Skip to main content
Log in

The Theory and Methods of the Stress–Strain Analysis of Ribbed Shells

  • Published:
International Applied Mechanics Aims and scope

Abstract

Studies are reviewed where basic tenets of the theory and methods of the stress–strain analysis of discretely rib-reinforced shells are formulated. The major results of the investigations carried out by the department of thin-walled structure mechanics headed by I. Ya. Amiro at the S. P. Timoshenko Institute of Mechanics of the National Academy of Sciences of Ukraine are presented

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

Access this article

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

Instant access to the full article PDF.

Similar content being viewed by others

REFERENCES

  1. A. Z. Averbukh, R. I. Veidman, and M. D. Genkin, The Vibrations of Structural Elements in a Liquid [in Russian], Nauka, Moscow (1987).

    Google Scholar 

  2. I. Ya. Amiro and V. A. Zarutskii, The Theory of Ribbed Shells, Vol. 2 of the five-volume series Methods of Shell Design [in Russian], Naukova Dumka, Kiev (1980).

    Google Scholar 

  3. I. Ya. Amiro and V. A. Zarutskii, “Studies on the dynamics of ribbed shells,” Prikl. Mekh., 17, No. 11, 3–20 (1981).

    Google Scholar 

  4. I. Ya. Amiro, V. A. Zarutskii, and V. G. Palamarchuk, The Dynamics of Ribbed Shells [in Russian], Naukova Dumka, Kiev (1983).

    Google Scholar 

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

    Google Scholar 

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

    Google Scholar 

  7. I. Ya. Amiro and V. A. Zarutskii, “The statics, dynamics, and stability of ribbed shells,” Itogi Nauki Tekhn., Ser. Mekh. Deform. Tverd. Tela, VINITI, Moscow, 21, 132–191 (1990).

    Google Scholar 

  8. I. Ya. Amiro and V. A. Zarutskii, “Experimental investigations of the stability of ribbed shells (review),” Prikl. Mekh., 32, No. 9, 3–15 (1996).

    Google Scholar 

  9. I. V. Andrianov, V. A. Lesnichaya, V. V. Loboda, and L. I. Manevich, Strength Analysis of Ribbed Shells of Revolution [in Russian], Vyshcha Shkola, Kiev–Donetsk (1986).

    Google Scholar 

  10. I. V. Andrianov, V. A. Lesnichaya, and L. I. Manevich, The Averaging Method in the Statics and Dynamics of Ribbed Shells [in Russian], Nauka, Moscow (1985).

    Google Scholar 

  11. V. A. Bazhenov and V. A. Zarutskii, “Hoop stresses in cylindrical shells reinforced with longitudinal ribs,” Prikl. Mekh., 4, No. 11, 125–129 (1968).

    Google Scholar 

  12. D. V. Vainberg, V. A. Zarutskii, and B. Z. Itenberg, “The stress state of rib-reinforced shells,” Prikl. Mekh., 4, No. 4, 375–384 (1960).

    Google Scholar 

  13. A. T. Vasilenko, Ya. M. Grigorenko, and N. D. Pankratova, “Stress analysis of noncircular cylindrical shells with longitudinal stiffening ribs,” Prikl. Mekh., 12, No. 4, 117–121 (1976).

    Google Scholar 

  14. A. P. Varvak and V. A. Zarutskii, “The accuracy of the theory of ribbed shells based on the Kirchhoff–Love hypotheses,” Prikl. Mekh., 6, No. 6, 49–57 (1970).

    Google Scholar 

  15. A. P. Varvak, “Design of flat ribbed shells in a double trigonometric series,” Prikl. Mekh., 7, No. 1, 38–42 (1971).

    Google Scholar 

  16. A. P. Varvak, “Integral equations in the theory of plates and shells reinforced with crossed ribs,” Rasch. Prostr. Konstr., No. 15, 113–120 (1973).

    Google Scholar 

  17. V. Z. Vlasov, Thin-Walled Spatial Systems [in Russian], Gosstroiizdat, Moscow (1958).

    Google Scholar 

  18. P. I. Galaka, V. A. Zarutskii, P. G. Kaplya, et al., “Study of the effect of axial compressive forces on the frequencies and vibration modes of ribbed cylindrical shells,” Prikl. Mekh., 11, No. 8, 41–48 (1975).

    Google Scholar 

  19. P. I. Galaka, V. A. Zarutskii, V. I. Matsner, and A. M. Nosachenko, “The free vibrations of ribbed cylindrical shells,” Prikl. Mekh., 10, No. 7, 49–55 (1974).

    Google Scholar 

  20. A. L. Gol'denveizer, The Theory of Elastic Thin Shells [in Russian], Gostekhizdat, Moscow (1953).

    Google Scholar 

  21. E. S. Greben', “The basic equations of the theory of ribbed shallow shells and plates,” Rasch. Prostr. Konstr., No. 10, 81–91 (1965).

