Skip to main content
SpringerLink
Log in

Stability of smooth and ribbed shells of revolution in a nonuniform stress-strain state (survey)

  • Published:
International 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

References

  1. É. L. Axelrod, Flexible Shells [Russian translation], Nauka, Moscow (1976).

    Google Scholar 

  2. N. A. Alumyae, "Representation of the basic relations of the nonlinear theory of shells," Prikl. Mat. Mekh.,20, No. 1, 136–139 (1956).

    Google Scholar 

  3. I. Ya. Amiro, O. A. Grachev, V. A. Zarutskii, et al., Stability of Ribbed Shells of Revolution [in Russian], Nauk. Dumka, Kiev (1987).

    Google Scholar 

  4. I. Ya. Amiro, V. A. Zarutskii, and P. S. Polyakov, Ribbed Cylindrical Shells [in Russian], Nauk. Dumka, Kiev (1973).

    Google Scholar 

  5. I. Ya. Amiro and V. A. Zarutskii, Theory of Ribbed Shells [in Russian], Vol. 2 of Methods of Shell Design (5 vols.), Nauk. Dumka, Kiev (1973).

    Google Scholar 

  6. I. Ya. Amiro and V. A. Zarutskii, "Studies in the area of the stability of ribbed shells," Prikl. Mekh.,19, No. 11, 3–20 (1983).

    Google Scholar 

  7. I. Ya. Amiro and V. A. Zarutskii, "Statics, dynamics, and stability of ribbed shells," Mekh. Def. Tv. Tela,21, 132–91 (1990).

    Google Scholar 

  8. I. Ya. Amiro and N. Ya. Prokopenko, "Refinement of critical loads for a ribbed cylindrical shell determined on the basis of a monomial approximation of the displacements," Prikl. Mekh.,23, No. 7, 20–26 (1987).

    Google Scholar 

  9. I. Ya. Amiro, V. A. Zarutskii, V. N. Revutskii, Yu. V. Skosarenko, A. I. Telalov, and S. Yu. Fialko, Vibrations of Ribbed Shells of Revolution [in Russian], Nauk. Dumka, Kiev (1988).

    Google Scholar 

  10. I. Arboch, "Investigation of the stability of shells: theory and practice," in: Loss of Stability and Buckling of Structures: Theory and Practice [Russian translation], Nauka, Moscow (1991).

    Google Scholar 

  11. I. Arboch, G. V. Babel, S. Ch. Butterman, et al., in: Thin-Walled Shell Structures: Theory, Experiment, and Design [Russian translation], Mashinostroenie, Moscow (1980).

    Google Scholar 

  12. V. A. Bazhenov, E. A. Gotsulyak, A. I. Ogloblya, et al., Design of Composite Structures with Allowance for Delamination [in Russian], Budivel'nik, Kiev (1992).

    Google Scholar 

  13. R. Bellman and R. Kalaba, Quasilinearization and Nonlinear Boundary-Value Problems [Russian translation], Mir, Moscow (1968).

    Google Scholar 

  14. I. A. Birger, Circular Plates and Shells of Revolution [in Russian], Oborongiz, Moscow (1961).

    Google Scholar 

  15. G. A. Vanin, N. P. Semenyuk, and R. F. Emel'yanov, Stability of Shells Made of Reinforced Materials [in Russian], Nauk. Dumka, Kiev (1978).

    Google Scholar 

  16. V. Z. Vlasov, General Theory of Shells and Its Use in Engineering [in Russian], Gostekhizdat, Moscow, Leningrad (1949).

    Google Scholar 

  17. A. S. Vol'mir, Stability of Deformable Systems [in Russian], Nauka, Moscow (1967).

    Google Scholar 

  18. I. I. Vorovich, "Existence of solutions in the nonlinear theory of shells," Izv. Akad. Nauk SSSR Ser. Mat.,19, 173–176 (1955).

    Google Scholar 

  19. I. I. Vorovich, "Some direct methods in the nonlinear theory of shallow shells," Prikl. Mat. Mekh.,20, No. 4, 449–474 (1956).

    Google Scholar 

  20. I. I. Vorovich, Mathematical Problems of the Nonlinear Theory of Shallow Shells [in Russian], Nauka, Moscow (1989).

    Google Scholar 

  21. I. I. Vorovich and V. F. Zipalova, "Solution of nonlinear boundary-value problems of the theory of elasticity by the method of conversion to a Cauchy problem," Prikl. Mat. Mekh.,29, No. 5, 894–901 (1965).

    Google Scholar 

  22. I. I. Vorovich and N. M. Minakova, "Stability of a nonshallow spherical dome," Prikl. Mat. Mekh.,32, No. 2, 332–338 (1968).

    Google Scholar 

  23. I. I. Vorovich and N. M. Minakova, "Stability problems and numerical methods in the theory of spherical shells," Itogi Nauki Tekh. Ser. Mekh. Deform. Tela,7, 5–86 (1973).

    Google Scholar 

  24. I. I. Vorovich and V. G. Shepeleva, "Study of the nonlinear stability of a shallow shell of double curvature in high approximations," Izv. Akad. Nauk SSSR Mekh. Tverd. Tela, No. 3, 69–73 (1969).

