–12 (1985).

    Google Scholar 

  14. S. D. Akbarov and A. N. Guz', “On the stress in a fibrous composite material with structural distortions and a small concentration of fibers,” Prikl. Mekh.,21, No. 6, 37–44 (1985).

    Google Scholar 

  15. S. N. Babyuk and I. A. Tsurpal, “Nonlinear problem on the stress concentration for a plate with curved apertures,” Izv. Arm. SSR Mekh.,23, No. 6, 24–31 (1970).

    Google Scholar 

  16. N. V. Banichuk, “Determination of the shape of curved cracks using the method of a small parameter,” Izv. Akad. Nauk SSSR, Mekh. Tverd. Tela, No. 2, 130–137 (1970).

    Google Scholar 

  17. G. E. Belashevskii, “Stress concentration in a circular cylindrical shell with a curved aperture,” Tr. Kuibyshev. Aviation Inst., No. 48, 41–50 (1971).

    Google Scholar 

  18. G. E. Belashevskii, “Stress distribution in a cylindrical shell with a noncircular aperture or rigid inclusion,” Calculation of Three-Dimensional Systems in Engineering Mechanics [in Russian], Saratov Univ. (1972), pp. 98–99.

  19. N. I. Belozerov and I. I. Dolgova, “On the diffraction of cylindrical waves by a cylindrical shell of arbitrary cross section,” Akust. Zh.,17, No. 3, 457–459 (1971).

    Google Scholar 

  20. N. M. Bloshko, “On the stress of a transversely isotropic corrugated cylinder of finite length,” Prikl. Mekh.,19, No. 12, 38–43 (1983).

    Google Scholar 

  21. N. M. Bloshko, “Axisymmetric stress state of an elastic cylinder of finite length with circular grooves,” Author's Abstract of Candidate's Dissertation, Physicomathematical Sciences, Kiev (1984).

  22. N. M. Bloshko and Yu. N. Nemish, “Elastic equilibrium of a transversely isotropic solid cylinder with perturbed surfaces,” Izv. Akad. Nauk SSSR, Mekh. Tverd. Tela, No. 4, 93–99 (1984).

    Google Scholar 

  23. E. V. Bruyatskii, “Approximate method of solving Oseen boundary-value problems for a cylinder of arbitrary shape,” Prikl. Mekh.,2, No. 10, 121–127 (1966).

    Google Scholar 

  24. E. V. Bruyatskii, “Application of the Vekua method to the Oseen equations,” Prikl. Mekh.,2, No. 5, 121–127 (1966).

    Google Scholar 

  25. E. V. Bruyatskii, “Study of the drag of poorly streamlined bodies at small Reynolds numbers,” Author's Abstract of Candidate's Dissertation, Physicomathematical Sciences, Kiev (1967).

  26. Ya. I. Burak, Ya. P. Romanchuk, and B. M. Trits, “Optimization of temperature and stress fields in a doubly-connected plate,” Prikl. Mekh.,22, No. 1, 68–73 (1986).

    Google Scholar 

  27. M. Van Dyke, Perturbation Methods in Fluid Mechanics, Academic Press, New York (1964).

    Google Scholar 

  28. L. M. Vardanyan, “Stress concentration near an aperture of arbitrary shape in a nonlinear elastic plate,” Prikl. Mekh.,6, No. 5, 125–130 (1970).

    Google Scholar 

  29. L. M. Vardanyan, “Stress concentration near an aperture of arbitrary shape in an isotropic physically nonlinear plate under a pure shear,” Izv. Akad. Nauk Arm. SSR, Mekh.,23, No. 1, 28–65 (1970).

    Google Scholar 

  30. L. M. Vardanyan, “Stress concentration near an oval aperture in an elastically nonlinear plate,” Kontsentratsiya Napryazhenii, Issue 3, 28–31 (1971).

    Google Scholar 

  31. L. M. Vardanyan, “Physically nonlinear problems for the stress concentration in singly connected and multiply connected regions,” Author's Abstract of Candidate's Dissertation, Technical Sciences, Erevan (1971).

  32. L. M. Vardanyan and I. A. Tsurpal, “Stress concentration for singly connected and multiply connected regions for a physically nonlinear material,” Tr. 7th All-Union Conf. on the Theory of Shells and Plates, Dnepropetrovsk, 1969 [in Russian], Nauka, Moscow (1970), pp. 137–141.

    Google Scholar 

  33. S. A. Vorob'ev, “Nature of the asymptotic radiation field emitted by a noncircular cylindrical shell in a fluid,” Central Scientific-Research Institute (TsNII), “Rumb” (1983); manuscript in VINITI, No. 1804.

  34. S. A. Vorob'ev, “Solution of dynamical problems for noncircular cylindrical shells in a fluid,” Dokl. Akad. Nauk Ukr. SSR, Ser. A, No. 5, 28–32 (1983).

    Google Scholar 

  35. S. A. Vorob'ev, “Dynamics of noncircular cylindrical shells in a fluid,” Author's Abstract of Candidate's Dissertation, Physicomathematical Sciences, Kiev (1983).

  36. S. A. Vorob'ev and A. N. Guz', “Emission of sound by noncircular cylindrical shells in a fluid,” Prikl. Mekh.,19, No. 8, 3–10 (1983).

    Google Scholar 

  37. 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 

  38. S. A. Goloborod'ko, “Stress near a square aperture with rounded corners in a cylindrical shell,” Prikl. Mekh.,1, No. 10, 21–29 (1965).

    Google Scholar 

  39. G. P. Grechka and D. I. Chernopiskii, “Stress concentration in nearly spherical cavities,” Prikl. Mekh.,19, No. 2, 29–32 (1983).

    Google Scholar 

  40. O. M. Guz', Prikl. Mekh.,8, No. 6, 605–612 (1962).

    Google Scholar 

  41. A. N. Guz', “Approximate solutions for the stress concentration near apertures in isotropic and orthotropic shells,” Author's Abstract of Candidate's Dissertation, Physicomathematical Sciences, Kiev (1962).

  42. O. M. Guz', “Stress concentration near an elliptical aperture of small eccentricity in a cylindrical shell,” Dop. Akad. Nauk Ukr. RSR, No. 10, 1326–1330 (1963).

    Google Scholar 

  43. O. M. Guz', Prikl. Mekh.,9, No. 1, 103–108 (1963).

    Google Scholar 

  44. A. N. Guz', “Stress concentration near curved apertures on the lateral surface of a circular cylinder,” Inzh. Zh., No. 2, 360–364 (1964).

    Google Scholar 

  45. O. M. Guz', “Torsion of a cylindrical shell weakened by a square aperture,” Dop. Akad. Ukr. RSR, No. 1, 41–44 (1965).

    Google Scholar 

  46. O. M. Guz', “Stress concentration near a square aperture in a spherical shell,” Dop. Akad. Nauk Ukr. RSR, No. 9, 1145–1150 (1964).

    Google Scholar 

  47. A. N. Guz', “Equilibrium of a spherical shell weakened by an aperture in the shape of an equilateral triangle,” Prikl. Mekh.,1, No. 3, 35–40 (1965).

    Google Scholar 

  48. O. M. Guz', “Torsion of a cylindrical shell weakened by an aperture in the shape of an equilateral triangle,” Dop. Akad. Nauk Ukr. RSR, No. 4, 472–476 (1964).

    Google Scholar 

  49. A. N. Guz', “Thin elastic shell weakened by apertures,” Author's Abstract of Candidate's Dissertation, Technical Sciences, Kiev (1965).