    Google Scholar 

  22. E. S. Greben', “The basic relations of the engineering theory of ribbed shells,” Izv. Akad. Nauk SSSR, Mekh., No. 3, 124–135 (1965).

    Google Scholar 

  23. E. S. Greben', “Strains and equilibrium of thin ribbed shells,” Izv. Akad. Nauk SSSR, Mekh. Tverd. Tela, No. 5, 106–114 (1969).

    Google Scholar 

  24. G. I. Diamant and V. A. Zarutskii, “The stress–strain state of rigidly clamped longitudinally reinforced cylindrical shell,” Soprot. Mater. Teor. Sooruzh., No. 14, 134–141 (1971).

    Google Scholar 

  25. G. I. Diamant and V. A. Zarutskii, “Determination of the natural frequencies of longitudinally reinforced cylindrical shells,” Prikl. Mekh., 14, No. 1, 53–58 (1978).

    Google Scholar 

  26. G. I. Diamant, V. A. Zarutskii, and L. A. Senchenko, “Optimization of the parameters of ribbed cylindrical shells for the minimum natural frequency,” Soprot. Mater. Teor. Sooruzh., No. 32, 48–50 (1978).

    Google Scholar 

  27. G. I. Diamant, V. A. Zarutskii, and É. F. Sivak, “Study of the effect of ribs on the natural frequencies and vibration modes of cylindrical shells,” Stroit. Mekh. Teor. Sooruzh., No. 3, 48–50 (1978).

    Google Scholar 

  28. P. A. Zhilin, “Analysis of boundary-value problems for ribbed shells,” Tr. TsKTI, Prochn. Gidroturb., No. 72, 26–40 (1966).

    Google Scholar 

  29. P. A. Zhilin, “The general theory of ribbed shells,” Tr. TsKTI, Prochn. Gidroturb., No. 88, 46–70 (1968).

    Google Scholar 

  30. P. A. Zhilin, “The linear theory of ribbed shells,” Izv. Akad. Nauk SSSR, Mekh. Tverd. Tela, No. 4, 150–162 (1970).

    Google Scholar 

  31. P. A. Zhilin and G. A. Kizima, “Shells of zero Gaussian curvature with meridional ribs,” Tr. TsKTI, Prochn. Gidroturb., No. 72, 41–52 (1966).

    Google Scholar 

  32. P. A. Zhilin and G. A. Kizima, “Shells of zero Gaussian curvature with meridional ribs,” Inzh. Zhurn. Mekh. Tverd. Tela, No. 3, 102–105 (1967).

    Google Scholar 

  33. P. A. Zhilin and G. A. Kizima, “A spherical belt with meridional ribs,” Izv. Akad. Nauk SSSR, Mekh. Tverd. Tela, No. 5, 97–105 (1969).

    Google Scholar 

  34. V. A. Zarutskii, “Equilibrium equations for ribbed cylindrical shells and their approximate solution,” Prikl. Mekh., 7, No. 5, 503–511 (1961).

    Google Scholar 

  35. V. A. Zarutskii, “Equilibrium equations for ribbed cylindrical shells,” in: Proc. 11th All-Union Conf. on the Theory of Plates and Shells [in Russian] (Lvov, 1961), Izd. Akad. Nauk Ukr. SSR, Kiev (1962), pp. 396–400.

    Google Scholar 

  36. V. A. Zarutskii, “Design of cylindrical shells reinforced with stringers,” Prikl. Mekh., 8, No. 3, 271–281 (1962).

    Google Scholar 

  37. V. A. Zarutskii, “Design of cylindrical shells reinforced with stringers and frames,” Prikl. Mekh., 1, No. 5, 127–128 (1965).

    Google Scholar 

  38. V. A. Zarutskii, “Design of reinforced shells,” Inzh. Zhurn., 5, No. 5, 895–906 (1965).

    Google Scholar 

  39. V. A. Zarutskii, “The equilibrium of ribbed cylindrical shells,” Prikl. Mekh., 1, No. 11, 28–38 (1965).

    Google Scholar 

  40. V. A. Zarutskii, “Design of ribbed cylindrical shells subject to arbitrary loads,” Prikl. Mekh., 2, No. 4, 17–25 (1966).

    Google Scholar 

  41. V. A. Zarutskii, “Application of double trigonometric series to the design of ribbed cylindrical shells,” Prikl. Mekh., 2, No. 6, 55–62 (1966).

    Google Scholar 

  42. V. A. Zarutskii, “The momentless state of ribbed cylindrical shells,” Prikl. Mekh., 6, No. 10, 9–16 (1970).

    Google Scholar 

  43. V. A. Zarutskii, “An approximate method for stress–strain analysis of ribbed cylindrical shells,” Prikl. Mekh., 7, No. 2, 51–56 (1971).