  25. G. D. Gavrilenko, "Finite-difference equations for calculating the stress — strain state of ribbed cylindrical shells," Samoletostr. Tekh. Vozdushn. Flota,42, 102–106 (1977).

    Google Scholar 

  26. G. D. Gavrilenko, "Study of nonuniform nonlinear problems of the theory of ribbed shells," Prikl. Mekh., No. 9, 25–31 (1979).

  27. G. D. Gavrilenko, "Stability of flawed cylindrical shells," Dopov. Akad. Nauk Ukr. RSR, Ser. A, No. 7, 523–528 (1979).

  28. G. D. Gavrilenko, "Stability of stringer-reinforced shells in a nonuniform stress-strain state," Prikl. Mekh.,16, No. 11, 41–46 (1980).

    Google Scholar 

  29. G. D. Gavrilenko, "Method of numerically solving nonaxisymmetric nonlinear problems of the statics and vibration of thin-walled ribbed cylindrical shells," Dopov. Akad. Nauk Ukr. RSR Ser. A, No. 3, 22–26 (1981).

  30. G. D. Gavrilenko, "Stability of cylindrical shells with longitudinal indentations," Din. Prochn. Mash.,33, 32–35 (1981).

    Google Scholar 

  31. G. D. Gavrilenko, "Stability of flawed ribbed cylindrical shells with linear and nonlinear subcritical states," in: Stability of Plates and Shells [in Russian], Izd. Saratov, Un-ta, Saratov (1981), pp. 20–22.

    Google Scholar 

  32. G. D. Gavrilenko, "Study of the effect of local and regular asymmetric deflections on the critical loads of ribbed shells," Prikl. Mekh.,18, No. 4, 53–57 (1982).

    Google Scholar 

  33. G. D. Gavrilenko, "Basic nonlinear equations of the theory of imperfect ribbed shells of revolution," Dopov. Akad. Nauk Ukr. RSR Ser. A, No. 7, 523–528 (1982).

  34. G. D. Gavrilenko, Stability of thin-walled ribbed conical shells," Prikl. Mekh.,19, No. 1, 36–40 (1983).

    Google Scholar 

  35. G. D. Gavrilenko, "Basic nonlinear and linearized equations of the theory of imperfect ribbed shells of revolution," Prikl. Mekh.,19, No. 7, 55–60 (1983).

    Google Scholar 

  36. G. D. Gavrilenko, "Stability of cylindrical shells subjected to concentrated forces," Prikl. Mekh.,6, No. 3, 25–31 (1970).

    Google Scholar 

  37. G. D. Gavrilenko, "Effect of shape defects and the stiffness characteristics of the ribs on the stability of conical shells," Prikl. Mekh.,22, No. 11, 55–60 (1986).

    Google Scholar 

  38. G. D. Gavrilenko, "Boundary conditions and differential equations of equilibrium and stability of nonideal ribbed shells of revolution," Probl. Prochn., No. 6, 96–99 (1987).

  39. G. D. Gavrilenko, "Calculation of the stress-strain state of laminated cylindrical shells with ribs," Probl. Prochn., No. 6, 74–78 (1988).

  40. G. D. Gavrilenko, "Stability of flawed spherical sections under external pressure," Dokl. Akad. Nauk Ukr. RSR Ser. A, No. 7, 33–36 (1988).

  41. G. D. Gavrilenko, "Stability of spherical sections," Probl. Prochn., No. 10, 118–120 (1990).

  42. G. D. Gavrilenko, Stability of Ribbed Cylindrical Shells in a Nonuniform Stress-Strain State [in Russian], Nauk. Dumka, Kiev (1989).

    Google Scholar 

  43. G. D. Gavrilenko, Numerical Methods of Calculating the Stability of Reinforced Shells [in Russian], Nauk. Dumka, Kiev (1991).

    Google Scholar 

  44. G. D. Gavrilenko, "Stability of cylindrical shells under combination loading," Dopov. Akad. Nauk Ukr. RSR Ser. A, No. 7, 41–43 (1992).

  45. G. D. Gavrilenko and N. E. Aranchii, "Method of calculating the stability of imperfect elastic and inelastic ribbed shells of revolution," Sopr. Mater. Teor. Sooruzh.,56, 19–24 (1990).

    Google Scholar 

  46. G. D. Gavrilenko, M. F. Dudnik, and I. F. Larionov, "Stability of ribbed cylindrical shells in the presence of nonaxisymmetric dents," Prikl. Mekh.,20, No. 21, 31–35 (1984).

    Google Scholar 

  47. G. D. Gavrilenko and V. I. Matsner, "Subcritical state of ribbed spherical sections," Prikl. Mekh.,27, No. 11, 118–121 (1991).

    Google Scholar 

  48. G. D. Gavrilenko and V. I. Matsner, "Stability of cylindrical shells with a spiral reinforcement," Probl. Prochn., No. 3, 110–113 (1990).

  49. G. D. Gavrilenko and V. I. Matsner, "Study of the local strength and stability of reinforced elements by the finite-differences method," Sudostroenie,40, 17–21 (1991).

    Google Scholar 

  50. G. D. Gavrilenko, V.I. Matsner, and V. N. Vaisman, "Effect of the angle of inclination of the spiral reinforcement on the stability of conical shells," Sopr. Mater. Teor. Sooruzh.,58, 35–38 (1991).