  50. A. N. Guz', “Stress concentration near apertures in thin shells (Review),” Prikl. Mekh.,5, No. 3, 1–17 (1969).

    Google Scholar 

  51. A. N. Guz', “Stress concentration near apertures (Review),” Tr. 7th All-Union Conf. on the Theory of Plates and Shells [in Russian], Nauka, Moscow (1970), pp. 788–794.

    Google Scholar 

  52. A. N. Guz', Dop. Akad. Nauk Ukr. RSR, Ser. A, No. 4, 352–355 (1970).

    Google Scholar 

  53. A. N. Guz', “On the diffraction of waves by finite bodies of revolution,” Prikl. Mekh.,9, No. 7, 10–18 (1973).

    Google Scholar 

  54. A. N. Guz', “On the propagation and diffraction of waves in bodies with noncircular cylindrical boundaries,” Prikl. Mekh.,9, No. 9, 3–11 (1973).

    Google Scholar 

  55. A. N. Guz', “On the continuum theory of composite materials with small-scale structural distortions,” Dokl. Akad. Nauk SSSR,208, No. 2, 307–313 (1983).

    Google Scholar 

  56. A. N. Guz', “Theory of vibration of composite materials with small-scale structural distortions,” Dokl. Akad. Nauk SSSR,270, No. 5, 1078–1081 (1983).

    Google Scholar 

  57. A. N. Guz', “Mechanics of composite materials with small-scale structural distortions,” Prikl. Mekh.,19, No. 5, 3–15 (1983).

    Google Scholar 

  58. A. N. Guz', “Quasiuniform state in composite materials with small-scale structural distortions,” Prikl. Mekh.,19, No. 6, 3–14 (1983).

    Google Scholar 

  59. G. V. Guz', “On a variant of the method of small parameter in a two-dimensional problem of the thermoelasticity of a cylindrically orthotropic body,” Mat. Fiz., No. 29, 82–87 (1981).

    Google Scholar 

  60. O. M. Guz' and S. O. Goloborod'ko, Prikl. Mekh.,10, No. 6, 595–599 (1964).

    Google Scholar 

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

    Google Scholar 

  62. A. N. Guz', R. Yu. Kerimov, and S. Yu. Kerimov, “On the diffraction of torsional waves by finite bodies of revolution,” Izv. Akad. Nauk Azer. SSR, Ser. Fiz.-Tekh. Mat. Nauk, No. 2, 144–149 (1973).

    Google Scholar 

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

    Google Scholar 

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

    Google Scholar 

  65. A. N. Guz' and Yu. N. Nemish, Perturbation Methods in Three-Dimensional Elastic Problems [in Russian], Vishchaya Shkola, Kiev (1982).

    Google Scholar 

  66. A. N. Guz' and Yu. N. Nemish, Statics of Elastic Bodies of Noncanonical Shape [in Russian], Naukova Dumka, Kiev (1984) (Three-Dimensional Problems of the Theory of Elasticity and Plasticity [in Russian], 6 vols., Vol. 2).

    Google Scholar 

  67. A. N. Guz' and G. N. Savin, “On the stress near curved fortified apertures in shells,” Inzh. Zh.,5, No. 1, 103–109 (1965).

    Google Scholar 

  68. A. N. Guz', G. N. Savin, and I. A. Tsurpal, “Stress concentration near curved apertures in a physically nonlinear elastic plate,” Arch. Mech. Stos.16, No. 4, 1009–1021 (1964).

    Google Scholar 

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

    Google Scholar 

  70. A. N. Guz', I. S. Chernyshenko, Val. N. Chekhov, Vik. N. Chekhov, and K. I. Shnerenko, Theory of Thin Shells Weakened by Apertures [in Russian], Naukova Dumka, Kiev (1980) (Computation Methods for Shells [in Russian], 6 vols., Vol. 1).

    Google Scholar 

  71. A. N. Guz', I. S. Chernyshenko, and K. I. Shnerenko, Spherical Caps Weakened by Apertures [in Russian], Naukova Dumka, Kiev (1970).

    Google Scholar 

  72. A. N. Guz' and K. I. Shnerenko, “On the stress of a shell weakened by two curved apertures,” Prikl. Mekh.,1, No. 5, 21–28 (1965).

    Google Scholar 

  73. A. N. Guz' and K. I. Shnerenko, “On the stress in a spherical shell weakened by two curved apertures,” Kontsentratsiya Napryazhenii, Issue 1, 120–124 (1965).

    Google Scholar 

  74. D. D. Ivlev and L. V. Ershov, Perturbation Method in the Theory of an Elastic-Plastic Body [in Russian], Nauka, Moscow (1978).

    Google Scholar 

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

    Google Scholar 

  76. R. M. Israfilov, “On the stress of a gas-saturated massif near an elliptical shaft,” Prikl. Mekh.,20, No. 2, 52–58 (1984).

    Google Scholar 

  77. R. M. Israfilov, “Stress in a massif near a shaft of arbitrary cross section,” Prikl. Mekh.,22, No. 8, 14–21 (1986).

    Google Scholar 

  78. S. M. Zverev, “Method of metaharmonic potentials in problems of hydroelasticity,” Dokl. Akad. Nauk Ukr. SSR, Ser. A., No. 11, 46–49 (1980).

    Google Scholar 

  79. M. A. Kan and I. E. Troyanovskii, “Three-dimensional elastic problems for a hollow, nearly circular cylinder,” Moscow Inst. of Electrical Eng., Moscow (1979); in VINITI, Nov. 13, 1979, No. 3859-79.

    Google Scholar 

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

    Google Scholar 

  81. G. Kauderer, Nonlinear Mechanics [Russian translation], IL, Moscow (1961).

    Google Scholar 

  82. Ya. F. Kayuk, Some Questions on Methods of Expansion in a Parameter [in Russian], Naukova Dumka, Kiev (1980).

    Google Scholar 

  83. A. D. Kovalenko and V. G. Karnaukhov, “On an approximate method of solving three-dimensional porblems in elasticity and viscoelasticity,” Prikl. Mekh.,5, No. 8, 1–10 (1969).

    Google Scholar 

  84. A. D. Kovalenko and V. G. Karnaukhov, “Approximate method of calculating the stress in thick shells of revolution,” Prikl. Mekh.,6, No. 6, 3–12 (1970).

    Google Scholar 

  85. M. A. Kovyryagin, “Stress in plates with complicated inner contours and under distributed loads,” Prikl. Teor. Uprug., pp. 89–93, Saratov (1980).

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

  87. A. S. Kosmodamianskii, Plane Elastic Problems of Plates with Apertures, Slots, and Ridges [in Russian], Vischaya Shkola, Kiev (1975).

    Google Scholar 

  88. A. S. Kosmodamianskii, Stress in an Anisotropic Medium with Apertures or Cavities [in Russian], Vischaya Shkola, Kiev; Donetsk (1976).

    Google Scholar 

  89. A. S. Kosmodamianskii, “Bending of anisotropic plates with curved apertures (Review),” Prikl. Mekh.,17, No. 2, 3–10 (1981).

    Google Scholar 

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

    Google Scholar 

  91. V. F. Kravtsov, “Stress state of a rotating noncircular disk,” Prikl. Teor. Uprug, pp. 84–88, Saratov (1980).

  92. V. F. Kravtsov, “On the effect of aperture radius on the stress of a rotating noncircular disk,” Zadachi Prikl. Teor. Uprug., pp. 74–78, Saratov (1985).