    Google Scholar 

  44. V. A. Zarutskii, “Design of ribbed cylindrical shells,” Probl. Prochn., No. 8, 8–10 (1971).

    Google Scholar 

  45. V. A. Zarutskii, “Singularities in forces when concentrated loads act on ribbed shells,” Soprot. Mater. Teor. Sooruzh., No. 19, 3–5(1973).

    Google Scholar 

  46. V. A. Zarutskii, “Approximate formulas for calculation of the minimum natural frequencies of reinforced cylindrical shells,” Prikl. Mekh., 13, No. 5, 43–51 (1977).

    Google Scholar 

  47. V. A. Zarutskii, “Determination of the natural frequencies of prestretched soft cylindrical shells reinforced with ribs in one direction,” Prikl. Mekh., 23, No. 10, 126–129 (1987).

    Google Scholar 

  48. V. A. Zarutskii, “Analysis of dispersion equations for longitudinally reinforced cylindrical shell,” in: Proc. 14th All-Union Conf. on the Theory of Plates and Shells [in Russian] (Kutaisi, 1987), Vol. 1, Tbilisi (1987), pp. 579–584.

    Google Scholar 

  49. V. A. Zarutskii, “Waves running along multilayered orthotropic cylindrical shells reinforced with longitudinal ribs,” Prikl. Mekh., 28, No. 6, 41–45 (1991).

    Google Scholar 

  50. V. A. Zarutskii, “Waves running along the directrix of a multilayered orthotropic cylindrical shell reinforced with ring ribs,” Prikl. Mekh., 28, No. 9, 68–72 (1992).

    Google Scholar 

  51. V. A. Zarutskii, “Approximate allowance for the discrete arrangement of ribs in solving problems on the natural and forced vibrations of ribbed cylindrical shells,” Prikl. Mekh., 29, No. 6, 37–44 (1993).

    Google Scholar 

  52. V. A. Zarutskii, “Approximate nonlinear equations of motion of cylindrical shells made of composites,” Prikl. Mekh., 34, No. 10, 55–59 (1998).

    Google Scholar 

  53. V. A. Zarutskii, “Approximate equations for calculation of the natural frequencies of longitudinally reinforced cylindrical shells derived under the refined theory,” Prikl. Mekh., 31, No. 3, 40–44 (1995).

    Google Scholar 

  54. V. A. Zarutskii, “Stationary waves in multilayered orthotropic ribbed cylindrical shells,” in: Vol. 9 of the 12-volume series The Mechanics of Composites [in Russian], ASK, Kiev (1999), pp. 44–82.

    Google Scholar 

  55. V. A. Zarutskii “Features of the buckling of ribbed shells,” Int. Appl. Mech., 36, No. 5, 559–585 (2000).

    Google Scholar 

  56. V. A. Zarutskii and G. A. Kizima, “Reinforced shells (methods and results of studies),” in: Proc. 9th All-Union Conf. on the Theory of Shells and Plates [in Russian], Sudostroenie, Leningrad (1975), pp. 54–58.

    Google Scholar 

  57. V. A. Zarutskii and G. I. Kogut, “The influence of small elastoplastic strains on the stress–strain state of ribbed cylindrical shells,” Prikl. Mekh., 5, No. 10, 42–49 (1969).

    Google Scholar 

  58. V. A. Zarutskii, G. I. Kogut, and T. A. Neshumaeva, “Determination of the stress–strain state of ribbed cylindrical shells on an EDC,” Dinam. Prochn. Mashin, No. 5, 40–43 (1967).

    Google Scholar 

  59. V. A. Zarutskii, G. I. Kogut, and T. A. Neshumaeva, “The effect of the parameters of ribbed cylindrical shells on their stress–strain state,” Soprot. Mater. Teor. Sooruzh., No. 8, 48–56 (1969).

    Google Scholar 

  60. V. A. Zarutskii and T. A. Neshumaeva, “Thermoelastic stresses in ribbed cylindrical shells,” Tepl. Napryazh. Elem. Konstr., No. 7, 202–208 (1967).

    Google Scholar 

  61. V. A. Zarutskii and A. A. Pryadko, “Design of reinforced shells,” Prikl. Mekh., 1, No. 7, 50–56 (1965).

    Google Scholar 

  62. V. A. Zarutskii, V. F. Sivak, and A. S. Pal'chevskii, “The influence of the meridian shape on the natural frequencies and vibration modes of shells of revolution,” Prikl. Mekh., 33, No. 1, 59–60 (1997).