    Google Scholar 

  51. G. D. Gavrilenko, V. I. Matsner, and A. S. Sitnik, "Stability of flawed conical shells with a spiral reinforcement," Probl. Prochn., No. 12, 67–70 (1991).

  52. G. D. Gavrilenko, V. I. Matsner, A. S. Sitnik, and S. N. Bilyk, "Stability of ribbed cylindrical shells under combination loading," Prikl. Mekh.,30, No. 1, 31–35 (1994).

    Google Scholar 

  53. G. D. Gavrilenko, A. S. Pal'chevskii, and Yu. E. Yakubovskii, "Determination of the critical loads of nonideal models of shells," Probl. Prochn., No. 6, 68–72 (1985).

  54. G. D. Gavrilenko, V. A. Polyakov, and A. S. Sitnik, "Experimental and theoretical study of the stability of elements of air flues," Probl. Prochn., No. 7, 119–120 (1988).

  55. G. D. Gavrilenko, A. A. Rudometskin, A. S. Sitnik, and S. S. Khalyuk, "Distribution of deflections and forces in a panel with an irregular reinforcement," Prikl. Mekh.,25, No. 9, 68–72 (1989).

    Google Scholar 

  56. G. D. Gavrilenko and A. S. Sitnik, "Study of the upper critical loads associated particular buckling modes for stringer-reinforced shells," Prikl. Mekh.,17, No. 3, 68–73 (1981).

    Google Scholar 

  57. G. D. Gavrilenko and A. S. Sitnik, "Analysis of buckling modes of ribbed shells," Probl. Prochn., No. 2, 68–70 (1984).

  58. G. D. Gavrilenko and A. S. Sitnik, "Stability of ribbed shells with local indentations," Prikl. Mekh.,21, No. 11, 128–130 (1985).

    Google Scholar 

  59. G. D. Gavrilenko and A. S. Sitnik, "Stability of nonideal ribbed spherical sections," Prikl. Mekh.,26, No. 8, 43–46 (1990).

    Google Scholar 

  60. G. D. Gavrilenko, A. S., Sitnik, and A. L. Livshitz, "Stability of ring-reinforced shells subjected to nonuniform external pressure," Teor. Avtomat. Proektr., No. 4, 115–120 (1982).

  61. G. D. Gavrilenko and A. S. Stepanenko, "Stability of orthotropic cylindrical shells with allowance for the moments in the subcritical state," Prikl. Mekh.,5, No. 3, 36–42 (1969).

    Google Scholar 

  62. G. D. Gavrilenko and A. S. Stepanenko, "Effect of boundary conditions and elastic characteristics on the stability of orthotropic cylindrical shells," Prikl. Mekh.,7, No. 10, 62–66 (1971).

    Google Scholar 

  63. G. D. Gavrilenko and S. Yu. Fialko, "Study of the free vibration of ribbed cylindrical shells," Sopr. Mater. Teor. Sooruzh.,38, 25–30 (1981).

    Google Scholar 

  64. G. D. Gavrilenko, S. S. Khalyuk, A. S. Sitnik, and A. A. Rudometkin, Rudometkin, Algorithms and Programs for Calculating the Strength and Stability of Ribbed Shells [in Russian], Est. NIINTI, Tallin (1990).

    Google Scholar 

  65. G. D. Gavrilenko, S. S. Khalyuk, S. S. Sitnik, A. A. Rudometkin, and A. S. Volkov, Method of Calculating the Stress-Strain State of Irregular Ribbed Shell-Panels with Cylindrical and Conical Generatrices [in Russian], EK "Bit," Tallin (1989).

    Google Scholar 

  66. G. D. Gavrilenko, S. S. Khalyuk, and A. A. Rudometkin, "Development of a method of designing ribbed shells with irregular reinforcement," in: Structural Mechanics of Ships [in Russian], NKI, Nikolaev (1990), pp. 98–105.

    Google Scholar 

  67. S. K. Godunov, "Numerical solution of boundary-value problems for systems of linear differential equations," Usp. Mat. Nauk,16, No. 3, 171–174 (1961).

    Google Scholar 

  68. A. L. Gol'denveizer, Theory of Elastic Thin Shells, Gostekhizdat, Moscow (1953).

    Google Scholar 

  69. E. S. Greben', "Basic equations of ribbed shallow shells and plates," Raschet Prostr. Konstr.,10, 81–91 (1965).

    Google Scholar 

  70. É. I. Grigolyuk, "Buckling of thin shells beyond the elastic limit," Izv. Akad. Nauk SSSR Otd. Tekh. Nauk, No. 10, 3–20 (1957).

  71. É. I. Grigolyuk, "Theoretical and experimental study of the stability of thin shells beyond the elastic limit," in: Progress in Science: Mechanics. Elasticity and Strength [in Russian], VINITI, Moscow (1966), pp. 7–80.

    Google Scholar 

  72. É. I. Grigolyuk and V. V. Kabanov, "Stability of circular cylindrical shells," in: Itogi Nauki, Mekh. Tverd. Deformiruemykh Tel, Vol. 5, VINITI AN SSSR, Moscow (1969).