  93. V. D. Kubenko, “Some dynamical problems on the stress concentration near apertures,” Author's Abstract of Candidate's Dissertation, Physicomathematical Sciences, Kiev (1965).

  94. V. D. Kubenko, “Stress near an elliptical aperture subjected to an oscillating pressure,” Prikl. Mekh.,1, No. 5, 133–137 (1965).

    Google Scholar 

  95. V. D. Kubenko, “Dynamical stress concentration near a square aperture under a steady-state wave motion,” Prikl. Mekh.,2, No. 12, 67–75 (1966).

    Google Scholar 

  96. V. D. Kubenko, “Dynamical stress concentration near an elliptical aperture,” Dop. Akad. Nauk Ukr. RSR, No. 3, 60–64 (1967).

    Google Scholar 

  97. V. D. Kubenko, “On the propagation of plane harmonic shear waves in a plate with a square aperture,” Prikl. Mekh.4, No. 2, 129–133 (1968).

    Google Scholar 

  98. V. D. Kubenko, Yu. N. Nemish, K. I. Shnerenko, and N. A. Shul'ga, “Perturbation method in boundary-value problems of the mechanics of a deformable body,” Prikl. Mekh.,18, No. 11, 3–20 (1982).

    Google Scholar 

  99. V. V. Kuznetsov and I. V. Fedorkova, “Application of the method of perturbation of the region of integration in the calculation and design of elastic shells of revolution,” Saratov Polytechnic Inst. (1984); in VINITI, Feb. 25, 1985, No. 1413-85.

  100. G. G. Kuliev, “Effect of the rigidity of the reinforcing element on the stress concentration in singly connected and multiply connected physically nonlinear media,” Author's Abstract of Candidate's Dissertation, Physicomathematical Sciences, Kiev (1971).

  101. G. G. Kuliev, Dop. Akad. Nauk Ukr. RSR, Ser. A, No. 9, 801–804 (1971).

    Google Scholar 

  102. S. A. Kuliev, “Tapered groove of arbitrary shape at the edge of a half-plane,” Izv. Akad. Nauk SSSR, Ser. Fiz.-Tekh. Mat. Nauk,4, No. 2, 144–148 (1983).

    Google Scholar 

  103. G. V. Kutsenko and A. F. Ulitko, “Axisymmetric deformation in a hollow ellipsoid of revolution,” Tepl. Napryazh. Elem. Konstruk., Issue 11, 37–42 (1971).

    Google Scholar 

  104. M. A. Lavrent'ev, A. A. Deribas, E. I. Bichenkov, et al., “Explosive welding of metals,” in: Fundamental Research [in Russian], Nauka, Novosibirsk (1977), pp. 259–262.

    Google Scholar 

  105. A. D. Lapin, “Scattering of sound by an irregular waveguide at the critical frequencies of the normal wave,” Akust. Zh.,15, No. 4, 567–571 (1969).

    Google Scholar 

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

    Google Scholar 

  107. S. G. Lekhnitskii, Twisting of Anisotropic and Nonuniform Rods [in Russian], Nauka, Moscow (1971).

    Google Scholar 

  108. V. A. Lomakin, “Stress concentration near a surface with rapidly oscillating irregularities,” Prikl. Mekh.,4, No. 2, 1–8 (1968).

    Google Scholar 

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

    Google Scholar 

  110. V. A. Lomakin, Theory of Elasticity of Nonuniform Bodies [in Russian], Moscow Univ. (1976).

  111. P. Z. Lugovoi and N. A. Shul'ga, “Stress distribution near a curved aperture in a conical shell,” Prikl. Mekh.,12, No. 4, 41–46 (1967).

    Google Scholar 

  112. P. Z. Lugovoi and N. A. Shul'ga, “Stress distribution near a curved aperture in a conical shell under torsion,” Coprot. Mat. Teor. Cooruzh., Issue 48, 72–78 (1976).

    Google Scholar 

  113. E. I. Lun', “Some questions on the theory of shells with transverse shears,” Author's Abstract of Candidate's Dissertation, Physicomathematical Sciences, Lvov (1970).

  114. E. I. Lun' and A. A. Syas'kii, “On the calculation of the stress state near a curved aperture in a transversely isotropic shell,” Izv. Akad. Nauk Arm. SSR, Mekh.,26, No. 3, 64–70 (1973).

    Google Scholar 

  115. D. F. Lyalyuk, “On the stress state in thick noncanonical shells of revolution,” Prikl. Mekh.,17, No. 10, 120–123 (1981).

    Google Scholar 

  116. D. F. Lyalyuk, “Elastic equilibrium in thick noncanonial, nearly spherical shells,” Author's Abstract of Candidate's Dissertation, Physicomathematical Sciences, Kiev (1982).

  117. D. F. Lyalyuk and Yu. N. Nemish, “Approximate method of calculating the stress state of thick noncanonical shells of revolution,” Trans. 9th All-Union Conf. on the Theory, of Shells and Plates [in Russian], Sudostroenie, Leningrad (1975), pp. 280–282.

    Google Scholar 

  118. D. F. Lyalyuk, Yu. N. Nemish, and D. I. Chernopiskii, “Elastic equilibrium in thick transversely isotropic, nearly spherical shells,” Trans. 12th All-Union Conf. of the Theory of Shells and Plates [in Russian], Vol. 3, Erevan Univ. (1980), pp. 38–44.

    Google Scholar 

  119. A. P. Matkovskii, “Thermal stress in a thin spherical shell with a curved aperture,” Prikl. Mekh.,19, No. 3, 46–49 (1983).

    Google Scholar 

  120. Yu. I. Matyash, “Axisymmetric elastic equilibrium of a trilayered, transversely corrugated, transversely isotropic cylinder,” Prikl. Mekh.19, No. 6, 39–46 (1983).

    Google Scholar 

  121. Yu. I. Matyash, “Elastic equilibrium of multilayered corrugated thick-walled cylinders,” Author's Abstract of Candidate's Dissertation, Physicomathematical Sciences, Kiev (1984).

  122. Z. A. Medvedeva, “Bending of a transversely isotropic plate weakened by a curved aperture,” Prikl. Mekh.,22, No. 8, 35–41 (1986).

    Google Scholar 

  123. Ya. A. Metsavéér, N. D. Vexler, and A. S. Stulov, Diffraction of Acoustic Pulses by Elastic Bodies [in Russian], Nauka, Moscow (1979).

    Google Scholar 

  124. Yu. I. Mindlina, “Isotropic plate on an elastic foundation with a free noncircular boundary,” Prikl. Teor. Uprug., Saratov, 66–73 (1980).

    Google Scholar 

  125. A. N. Mikhailov, A. F. Belikov, and A. N. Dermin, “Experimental study of the process of wave formation in the explosive welding of metals,” Applied Methods [in Russian], Moscow (1977); Preprint, Academy of Sciences of the USSR, Inst. of Chemical Physics.

  126. A. K. Moiseenko and I. A. Tsurpal, “Thermal stress in a nonlinear hollow cylinder and in a plate with an aperture,” Tepl. Napryazh. Elem. Konstruk., Issue 7, 130–140 (1967).

    Google Scholar 

  127. P. M. Morse and H. Feshbach, Methods of Theoretical Physics (2 Vols.), McGraw-Hill, New York (1953), Vol. 2.

    Google Scholar 

  128. V. I. Mossakovskii and A. B. Kovura, “Contact problems for an elastic half-space with circular and nearly circular curves between boundary conditions,” Dinam. Prochn. Tyazh. Mashin, No. 5, 74–89 (1980).