    Google Scholar 

  73. É. I. Grigolyuk and V. V. Kabanov, Stability of Shells [in Russian], Nauka, Moscow (1978).

    Google Scholar 

  74. Ya. M. Grigorenko, "Computer solution of problems of the stress state of conical shells of variable stiffness," Computers in Structural Mechanics: Transactions of the First All-Union Conference on the Use of Computers in Structural Mechanics. Leningrad, 1963. Gosstroizdat, Moscow-Leningrad (1966), pp 535–543.

  75. Ya. M. Grigorenko, "Use of numerical methods to design machine parts," Din. Prochn. Mash.,5, 11–17 (1967).

    Google Scholar 

  76. Ya. M. Grigorenko, Isotropic and Anisotropic Shells of Revolution of Variable Stiffness [in Russian], Nauk. Dumka, Kiev (1973).

    Google Scholar 

  77. Ya. M. Grigorenko, "Solution of the problem of the deformation of a long flexible cylindrical shell with variable parameters," Dokl. Akad. Nauk Ukr. RSR Ser. A, No. 5, 418–422 (1977).

  78. Ya. M. Grigorenko, "Solution of problems of the theory of shells by the methods of numerical analysis," Prikl. Mekh.,20, No. 10, 3–22 (1984).

    Google Scholar 

  79. Ya. M. Grigorenko and E. A. Abramidze, "One variant of the refined theory of flexible laminated orthotropic shells," Prikl. Mekh.,25, No. 8, 44–52 (1989).

    Google Scholar 

  80. Ya. M. Grigorenko, E. I. Bespalova, A. T. Vasilenko, et al., Numerical Solution of Boundary-Value Problems of the Statics of Orthotropic Laminated Shells of Revolution on an M-220 Computer [in Russian], Nauk. Dumka, Kiev (1971).

    Google Scholar 

  81. Ya. M. Grigorenko and A. T. Vasilenko, Theory of Shells of Variable Stiffness [in Russian], Vol. 4 of Methods of Shell Design (5 vols.), Nauk. Dumka, Kiev (1981).

    Google Scholar 

  82. Ya. M. Grigorenko and A. T. Vasilenko, Problems of the Statics of Anisotropic Nonuniform Shells [in Russian], Nauka, Moscow (1991).

    Google Scholar 

  83. Ya. M. Grigorenko, A. T. Vasilenko, E. I. Bespalova, et al., Numerical Solution of Boundary-Value Problems of the Statics of Orthotropic Shells with Variable Parameters [in Russian], Nauk. Dumka, Kiev (1975).

    Google Scholar 

  84. Ya. M. Grigorenko, N. D. Draigor, and A. I. Shinkar', "Solution of problems on the stress state of multilayered orthotropic cylindrical shells with variable stiffness in two directions," Sopr. Mater. Teor. Sooruzh.,30, 3–10 (1977).

    Google Scholar 

  85. Ya. M. Grigorenko, A. B. Kitaigorodskii, V. V. Semenova, et al., Design of Orthotropic Laminated Shells of Revolution with Variable Parameters on an ES-Series Computer [in Russian], Nauk. Dumka, Kiev (1980).

    Google Scholar 

  86. Ya. M. Grigorenko and N. N. Kryukov, "Numerical solution of nonlinear boundary-value problems of the theory of flexible circular plates," Vychisl. Prikl. Mat.,41, 46–52 (1980).

    Google Scholar 

  87. Ya. M. Grigorenko and N. N. Kryukov, "One approach to the numerical solution of boundary-value problems of the statics of flexible shells," Dopov. Akad. Nauk Ukr. RSR Ser. A, No. 4, 21–24 (1982).

  88. Ya. M. Grigorenko and N. N. Kryukov, Numerical Solution of Problems of the Statics of Flexible Laminated Shells with Variable Parameters [in Russian], Nauk. Dumka, Kiev (1988).

    Google Scholar 

  89. Ya. M. Grigorenko, n. N. Kryukov, and V. S. Demyanchuk, "Deformation of flexible shells of revolution of variable stiffness," Dokl. Akad. Nauk Ukr. RSR Ser. A, No. 4, 42–46 (1983).

  90. Ya. M. Grigorenko, N. N. Kryukov, and T. V. Krizhanovskaya, "Nonlinear deformation of laminated anisotropic shells of revolution under combined thermal and mechanical loads," Dokl. Akad. Nauk Ukr. RSR Ser. A, No. 11, 38–41 (1988).

  91. Ya. M. Grigorenko, N. N. Kryukov, and T. V. Krizhanovskaya, "Nonaxisymmetric deformation of flexible conical shells of variable thickness," Prikl. Mekh.,19, No. 51, 29–35 (1983).

    Google Scholar 

  92. Ya. M. Grigorenko and A. P. Mukoed, Solution of Problems of Shell Theory on a Computer [in Russian], Vishcha Shk., Kiev (1979).

    Google Scholar 

  93. Ya. M. Grigorenko and A. P. Mukoed, Solution of Nonlinear Problems of Shell Theory on a Computer [in Russian], Vishcha Shk., Kiev (1983).

    Google Scholar 

  94. Ya. M. Grigorenko and A. M. Timonin, "Solution of nonaxisymmetric nonlinear problems of the statics of shells of revolution with a low shear stiffness," Dokl. Akad. Nauk Ukr. RSR Ser. A, No. 10, 30–34 (1981).

  95. Ya. M. Grigorenko and A. M. Timonin, "Numerical solution of nonaxisymmetric problems of the nonlinear theory of laminated shells of revolution," Prikl. Mekh.,18, No. 5, 43–48 (1982).

    Google Scholar 

  96. Ya. M. Grigorenko and A. M. Timonin, "Numerical solution of problems of the deformation of flexible anisotropic plates of complex geometry," Dokl. Akad. Nauk Ukr. RSR Ser. A, No. 6, 43–44 (1990).

  97. Ya. M. Grigorenko and O. V. Tumashova, "Stress-strain state of flexible panels with variable geometric parameters," Prikl. Mekh.,25, No. 5, 36–45 (1989).

    Google Scholar 

  98. Ya. M. Grigorenko and V. I. Gulyaev, "Nonlinear problems of shell theory and methods of solving them (survey)," Prikl. Mekh., No. 10, 3–23 (1991).

  99. V. S. Gudramovich, V. P. Gerasimov, and A. F. Demenkov, Limit Analysis of Structural Elements [in Russian], Nauk. Dumka, Kiev (1990).

    Google Scholar 

  100. A. N. Guz', Stability of Elastic Bodies with Finite Strains [in Russian], Nauk. Dumka, Kiev (1973).

    Google Scholar 

  101. A. N. Guz', "Possibility of generalization in the nonlinear theory of small strains," Prikl. Mekh.,20, No. 1, 3–13 (1984).

    Google Scholar 

  102. A. N. Guz', Principles of the Three-Dimensional Theory of Stability of Deformable Bodies [in Russian], Vishcha Shkola, Kiev (1986).

    Google Scholar 

  103. A. N. Guz', I. S. Chernyshenko, Chekhov, et al., Theory of Thin Shells Weakened by Holes [in Russian], Vol. 1 of Methods of Shell Design, Nauk. Dumka, Kiev (1980).

    Google Scholar 

  104. V. I. Gulyaev, V. A. Bazhenov, and E. A. Gotsulyak, Stability of Nonlinear Mechanical Systems [in Russian], Vishcha Shk., Lvov (1982).

    Google Scholar 

  105. V. I. Gulyaev, V. A. Bazhenov, E. A. Gotsulyak, and V. V. Gaidachuk, Design of Shells of Complex Form [in Russian], Budivel'nik, Kiev (1990).

    Google Scholar 

  106. V. I. Gulyaev and G. I. Mel'nichenko, "Modes of supercritical equilibrium of cylindrical and conical shells of elliptical cross section under an axial load," Izv. Akad. Nauk SSSR Mekh. Tverd. Tela, No. 5, 60–66 (1976).

  107. M. I. Dlugach and G. D. Gavrilenko, "Realization of conditions for nonambiguity of the displacements in the design of shells with holes," Dokl. Akad. Nauk Ukr. RSR Ser. A, No. 3, 220–223 (1975).

  108. M. I. Dlugach and G. D. Gavrilenko, "Design of ribbed cylindrical shells with large rectangular holes by the grid method," Prikl. Mekh.,11, No. 12, 22–30 (1975).

    Google Scholar 

  109. M. I. Duglach and G. D. Gavrilenko, "Stability design of ribbed cylindrical shells with large rectangular holes in a subcritical state with moments," Dokl. Akad. Nauk Ukr. RSR Ser. A, No. 1, 33–37 (1977).

  110. M. I. Dlugach, G. D. Gavrilenko, and P. S. Polyakov, "Theoretical and experimental study of the stress-strain state of ribbed shells with large rectangular holes," Prikl. Mekh.,13, No. 6, 117–120 (1977).

    Google Scholar 

  111. D. G. Donnell, Beams, Plates, and Shells [Russian translation], Nauka, Moscow (1982).

    Google Scholar 

  112. O. Zenkevich, Finite-Element Method in Engineering [Russian translation], Mir, Moscow (1975).

    Google Scholar 

  113. V. V. Kabanov, "Study of the stability of shells by the finite-differences method," Izv. Akad. Nauk SSSR Mekh. Tverd. Tela, No. 1, 24–29 (1971).

  114. V. V. Kabanov and L. P. Zheleznov, "Nonlinear deformation of circular cylindrical shells under nonaxisymmetric pressure," in: Design of the Structural Elements of Aircraft [in Russian], Mashinostroenie, Moscow (1982).

    Google Scholar 

  115. A. V. Karmishin, V. A. Lyaskovets, V. I. Myachenkov, and A. N. Frolov, Statics and Dynamics of Thin-Walled Shell Structures [in Russian], Mashinostroenie, Moscow (1975).

    Google Scholar 

  116. A. V. Karmishin, V. A. Lyaskovets, and V. I. Myachenkov, "Stability of eccentrically reinforced shells of revolution," in: Theory of Plates and Shells [in Russian], Nauka, Moscow (1971), pp. 134–141.