    Google Scholar 

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

    Google Scholar 

  130. A. Naife, Perturbation Methods [Russian translation], Mir, Moscow (1976).

    Google Scholar 

  131. A. Naife, Introduction to Perturbation Methods [Russian translation], Mir, Moscow (1984).

    Google Scholar 

  132. G. Neiber, Concentration of Stress [in Russian], Gostekhizdat, Moscow-Leningrad (1947).

    Google Scholar 

  133. V. N. Nemish, “Deformation of an isotropic sphere with noncanonical inclusions,” Mat. Fiz., Issue 19, 104–109 (1976).

    Google Scholar 

  134. V. N. Nemish, “Stress distribution near closed axisymmetric cavities and inclusions under torsion,” Prikl. Mekh.13, No. 11, 32–40 (1977).

    Google Scholar 

  135. V. N. Nemish, “Elastic equilibrium of three-dimensional deformable bodies bounded by surfaces of revolution,” Author's Abstract of Candidate's Dissertation, Physicomathematical Sciences, Kiev (1979).

  136. V. N. Nemish, “Stress concentration near a nearly spherical cavity in a transversely isotropic medium,” Teor. Prikl. Mekh., No. 17, 12–19 (1986).

    Google Scholar 

  137. Yu. N. Nemish, “Stress concentration near curved apertures in the nonsymmetric theory of elasticity,” Prikl. Mekh.,2, No. 4, 85–96 (1966).

    Google Scholar 

  138. Yu. N. Nemish, “Two-dimensional problem in the moment theory of elasticity for a region with an aperture,” Author's Abstract of Candidate's Dissertation, Physicomathematical Sciences, Kiev (1966).

  139. Yu. N. Nemish, Dop. Akad. Nauk. Ukr. RSR, Ser. A, No. 9, 860–864 (1968).

    Google Scholar 

  140. Yu. N. Nemish, “On the stress state in a Kosser medium weakened by a curved aperture,” Prikl. Mekh.,4, No. 9, 49–57 (1968).

    Google Scholar 

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

    Google Scholar 

  142. Yu. N. Nemish, Dop. Akad. Nauk. Ukr. RSR, Ser. A, No. 6, 542–547 (1970).

    Google Scholar 

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

    Google Scholar 

  144. Yu. N. Nemish, Dop. Akad. Nauk. Ukr. RSR, Ser. A, No. 11, 1015–1019 (1970).

    Google Scholar 

  145. Yu. N. Nemish, “On the stress state of elastically nonlinear bodies,” Izv. Akad. Nauk SSSR, Mekh. Tverd. Tela, No. 4, 81–89 (1971).

    Google Scholar 

  146. Yu. N. Nemish, “Axisymmetric problem on the stress of an orthotropic elastic body,” Prikl. Mekh.,7, No. 6, 17–24 (1971).

    Google Scholar 

  147. Yu. N. Nemish, “On the thermostress of a physically nonlinear medium,” Tepl. Napryazh. Elem. Konstruk., Issue 11, 81–86 (1971).

    Google Scholar 

  148. Yu. N. Nemish, “Method of a small parameter in three-dimensional axisymmetric problems for a cylindrically orthotropic body,” Dop. Akad. Nauk Ukr. RSR, Ser. A, No. 3, 247–249 (1972).

    Google Scholar 

  149. Yu. N. Nemish, “Approximate method of calculating the symmetric deformation of orthotropic bodies,” Izv. Akad. Nauk SSSR, Mekh. Tverd. Tela, No. 5, 81–87 (1972).

    Google Scholar 

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

    Google Scholar 

  151. Yu. N. Nemish, Dop. Akad. Nauk Ukr. RSR, Ser. A, No. 2, 155–158 (1973).

    Google Scholar 

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

    Google Scholar 

  153. Yu. N. Nemish, “Recursion relations for the method of perturbation in three-dimensional elastic problems,” Prikl. Mekh.,9, No. 9, 64–70 (1973).

    Google Scholar 

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

    Google Scholar 

  155. Yu. N. Nemish, “Boundary-value problems in the theory of elasticity for noncanonical regions,” Dop. Akad. Nauk Ukr. RSR, Ser. A, No. 8, 743–747 (1974).

    Google Scholar 

  156. Yu. N. Nemish, “Method of perturbation of boundary shape in three-dimensional problems in the mechanics of a deformable body,” Izv. Akad. Nauk SSSR, Mekh. Tverd. Tela, No. 1, 17–26 (1975).

    Google Scholar 

  157. Yu. N. Nemish, “On a method of calculating the stress in a corrugated thick shell,” Trans. 1st All-Union School on the Theory and Numerical Analysis of Shells and Plates [in Russian], Tbilisi Univ. (1975), pp. 381–393.

  158. Yu. N. Nemish, “On a method of solving three-dimensional problems in the mechanics of a deformable body bounded by arbitrary surfaces,” Dokl. Akad. Nauk Ukr. SSR, Ser. A, No. 1, 48–52 (1976).

    Google Scholar 

  159. Yu. N. Nemish, “Foundations of the method of perturbation in three-dimensional problems in the mechanics of a deformable medium,” Prikl. Mekh.,13, No. 12, 25–33 (1977).

    Google Scholar 

  160. Yu. N. Nemish, “Approximate method of solving three-dimensional elastic problems for a curved orthotropic body in the case of a noncanonical region,” Prikl. Mekh.,14, No. 7, 10–17 (1978).

    Google Scholar 

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

  162. Yu. N. Nemish, “Three-dimensional boundary-value problems of elasticity for noncanonical regions,” Prikl. Mekh.,16, No. 2, 3–39 (1980).

    Google Scholar 

  163. Yu. N. Nemish, “Three-dimensional elastic problems for multilayered cylinders with noncanonical surfaces between layers,” Prikl. Mekh.,17, No. 5, 19–26 (1981).

    Google Scholar 

  164. Yu. N. Nemish, “Three-dimensional elastic problems for multilayered shells with nearly spherical surfaces between layers,” Prikl. Mekh.,17, No. 7, 23–29 (1981).

    Google Scholar 

  165. Yu. N. Nemish, “On boundary-value problems in heat conduction and thermoelasticity for nearly spherical, deformable bodies,” Prikl. Mekh.,17, No. 10, 42–50 (1981).

    Google Scholar 

  166. Yu. N. Nemish, “On boundary-value problems in heat conduction and thermoelasticity for nearly cylindrical, deformable bodies,” Prikl. Mekh.,18, No. 1, 28–35 (1982).

    Google Scholar 

  167. Yu. N. Nemish, “On a method of solving three-dimensional problems on the mechanics of a deformable cylinder with nonplanar ends,” Dokl. Akad. Nauk Ukr. SSR, Ser. A, No. 5, 34–37 (1982).

    Google Scholar 

  168. Yu. N. Nemish, “Study of the temperature and stress fields in a layered corrugated body,” Prikl. Mekh.,18, No. 5, 36–42 (1982).

    Google Scholar 

  169. Yu. N. Nemish, “Three-dimensional boundary-value problems for deformable cylinders with nonplanar ends,” Prikl. Mekh.,18, No. 6, 15–21 (1982).

    Google Scholar 

  170. Yu. N. Nemish, “Three-dimensional problem for a deformable cone with a symmetrically perturbed surface,” Dokl. Akad. Nauk Ukr. SSR, Ser. A, No. 7, 44–47 (1983).

    Google Scholar 

  171. Yu. N. Nemish, “Three-dimensional problem for a deformable cone with an asymmetrically perturbed surface,” Prikl. Mekh.,19, No. 3, 19–24 (1983).

    Google Scholar 

  172. Yu. N. Nemish, “Method of calculating temperature and stress fields in layered bodies of noncanonical shape,” Teor. Prikl. Mekh., No. 14, 16–24 (1983).

    Google Scholar 

  173. Yu. N. Nemish, “Study of the stress state of thick homogeneous and composite cylindrical shells with grooves,” All-Union Conf. on the Theory of Elasticity, Tbilisi (1984), pp. 205–206.

  174. Yu. N. Nemish, “Diffraction of waves by nearly spherical corrugated bodies,” Mat. Fiz., No. 34, 89–95 (1983).

    Google Scholar 

  175. Yu. N. Nemish, “On the stress state of an elastic layer in a foreign medium with a noncanonical interface,” Prikl. Mekh.,20, No. 9, 20–29 (1984).

    Google Scholar 

  176. Yu. N. Nemish, “Three-dimensional problem for the deformation of a composite cone with noncanonical surfaces,” Prikl. Mekh.,21, No. 8, 28–34 (1985).

    Google Scholar 

  177. Yu. N. Nemish and N. M. Bloshko, “Elastic equilibrium in a finite corrugated cylinder,” Prikl. Mekh.,19, No. 5, 16–23 (1983).

    Google Scholar 

  178. Yu. N. Nemish and N. M. Bloshko, “Elastic equilibrium of a transversely isotropic hollow cylinder of finite length with circular grooves,” Prikl. Mekh.,21, No. 11, 24–31 (1985).

    Google Scholar 

  179. Yu. N. Nemish and N. M. Bloshko, “Stress in a hollow elastic cylinder with nonplanar ends,” Prikl. Mekh.,22, No. 2, 17–23 (1986).

    Google Scholar 

  180. Yu. N. Nemish and N. M. Bloshko, Stress in an Elastic Cylinder with Grooves [in Russian], Naukova Dumka, Kiev (1987).

    Google Scholar 

  181. Yu. N. Nemish, N. M. Bloshko, G. P. Grechka, and D. I. Chernopiskii, “Numerical study of boundary effects in hollow cylinders with circular grooves under axisymmetric self-balancing loads,” Prikl. Mekh.,21, No. 5, 8–13 (1985).

    Google Scholar 

  182. Yu. N. Nemish, N. M. Bloshko, and D. I. Chernopiskii, “Three-dimensional elastic problems for finite and infinite nearly canonical regions,” Prikl. Mekh.,20, No. 1, 32–38 (1984).

    Google Scholar 

  183. Yu. N. Nemish, N. M. Bloshko, and D. I. Chernopiskii, “Three-dimensional elastic problems for finite and infinite nearly canonical regions,” 6th All-Union Conf. on Theoretical and Applied Mechanics: Compilation of Notes [in Russian], Tashkent (1986).

  184. Yu. N. Nemish, L. I. Trushina, and N. M. Bloshko, “On the stress state in a transversely corrugated hollow cylinder of finite length,” Raschet Prostr. Stroit. Konstruk., Issue 12, 66–72 (1985).

    Google Scholar 

  185. Yu. N. Nemish and R. M. Israfilov, “Coupled problem for the stress of a saturated porous medium near a noncircular cylindrical cavity,” Prikl. Mekh.,23, No. 4, 9–18 (1987).

    Google Scholar 

  186. Yu. N. Nemish and R. M. Israfilov, “Effect of coupling between the processes of deformation and filtration on the stress in a saturated medium near an elliptical cavity,” Prikl. Mekh.,23, No. 6, 73–78 (1987).

    Google Scholar 

  187. Yu. N. Nemish and D. F. Lyalyuk, “On the stress in a thick, nearly spherical noncanonical shell,” Prikl. Mekh.,19, No. 8, 29–34 (1983).

    Google Scholar 

  188. Yu. N. Nemish, D. F. Lyalyuk, and D. I. Chernopiskii, “Axisymmetric stress state of thick, nearly spherical elastic shells,” Prikl. Mekh.,18, No. 12, 18–24 (1982).

    Google Scholar 

  189. Yu. N. Nemish and Yu. I. Matyash, “On the stress in multilayered, thick, longitudinally corrugated cylinders,” Prikl. Mekh.,19, No. 11, 12–22 (1983).

    Google Scholar 

  190. Yu. N. Nemish and Yu. I. Matyash, “Stress in multilayered, thick, transversely corrugated cylinders,” Prikl. Mekh.,20, No. 6, 29–34 (1984).

    Google Scholar 

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

    Google Scholar 

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

    Google Scholar 

  193. Yu. N. Nemish and V. N. Nemish, “Stress in a transversely isotropic medium weakened by a closed, conical cavity,” Mat. Fiz.,26, 110–114 (1979).

    Google Scholar 

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

    Google Scholar 

  195. Yu. N. Nemish and B. L. Pelekh, “On an analogy between the bending of a plate of the Timoshenko type and a plane problem in the moment theory of elasticity,” Prikl. Mekh.,5, No. 4, 127–132 (1969).

    Google Scholar 

  196. Yu. N. Nemish and B. L. Pelekh, “Bending of a transversely isotropic plate with curved inclusions,” Prikl. Mekh.,6, No. 1, 119–124 (1970).

    Google Scholar 

  197. Yu. N. Nemish, B. L. Pelekh, and I. Yu. Khoma, “Bending of a transversely isotropic plate with curved apertures,” Prikl. Mekh.,5, No. 10, 87–95 (1969).

    Google Scholar 

  198. Yu. N. Nemish, I. S. Sagalyuk, and D. I. Chernopiskii, “Study of the axisymmetric stress state of a medium with noncanonical elastic inclusions,” Prikl. Mekh.,21, No. 6, 23–30 (1985).

    Google Scholar 

  199. Yu. N. Nemish, I. S. Sagalyuk, and D. I. Chernopiskii, “Axisymmetric stress state of an elastic medium with a nearly spherical reinforced cavity,” Prikl. Mekh.,21, No. 12, 41–47 (1985).

    Google Scholar 

  200. Yu. N. Nemish, I. S. Sagalyuk, and D. I. Chernopiskii, “Stress distribution in an elastic medium with a reinforced noncanonical cavity under a nonuniform load,” Prikl. Mekh.,23, No. 1, 23–29 (1987).

    Google Scholar 

  201. Yu. N. Nemish and D. I. Chernopiskii, “Thermostress of an elastically nonlinear hollow sphere under aerodynamic heating,” Prikl. Mekh.,10, No. 6, 15–26 (1974).

    Google Scholar 

  202. Yu. N. Nemish and D. I. Chernopiskii, “Axisymmetric stress in deformable cylinders of variable thickness,” Prikl. Mekh.,11, No. 10, 9–18 (1975).

    Google Scholar 

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

    Google Scholar 

  204. Yu. N. Nemish and D. I. Chernopiskii, “Asymptotic methods for thick shells bounded by noncoordinate surface,” Trans. 10th All-Union Conf. on the Theory of Shells and Plates (Kutaisi, 1975), Metsniereba, Tbilisi (1975), Vol. 1, pp. 235–243.