    Google Scholar 

  117. A. V. Karmishin and V. I. Myachenkov, "Methods of solving problems of shell stability," Transactions of the VII All-Union Conference on the Theory of Plates and Shells, Nauka, Moscow (1970), pp. 794–807.

    Google Scholar 

  118. A. V. Karmishin, V. I. Maychenkov, A. A. Repin, and A. N. Frolov, "Unified method of solving problems of the stability and vibration of shells of revolution," in: Theory of Plates and Shells [in Russian], Nauka, Moscow (1971), pp. 141–146.

    Google Scholar 

  119. N. I. Karpov, "Stability of a cylindrical shell reinforced by stiffening ribs," Prikl. Mekh.,2, No. 7, 27–33 (1966).

    Google Scholar 

  120. Ya. F. Kayuk, Certain Problems of Parameter Expansion Methods [in Russian], Nauk. Dumka, Kiev (1980).

    Google Scholar 

  121. V. A. Krys'ko, Nonlinear Statics and Dynamics of Nonuniform Shells [in Russian], Saratov. Un-ta, Saratov (1976).

    Google Scholar 

  122. A. D. Kovalenko, Principles of Thermoelasticity [in Russian], Nauk. Dumka, Kiev (1970).

    Google Scholar 

  123. N. V. Kokunov, Principles of the Design of Elastic Shells [in Russian], Vyssh. Shkola, Moscow (1972).

    Google Scholar 

  124. Yu. V. Lipovtsev, "Stability of elastic and viscoelastic shells in the presence of local stresses," Izv. Akad. Nauk SSSR Mekh. Tverd. Tela, No. 5, 174–180 (1968).

  125. Yu. V. Lipovtsev and E. V. Shvarts, "Effect of eccentricity of the application of compressive loads on the stability of of a cylindrical shell," Izv. Akad. Nauk SSSR Mekh. Tverd. Tela, No. 5, 174–177 (1969).

  126. A. I. Lur'e, Statics of Thin-Walled Elastic Shells, Gostekhizdat, Moscow, Leningrad (1947).

    Google Scholar 

  127. I. S. Malyushin, "Stability and vibration of a cylindrical shell discretely reinforced by a semi-regular system of ribs," Transactions of the X All-Union Conference on the Theory of Plates and Shells. Kutaisi, 1975. Metsniereba, Tableilisi (1975), Vol. 1, pp. 671–679.

    Google Scholar 

  128. V. I. Myachenkov, "Stability of orthotropic shells of revolution under axisymmetric loads," Inzh. Zh. Mekh. Tverd. Tela, No. 1, 106–113 (1968).

  129. V. I. Myachenkov, "Stability of spherical shells under a combination of axial compression, external pressure, and concentrated annular loads," Izv. Akad. Nauk SSSR Mekh. Tverd. Tela, No. 6, 133–138 (1970).

  130. V. I. Myachenkov, "Stability of cylindrical shells under the influence of axisymmetric transverse pressure," Prikl. Mekh., No. 1, 27–33 (1970).

  131. V. I. Myachenkov, "Stability of cylindrical shells under the combined influence of axial compression and axisymmetric local loads," Izv. Akad. Nauk SSSR Mekh. Tverd. Tela, No. 5, 178–181 (1969).

  132. V. I. Maychenkov and I. V. Grigor'ev, Computer Design of Shell Structures: Handbook [in Russian], Mashinostroenie, Moscow (1981).

    Google Scholar 

  133. V. I. Maychenkov and V. P. Mal'tsev, Methods and Algorithms for the Design of Three-Dimensional Structures on a ES-Series Computer [in Russian], Mashinostroenie, Moscow (1984).

    Google Scholar 

  134. V. I. Myachenkov and L. A. Pakhomova, "Local stability of cylindrical shells during heating," Inzh. Zh. Mekh. Tverd. Tela, No. 2, 130–134 (1968).

  135. V. I. Myachenkov and L. A. Pakhomova, "Stability of cylindrical shells under concentrated annular loads," Inzh. Zh. Mekh. Tverd. Tela, No. 6, 143–147 (1968).

  136. V. I. Myachenkov and A. A. Repin, "Stability of a cylindrical shell under the combined influence of axial compression and heating," Izv. Akad. Nauk SSSR Mekh. Tverd. Tela, No. 4, 166–168 (1970).

  137. V. I. Myachenkov and P. F. Shablii, "Stability of spherical shells with local defects," Prikl. Mekh.,7, No. 8, 128–131 (1971).

    Google Scholar 

  138. Kh. M. Mushtari and K. Z. Galimov, Nonlinear Theory of Elastic Shells [in Russian], Tatknigoizdat, Kazan' (1957).

    Google Scholar 

  139. V. V. Novozhilov, Theory of Thin Shells [in Russian], Sudostroenie, Leningrad (1962).

    Google Scholar 

  140. P. M. Ogibalov and M. A. Koltunov, Shells and Plates [in Russian], Izd-vo Mosk. Un-ta, Moscow (1969).

    Google Scholar 

  141. V. A. Postnov, V. S. Korneev, and N. G. Slezina, "Design of thin shells of revolution of arbitrary form by the finiteelement method," Stroit. Mekh. Korablya,128, 5–18 (1970).