    Google Scholar 

  205. Yu. N. Nemish and D. I. Chernopiskii, “Some axisymmetric boundary-value problems on the statics of a transversely corrugated multilayered cylinder,” Prikl. Mekh.,13, No. 6, 38–46 (1977).

    Google Scholar 

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

    Google Scholar 

  207. Yu. N. Nemish and D. I. Chernopiskii, “Three-dimensional elastic boundary-value problems for a transversely corrugated, thick-walled cylinder,” Prikl. Mekh.,17, No. 12, 20–26 (1981).

    Google Scholar 

  208. Yu. N. Nemish and D. I. Chernopiskii, Elastic Equilibrium in Corrugated Bodies [in Russian], Naukova Dumka, Kiev (1982).

    Google Scholar 

  209. Yu. N. Nemish and D. I. Chernopiskii, “Three-dimensional stress state of a longitudinally corrugated elastic cylinder,” Izv. Akad. Nauk SSSR, Mekh. Tverd. Tela, No. 3, 55–62 (1983).

    Google Scholar 

  210. A. V. Netrebko and Z. S. Falaleeva, “Application of the method of perturbation to a problem on a strip with an irregular boundary,” Trans. Seminar on the Strength in Plates, Moscow (1984), pp. 4–9.

  211. V. A. Pal'mov, “Stress concentration near surface irregularities of an elastic body,” Izv. Akad. Nauk SSSR, Mekh. Tverd. Tela, No. 3, 104–108 (1963).

    Google Scholar 

  212. V. A. Pal'mov, “Stress state near surface irregularities of elastic bodies,” Prikl. Mat. Mekh.,27, No. 5, 963–969 (1963).

    Google Scholar 

  213. V. A. Pal'mov, “Elastic plane with an aperture of irregular shape,” Trans. Leningrad Polytechnic Inst., No. 235, 35–40 (1964).

    Google Scholar 

  214. B. L. Pelekh, “Solution of a problem on the bending of a plate for a multiply connected region,” Prikl. Mekh.,5, No. 9, 54–61 (1969).

    Google Scholar 

  215. B. L. Pelekh, Stress Concentration Near an Aperture of a Transversely Isotropic Plate Under Bend [in Russian], Naukova Dumka, Kiev (1977).

    Google Scholar 

  216. B. L. Pelekh and V. A. Laz'ko, Layered Anisotropic Plates and Shells with Stress Concentrators [in Russian], Naukova Dumka, Kiev (1982).

    Google Scholar 

  217. B. L. Pelekh and A. A. Syas'kii, Stress Distribution near Apertures in Anisotropic Shells Pliable to Shear [in Russian], Naukova Dumka, Kiev (1975).

    Google Scholar 

  218. B. L. Pelekh, A. A. Syas'kii, and V. A. Syas'kii, “Stress in a transversely isotropic spherical shell with a curved inclusion,” Mat. Met. Fiz.-Mekh. Polya, Issue 6, 49–53 (1977).

    Google Scholar 

  219. G. S. Pisarenko and A. A. Lebedev, Resistance of Materials to Deformation and Breakdown under Complicated Stress States [in Russian], Naukova Dumka, Kiev (1969).

    Google Scholar 

  220. G. V. Plyanko, O. V. Magiiovich, and V. N. Maksimovich, “Vibration of a hollow shell under a localized load,” Prikl. Mekh.,19, No. 8, 49–52 (1983).

    Google Scholar 

  221. Yu. N. Podil'chuk, “Approximation methods of solving boundary-value problems of elasticity for nearly-ellipsoidal figures,” Prikl. Mekh.,6, No. 9, 23–30 (1970).

    Google Scholar 

  222. Yu. N. Podil'chuk, Boundary Problems in the Statics of Elastic Bodies [in Russian], Naukova Dumka, Kiev (1984) [Three-Dimensional Problems of Elasticity and Plasticity (6 vols.); Vol. 1].

    Google Scholar 

  223. Yu. N. Podil'chuk and A. M. Kirichenko, “On an approximate method of solving boundary-value problems of elasticity for figures which are nearly ellipsoids of revolution,” Dokl. Akad. Nauk Ukr. SSR, Ser. A, No. 7, 650–655 (1970).

    Google Scholar 

  224. Yu. N. Podil'chuk and L. A. Neznakina, “Stress distribution near a short fiber soldered into a matrix,” Prikl. Mekh.,13, No. 5, 3–10 (1977).

    Google Scholar 

  225. Yu. N. Podil'chuk and L. A. Neznakina, “On an approximate method of solving threedimensional elastic problems,” Prikl. Mekh.,13, No. 10, 100–107 (1977).

    Google Scholar 

  226. V. K. Prokopov, “Review of the book ‘Statics of Elastic Bodies of Noncanonical Shape’,” Prikl. Mekh.,21, No. 8, 123–127 (1985).

    Google Scholar 

  227. G. N. Savin, “Stress distribution in thin shells weakened by an aperture”, Problems in Continuum Mechanics [in Russian], Izd. Akad. Nauk SSSR (1961), pp. 338–358.

  228. G. N. Savin, “Stress concentration near apertures in shells”, Theory of Plates and Shells [in Russian], Izd. Akad. Nauk Ukr. SSR, Kiev (1962), pp. 70–85.

    Google Scholar 

  229. G. N. Savin, “Stress concentration near curved apertures in plates and shells”, Konts. Napryazh., Issue 1, 5–38 (1965).

    Google Scholar 

  230. G. N. Savin, Fundamentals of Plane Problems in the Moment Theory of Elasticity [in Russian], Kiev Univ. (1965).

  231. G. N. Savin, “Stress concentration near curved apertures in plates and shells”, Trans. 2nd All-Union Conf. on Theoretical and Applied Mechanics, Issue 3, pp. 295–308 (1966).

    Google Scholar 

  232. G. N. Savin, Stress Distribution near Apertures [in Russian], Naukova Dumka, Kiev (1968).

    Google Scholar 

  233. G. N. Savin and A. N. Guz', “Stress concentration near an elliptical aperture in a spherical shell”, Dop. Akad. Nauk Ukr. RSR, Ser. A, No. 1, 54–58 (1964).

    Google Scholar 

  234. G. N. Savin and A. N. Guz', “Stress state near curved apertures in shells”, Izv. Akad. Nauk SSSR, Mekh. Mashinostr., No. 6, 96–105 (1964).

    Google Scholar 

  235. G. N. Savin and A. N. Guz', “On a method of solving plane problems of the moment theory of elasticity for multiply connected regions”, Prikl. Mekh.,2, No. 1, 3–19 (1968).

    Google Scholar 

  236. G. N. Savin, A. N. Guz', and I. A. Tsurpal, “Physically nonlinear problems for plates and shells weakened by apertures”, in: Physically and Geometrically Nonlinear Problems of the Theory of Plates and Shells [in Russian], Tartu Univ. (1966), pp. 204–234.

  237. G. N. Savin, A. S. Kosmodamianskii, and A. N. Guz', “Stress concentration near apertures”, Prikl. Mekh.,3, No. 10, 21–37 (1967).

    Google Scholar 

  238. G. N. Savin and Yu. N. Nemish, “On stress concentration in the moment theory of elasticity”, Prikl. Mekh.,4, No. 12, 1–17 (1968).

    Google Scholar 

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

    Google Scholar 

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

    Google Scholar 

  241. V. S. Sedykh, “Explosive welding”, in: Welding in Mechanical Engineering., N. A. Ol'shanskii (ed.), Mashinostroenie, Moscow (1978); Vol. 1, pp. 362–375.