    Google Scholar 

  142. V. A. Postnov and L. A. Rozin, "Finite-element method in the theory of plates and shells," Transactions of the IX All-Union Conference on the Theory of Plates and Shells, Sudostroenie, Leningrad (1975), pp. 292–296.

  143. V. M. Myachenkov, V. P. Mal'tsev, V. P. Maidoroda, et al., in: Design of Machine Elements by the Finite-Element Method: Handbook [in Russian], Mashinostroenie, Moscow (1989).

    Google Scholar 

  144. V. N. Revutskii, "Stability of flawed ribbed spherical shells," Submitted to VINITI 29.06.89. No. 4287–1989 (1989).

  145. L. A. Rozin and L. B. Grimze, "Design of arbitrary shells of revolution by the splitting method on a computer," Issled. Upr. Plast., No. 5, 70–118 (1966).

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

    Google Scholar 

  147. P. A. Sokolov, "Stability of a thin cylindrical shell reinforced by circular elastic ribs and subjected to transverse and longitudinal loads," Prikl. Mat. Mekh.,1, No. 2, 256–281 (1933).

    Google Scholar 

  148. S. P. Timoshenko and S. A. Woinowsky-Krieger, Plates and Shells [Russian translation], Nauka, Moscow (1971).

    Google Scholar 

  149. S. P. Timoshenko, Stability of Rods, Plates, and Shells [in Russian], Nauka, Moscow (1971).

    Google Scholar 

  150. J. M. T. Thompson and R. Gaffari, "Complex dynamic behavior of bilinear systems: bifurcative instability leading to chaos," in: Loss of Stability and Buckling of Structures: Theory and Practice [Russian translation], Nauka, Moscow (1991), pp. 132–144.

    Google Scholar 

  151. J. M. T. Thompson, Instability and Catastrophe in Science and Engineering [Russian translation], Mir, Moscow (1985).

    Google Scholar 

  152. A. P. Filin, Elements of the Theory of Shells, Stroizdat, Leningrad (1975).

    Google Scholar 

  153. Fine and Sekler, Thin-Walled Shell Structures: Theory, Experiment, and Design [Russian translation], Mashinostroenie, Moscow (1980).

    Google Scholar 

  154. K. F. Chernykh, Linear Theory of Shells [in Russian], Izd-vo LGU, Leningrad (1962)–(1964), Pts. 1 and 2.

    Google Scholar 

  155. L. Euler, "Method of finding curves having the properties of a minimum or maximum or solving an isoperimetric problem in the broadest sense," in: Classics of Natural Science (a series). Supplement 1: Elastic Curves [in Russian], ONTI, Moscow, Leningrad (1934).

    Google Scholar 

  156. K. P. Ellinas, J. G. A. Croll, "General elastoplastic loss of stability by ring-reinforced cylindrical shells," in: Loss of Stability and Buckling of Structures: Theory and Practice [in Russian], Nauka, Moscow (1991), pp. 81–93.

    Google Scholar 

  157. B. O. Almroth and D. Bushnell, "Computer analysis of various shells of revolution," AIAA J.,6, No. 10, 1848–1855 (1968).

    Google Scholar 

  158. J. Arbocz and J. M. A. M. Hol, "Koiter's stability theory in a computerized engineering (CAE) environment," Int. J. Solids Struct.,26, No. 9/10, 945–973 (1990).

    Google Scholar 

  159. J. Arbocz and J. M. A. M. Hol, "Collapse of axially compressed cylindrical shells with random imperfections," AIAA J.,29, No. 12, 2247–2256 (1991).

    Google Scholar 

  160. J. Arbocz, Shell Stability Analysis: Theory and Practice. Proceedings of the IUTAM Symposium on Collapse, the Buckling of Structures in Theory and Practice, J. M. T. Thompson and G. W. Hunt (eds.), Cambridge University Press, New York (1983), pp. 43–74.

    Google Scholar 

  161. J. Arbocz, The Imperfection Data Bank, a Means to Obtain Realistic Buckling Loads, Proceedings, Buckling of Shells. A State-of-the-Art Colloquium, E. Ramm (ed.), Springer-Verlag, Berlin (1982), pp. 537–567.

    Google Scholar 

  162. C. D. Babcock, "Shell stability," J. Appl. Mech.,50, 935–940 (1983).

    Google Scholar 

  163. D. Bushnell, "Symmetric and nonsymmetric buckling of finitely deformed eccentrically stiffened shells of revolution," AIAA J.,5, No. 8, 1455–1462 (1967).

    Google Scholar 

  164. D. Bushnell, "BOSOR-5 — program for buckling of elastic-plastic complex shells of revolution including large deflections and creep," Comput. Struct.,6, 221–239 (1976).

    Google Scholar 

  165. D. Bushnell, "PANDA-2 — program for minimum weight design of stiffened, composite, locally buckled panels," Comput. Struct.,25, No. 4, 469–505 (1987).

    Google Scholar 

  166. D. Bushnell, "Theoretical basis of the PANDA computer program for preliminary design of stiffened panels under combined in-plane loads," Comput. Struct.,27, No. 4, 541–563 (1987).

    Google Scholar 

  167. J. G. A. Croll and C. P. Ellinas, "A design formulation for axisymmetric collapse of stiffened and unstiffned cylinders," Trans. ASME: J. Energy Resource Technol.,107, No. 3, 350–355 (1985).