    Google Scholar 

  242. A. E. Andreev (ed.), Bellows. Calculation and Design [in Russian], Mashinostroenie, Moscow (1975).

    Google Scholar 

  243. L. V. Slepneva, “Effect of the boundary conditions on the stress distribution near an elliptical aperture in a spherical shell”, Prikl. Mekh.,4, No. 7, 40–48 (1968).

    Google Scholar 

  244. Slot and Moubray, “Note on the coefficients of stress concentration for symmetric U-shaped grooves in planar samples”, Tr. Am. o-va Inzh. Mekh., Ser. E, Prikl. Mekh.,36, No. 4, 241–242 (1969).

    Google Scholar 

  245. Collected Works of Academician A. N. Krylov, Publ. by the Academy of Sciences of the USSR, Moscow-Leningrad (1948), Vol. 10.

  246. A. A. Syas'kii, “Stress concentration near apertures in shells with finite rigidity to shear”, Author's Abstract of Candidate's Dissertation, Physicomathematical Sciences, Lvov (1972).

  247. A. A. Syas'kii, “Stress concentration in a piecewise-homogeneous orthotropic spherical shell with a curved aperture”, Prikl. Mekh.,14, 132–136 (1978).

    Google Scholar 

  248. A. A. Syas'kii and V. A. Syas'kii, “Stress in a piecewise-homogeneous spherical shell with a curved aperture”, Prikl. Mekh.,12, No. 7, 18–23 (1976).

    Google Scholar 

  249. A. G. Vgodchikov and V. A. Soboleva, “Stress concentration near curved apertures in plates in the Reissner theory”, Prikl. Mekh.,8, No. 6, 58–66 (1972).

    Google Scholar 

  250. A. I. Uzdalev, Thermal Stress in Plates Bounded by a Doubly Connected Contour [in Russian], Saratov Univ. (1975).

  251. K. U. Urazgil'dyaev, A. G. Cheberyak, V. A. Chubok, and P. G. Shishkin, “Stress state of a bilayered plate with a wavy surface”, Prikl. Mekh.,11, No. 12, 48–53 (1975).

    Google Scholar 

  252. N. N. Fotieva and V. G. Garaichuk, “Diffraction of harmonic elastic waves radiated by sources near apertures of arbitrary shape”, in: Theory and Application of Mechanics, 4th Congress, Bulg. Akad. Nauk, Sofia (1980), pp. 64–69.

  253. G. D. Khan'zhova, “Temperature distribution in a finite noncircular cylinder”, Mekh. Deform. Sred., Issue 4, 25–32 (1976).

    Google Scholar 

  254. G. M. Khatiashvili, “On the deformation of a cylindrical body with a slightly canted axis”, Tr. Vychisl. Tsentra GSSR,20, No. 1, 104–115 (1980).

    Google Scholar 

  255. G. M. Khatiashvili, “Approximate solution of a Saint-Venant problem for a nearly cylindrical body”, Prikl. Mekh.,17, No. 4, 10–15 (1981).

    Google Scholar 

  256. G. M. Khatiashvili, Almansi-Mitchell Problem for Homogeneous and Composite Bodies [in Russian], Metsniereba, Tbilisi (1983), Chap. 1.

    Google Scholar 

  257. L. P. Khoroshun, “Theory of saturated porous media”, Prikl. Mekh.,12, No. 12, 35–41 (1976).

    Google Scholar 

  258. L. P. Khoroshun and R. M. Israfilov, “Stress state near a shaft with a square cross section”, Prikl. Mekh.,20, No. 11, 108–111 (1984).

    Google Scholar 

  259. L. P. Khoroshun and E. N. Shikula, “Stress state near an ellipsoidal shaft in a gas-saturated massif for unsteady filtration of the gas”, Prikl. Mekh.,20, No. 4, 14–18 (1984).

    Google Scholar 

  260. L. P. Khoroshun and E. N. Shikula, “Nonaxisymmetric stress state near a cylindrical shaft in a gas-saturated massif for unsteady filtration of the gas”, Prikl. Mekh.,21, No. 8, 10–17 (1985).

    Google Scholar 

  261. A. P. Khusu, Yu. R. Vitenberg, and V. A. Pal'mov, Surface Irregularities: Probability-Theoretic Approach [in Russian], Nauka, Moscow (1975).

    Google Scholar 

  262. I. A. Tsurpal, “Stress concentration near a curved aperture in a plate for a nonlinear law of elasticity”, Tr. I Recp. Konf. Molodykh Uchenykh, Issue 2, pp. 705–716 (1965).

    Google Scholar 

  263. I. A. Tsurpal, “Stress concentration near a square aperture in a physically nonlinear elastic plate”, Izv. Akad. Nauk SSSR, Mekh., No. 6, 71–76 (1965).

    Google Scholar 

  264. I. A. Tsurpal, “Stress state near a curved aperture in a physically nonlinear elastic plate”, Prochn. Korp. Sudna, Issue 67, 125–139 (1965).

    Google Scholar 

  265. I. A. Tsurpal, “Physically nonlinear elastic plate weakened by an arbitrary aperture”, Kontsentr. Napryazh., Issue 1, 305–311 (1965).

    Google Scholar 

  266. I. A. Tsurpal, “Thermostress concentration near arbitrary apertures for elastically nonlinear materials”, Tepl. Napryazh. Elem. Konstruk, Issue 8, 182–187 (1969).

    Google Scholar 

  267. I. A. Tsurpal, “Some problems on the stress concentration near apertures for a physically nonlinear material”, Author's Abstract of Candidate's Dissertation, Technical Sciences, Kiev (1968).

  268. I. A. Tsurpal, “On a nonlinear stress concentration problem”, Prikl. Mekh.,4, No. 10, 51–58 (1968).

    Google Scholar 

  269. I. A. Tsurpal, “Stress concentration problems for highly elastic materials”, Stroit. Mekh. Korabl., Issue 10, 27–30 (1968).

    Google Scholar 

  270. I. A. Tsurpal, “Some problems of stress concentration near apertures and cavities for physically nonlinear material”, Kontsentr. Napryazh., Issue 2, 241–254 (1968).

    Google Scholar 

  271. I. A. Tsurpal, “Foundations of the theory of physically nonlinear bodies and its application to structural elements with apertures”, in: Polymers in Mechanical Engineering [in Russian], Kharkov Univ. (1972), Vol. 6, pp. 146–150.

  272. I. A. Tsurpal, Calculation of Structural Elements of Elastically Nonlinear Materials [in Russian], Tekhnika, Kiev (1976).

    Google Scholar 

  273. I. A. Tsurpal and M. A. Kuliev, “Solution of a plane, nonlinear elastic problem for the stress concentration in a biconical plate with a reinforced curved aperture”, 2nd Science and Engineering Conf. on Engineering Mechanics of Ships (Memory of Academician Yu. A. Shimanskii), Leningrad (1965), pp. 11–12.

  274. I. A. Tsurpal and G. G. Kuliev, “Problems of stress concentration in physically non-linear materials (Review)”, Prikl. Mekh.,10, No. 7, 3–22 (1974).

    Google Scholar 

  275. I. A. Tsurpal and N. G. Tamurov, Calculation of Multiply Connected and Elastically Nonlinear Plates and Shells [in Russian], Vyshchaya Shkola, Kiev (1977).

    Google Scholar 

  276. I. A. Tsurpal and N. A. Shul'ga, “Stress state near curved apertures in shells for a nonlinear law of elasticity”, Prikl. Mekh.,2, No. 8, 51–58 (1966).