    Google Scholar 

  168. C. P. Ellinas, J. G. A. Croll, and R. C. Batista, "Overall buckling of stringer-stiffened cylinders," Proc. Inst. Civ. Eng.,71, Pt. 2, 479–512 (1981).

    Google Scholar 

  169. C. P. Ellinas and J. G. A. Croll, "Overall buckling of ring-stiffened cylinders," Proc. Inst. Civ. Eng.,71, Pt. 2, 637–661 (1981).

    Google Scholar 

  170. I. Elishakoff and J. Arbocz, "Reliability of axially compressed cylindrical shells with general nonsymmetric imperfections," J. Appl. Mech.,52, 122–128 (1985).

    Google Scholar 

  171. N. J. Hoff, "Buckling of thin shells," Proc. of an Aerospace Symp. of Distinguished Lecturers in Honor of Theodore von Karman on his 80th Anniversary. Inst. of Aerosp. Sci., New York (1961), pp. 1–42.

  172. J. W. Hutchinson, "Plastic buckling," Adv. Appl. Mech.,14, 67–143 (1974).

    Google Scholar 

  173. J. W. Hutchinson, "Post-bifurcation behavior in the plastic range," J. Mech. Phys. Solids,21, 163–190 (1973).

    Google Scholar 

  174. J. W. Hutchinson and W. T. Koiter, "Postbuckling theory," Appl. Mech. Rev.,23, 1353–1366 (1970).

    Google Scholar 

  175. W. T. Koiter, "Current trends in the theory of buckling," Buckling Structure, Berlin (1976), pp. 1–16.

    Google Scholar 

  176. R. Lorenz, "Die nicht achsensymmetrische knibkung durationnwandiger Hohlzylinder." Phys. Z.,12, No. 7, 241–260 (1911).

    Google Scholar 

  177. H. Ohira, "Local buckling theory of axially compressed cylindrical shells," Proc. Eleventh Japan National Congress of Applied Mechanics (1961), pp. 37–40.

  178. E. Riks, C. C. Rankin, and F. A. Brogan, The Numerical Simulation of the Collapse Process of Axially Compressed Cylindrical Shells with Measured Imperfections. Report LR. — 705, pp. 1–9.

  179. J. Scogh, P. Stern, and F. Brogan, "Instability analysis of Sklylab structure," J. Comput. Struct.,3, 1219–1240 (1973).

    Google Scholar 

  180. M. J. Sewell, A Survey of Plastic Buckling. Study No. 6, S. T. Ariarathman et al. (eds.), Solid Mechanics Division, University of Waterloo, Ontario, Canada (1972), pp. 85–197.

    Google Scholar 

  181. J. Singer and A. Rosen, "The influence of boundary conditions on the buckling of stiffened cylindrical shells," Proc. IUTAM Symp. Buckling of Structures, Harvard Univ., Cambridge, Mass., June 1974. Springer-Verlag, Berlin (1976), pp. 227–250.

    Google Scholar 

  182. R. Southwell, "On the collapse of tubes by external pressure. Parts I, II, III," Philos. Mag., Ser. 6,25, No. 149, 687–697;26, No. 153, 502–510;29, No. 169, 67–76 (1913).

  183. J. M. T. Thompson, "Basic principles in the general theory of elastic stability," J. Mech. Phys. Solids,11, 13–20 (1963).

    Google Scholar 

  184. J. M. T. Thompson, "Discrete branching points in the general theory of elastic stability," J. Mech. Phys. Solids,13, 295–310 (1965).

    Google Scholar 

  185. J. M. T. Thompson, "Catastrophe in mechanics: progress or digression," J. Struct. Mech.,10(2, 162–175 (1982).

    Google Scholar 

  186. J. M. T. Thompson, "A general theory for the equilibrium and stability of discrete conservative systems," Z. Angew. Math. Phys.,20, 797–846 (1969).

    Google Scholar 

  187. J. M. T. Thompson and G. W. Hunt, A General Theory of Elastic Stability, Wiley, London (1973).

    Google Scholar 

  188. J. M. T. Thompsonn and G. W. Hunt, "Towards a unified bifurcation theory," Z. Angew. Math. Phys.,26, 581–604 (1975).

    Google Scholar 

  189. T.-S. Wang and Y. Lin, "Stability of discretely stringer-stiffened shells," AIAA J.,11, No. 6, 810–814 (1973).

    Google Scholar 

  190. V. I. Weingarten, E. J. Morgan, and P. Seide, "Elastic stability of thin-walled cylindrical and conical shells under axial compression," AIAA J., No. 3, 500–505 (1965).

Download references

Authors
  1. G. D. Gavrilenko
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

S. P. Timoshenko Institute of Mechanics, National Academy of Sciences of Ukraine, Kiev. Translated from Prikladnaya Mekhanika, Vol. 31, No. 7, pp. 3–25, July, 1995.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Gavrilenko, G.D. Stability of smooth and ribbed shells of revolution in a nonuniform stress-strain state (survey). Int Appl Mech 31, 501–520 (1995). https://doi.org/10.1007/BF00846784

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00846784

Search

Navigation