    Google Scholar 

  277. D. I. Chernopiskii, “On the stress in thick corrugated spherical shells”, Prikl. Mekh.,15, No. 10, 128–133 (1979).

    Google Scholar 

  278. D. I. Chernopiskii, “Study of the stress in thick elastic corrugated shells”, Author's Abstract of Candidate's Dissertation, Physicomathematical Sciences, Kiev (1980).

  279. V. N. Chekhov, “Stress in a cylindrical shell with a moderately large curved aperture”, Prikl. Mekh.,6, No. 6, 116–120 (1970).

    Google Scholar 

  280. V. N. Chekhov, “On the stress distribution in a cylindrical shell with an elliptical aperture”, Prikl. Mekh.,7, No. 11, 41–46 (1971).

    Google Scholar 

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

    Google Scholar 

  282. R. N. Shvets and V. I. Éleiko, Dop. Akad. Nauk Ukr. RSR, Ser. A, No. 11, 1020–1023 (1977).

    Google Scholar 

  283. R. N. Shvets and V. I. Eleiko, “Stochastic thermal stress in a cylinder with an irregular surface”, Prikl. Mekh.,13, No. 12, 39–45 (1977).

    Google Scholar 

  284. R. N. Shvets and A. P. Matkovskii, “Thermal stress in a hollow cylindrical shell with a curved aperture”, Prikl. Mekh.,20, No. 12, 63–70 (1984).

    Google Scholar 

  285. R. N. Shvets, A. P. Matkovskii, and V. D. Pavlenko, “Temperature field in a thin shell with a curved aperture”, in: Applied Thermoelasticity [in Russian], Naukova Dumka, Kiev (1979), pp. 31–36.

    Google Scholar 

  286. E. N. Shikula, “Axisymmetric stress state near a shaft in the shape of an ellipsoid of revolution caused by unsteady filtration”, Trans. 9th Sci. Conf. of Students of the Inst. of Mechanics, Academy of Sciences of the Ukrainian SSR, Kiev (1982), pp. 230–234; in: VINITI, May 27, 1982, No. 2644-82.

  287. E. N. Shikula, “Nonaxisymmetric stress state near an ellipsoidal shaft in a gas-saturated massif for unsteady filtration of the gas”, Prikl. Mekh.,20, No. 8, 18–24 (1984).

    Google Scholar 

  288. E. N. Shikula, “Axisymmetric stress state near a cylindrical shaft in a gas-saturated massif for unsteady filtration of the gas”, Prikl. Mekh.,21, No. 9, 16–21 (1985).

    Google Scholar 

  289. E. N. Shikula, “Stress state near shafts in a gas-saturated porous massif for unsteady filtration of the gas”, Author's Abstract of Candidate's Dissertation, Physicomathematical Sciences, Kiev (1985).

  290. K. I. Shnerenko, “Stress distribution in a spherical shell around reinforced curved apertures”, Prikl. Mekh.,2, No. 11, 55–62 (1966).

    Google Scholar 

  291. K. I. Shnerenko, “Some equilibrium problems for spherical shells with apertures”, Author's Abstract of Candidate's Dissertation, Physicomathematical Sciences, Kiev (1966).

  292. K. I. Shnerenko, “Stress in composite shells with apertures”, Author's Abstract of Candidate's Dissertation, Technical Sciences, Kiev (1981).

  293. N. A. Shul'ga, “Bending of a thin plate weakened by a curved aperture for a nonlinear law of elasticity”, Prikl. Mekh.,2, No. 4, 50–54 (1966).

    Google Scholar 

  294. N. A. Shul'ga, “Stress concentration near apertures for the bending of a thin, physically nonlinear plate”, Author's Abstract of Candidate's Dissertation, Physicomathematical Sciences, Kiev (1966).

  295. N. A. Shul'ga, “Stress state near an aperture in a thin, physically nonlinear plate”, Prikl. Mekh.,3, No. 12, 115–118 (1967).

    Google Scholar 

  296. N. A. Shul'ga, “Stress concentration near an aperture for the bending of a physically nonlinear plate”, Sci.-Eng. Conf. on the Effect of Stress Concentration on the Strength of the Components of Machines and of Structural Elements, Kiev (1970), pp. 44–46.

  297. N. A. Shul'ga and P. Z. Lugovoi, “Stress concentration near a curved aperture in a conical shell”, Dop. Akad. Nauk Ukr. RSR, Ser. A, No. 8, 725–729 (1976).

    Google Scholar 

  298. J. I. D. Alexander, P. H. Leo, and R. F. Sekerka, “Elastic fields about a perturbed cylindrical inclusion”, Acta Met.,33, No. 6, 975–983 (1985).

    Google Scholar 

  299. A. J. Basu and T. J. Lardner, “Deformation of a strip containing wavy inextensible fibers”, Mech. Res. Commun.,12, No. 3, 163–171 (1985).

    Google Scholar 

  300. J. P. Curtis, “Optimization of homogeneous thermal insulation layers”, Int. J. Sol. Struct.,19, No. 9, 813–823 (1983).

    Google Scholar 

  301. 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 

  302. Gai Biengzbeg, “The asymptotic method for problems of the diffraction of SH waves from a noncircular cylinder”, Acta Mech. Sin.,16, No. 1, 96–103 (1984).

    Google Scholar 

  303. P. H. Leo, J. I. D. Alexander, and R. F. Sekerka, “Elastic fields about a perturbed spherical inclusion”, Acta Met.,33, No. 6, 985–989 (1985).

    Google Scholar 

  304. M. Misicu, Teoria Mobilitatii Elastice, Editura Akademie R. S., Romaina Bucharest, (1972).

    Google Scholar 

  305. C. Panek and J. Dundurs, “Thermoelastic contact between bodies with wavy surfaces”, Trans. ASME, J. Appl. Mech.,46, No. 4, 854–860 (1979).

    Google Scholar 

  306. S. R. Reid, “A discussion of the mechanism of interface wave generation in explosive welding”, Int. J. Mech. Sci.,16, No. 6, 399–413 (1974).

    Google Scholar 

  307. G. N. Savin (Sawin), A. N. Guz' (Guz), and A. S. Kosmodamianskii (Kosmodamiaskij), Mech. Teor. Stosowana,8, No. 1, 3–18 (1970).

    Google Scholar 

  308. M. Skowronek, Rozpr. Inz.,29, No. 4, 527–543 (1981).

    Google Scholar 

  309. R. S. Tennyson, D. K. Roberts, and D. Zimcik, “Analysis of the stress distribution around unreinforced cutouts in circular cylindrical shells under axial compression”, NRC, NASA, Ann. Progr. Rept., UTJAS (1968), pp. 118–129.

  310. Z. Zhou and Shu Wang, “The method of matrix conjoint multiplication for the problem of a circular arc corrugated diaphragm”, Appl. Math. Mech.,6, No. 6, 551–566 (1985).

    Google Scholar 

Download references

Authors
  1. A. N. Guz'
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Yu. N. Nemish
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Institute of Mechanics, Academy of Sciences of the Ukrainian SSR, Kiev. Translated from Prikladnaya Mekhanika, Vol. 23, No. 9, pp. 3–29, September, 1987.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Guz', A.N., Nemish, Y.N. Perturbation of boundary shape in continuum mechanics (review). Soviet Applied Mechanics 23, 799–822 (1987). https://doi.org/10.1007/BF00887782

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00887782

Keywords

Search

Navigation