    Google Scholar 

  63. V. A. Zarutskii and Yu. V. Skosarenko, “The influence of lateral-shear strains on the natural vibrations of orthotropic cylindrical shells reinforced with longitudinal ribs,” Prikl. Mekh., 25, No. 2, 48–55 (1989).

    Google Scholar 

  64. V. A. Zarutskii and Yu. V. Skosarenko, “The influence of lateral-shear strains on the natural vibrations of cylindrical shells reinforced with ring ribs,” Prikl. Mekh., 25, No. 2, 54–61 (1991).

    Google Scholar 

  65. V. A. Zarutskii and A. I. Telalov, “The vibrations of thin-walled structures with design features. A review of experimental investigations,” Prikl. Mekh., 27, No. 4, 3–9 (1991).

    Google Scholar 

  66. V. A. Zarutskii and Yu. A. Tolbatov, “The influence of the excitation level on the natural frequencies of ribbed cylindrical shells,” Soprot. Mater. Teor. Sooruzh., No. 33, 18–22 (1978).

    Google Scholar 

  67. M. I. Karpov, “On one strength problem for a reinforced shell,” Prikl. Mekh., 8, No. 6, 619–626 (1962).

    Google Scholar 

  68. M. I. Karpov, “One technique for stress–strain analysis of a shell reinforced with nonequidistant ribs,” Prikl. Mekh., 9, No. 3, 270–274 (1963).

    Google Scholar 

  69. M. I. Karpov, “The free vibrations of a cylindrical rib-reinforced shell,” Dop. Akad. Nauk Ukr. RSR, No. 8, 1018–1021 (1963).

    Google Scholar 

  70. M. I. Karpov, “Determination of the natural frequencies of a cylindrical shell reinforced with nonequidistant ribs,” Prikl. Mekh., 10, No. 1, 32–39 (1964).

    Google Scholar 

  71. V. G. Palamarchuk, “The free vibrations of a system consisting of a ribbed cylindrical shell and a perfectly rigid body,” Prikl. Mekh., 11, No. 4, 52–62 (1975).

    Google Scholar 

  72. V. G. Palamarchuk, “The problem of the free vibrations of a ribbed cylindrical shell with a perfectly rigid body,” Prikl. Mekh., 15, No. 9, 37–41 (1979).

    Google Scholar 

  73. V. G. Palamarchuk, “The free vibrations of a ribbed cylindrical shell with a beam,” Prikl. Mekh., 16, No. 3, 45–49 (1980).

    Google Scholar 

  74. V. G. Palamarchuk, “The natural vibrations of a system consisting of a ribbed cylindrical shell, a frame, and an apparent mass,” Prikl. Mekh., 26, No. 7, 43–50 (1990).

    Google Scholar 

  75. V. G. Palamarchuk, “The free vibrations of a ribbed cylindrical shell with intermediate supports and a perfectly rigid body,” Prikl. Mekh., 19, No. 2, 28–32 (1983).

    Google Scholar 

  76. V. G. Palamarchuk, “The natural vibrations of a ribbed cylindrical shell supported along two generatrices and carrying a perfectly rigid body,” Prikl. Mekh., 26, No. 3, 49–54 (1990).

    Google Scholar 

  77. V. G. Palamarchuk and A. M. Nosachenko, “The free vibrations of a ribbed conic shell with a spring-supported mass,” Prikl. Mekh., 16, No. 1, 40–46 (1980).

    Google Scholar 

  78. V. G. Palamarchuk and A. M. Nosachenko, “The dynamic instability of a ribbed cylindrical shell with an apparent mass,” Prikl. Mekh., 13, No. 7, 42–50 (1977).

    Google Scholar 

  79. I. V. Podol'skii, “The natural frequencies of ribbed cylindrical shells in a liquid,” Prikl. Mekh., 30, No. 8, 59–63 (1994).

    Google Scholar 

  80. N. Ya. Prokopenko, “The natural vibrations of a reinforced laminated cylindrical shell,” Prikl. Mekh., 15, No. 9, 42–49 (1979).

    Google Scholar 

  81. V. N. Revutskii, “The natural vibrations of ribbed spherical shells,” Prikl. Mekh., 20, No. 7, 42–48 (1984).

    Google Scholar 

  82. V. N. Revutskii, “The natural vibrations of spherical shells reinforced with meridional ribs,” Prikl. Mekh., 20, No. 9, 119–121 (1984).

    Google Scholar 

  83. V. N. Revutskii and A. I. Telalov, “Determination of frequencies and modes of the natural vibrations of spherical shells with a regular ring reinforcement,” Prikl. Mekh., 23, No. 11, 112–116 (1987).

    Google Scholar 

  84. Yu. V. Skosarenko, “The forced vibrations of a ribbed conic shell under a dynamic load,” Prikl. Mekh., 15, No. 6, 55–61 (1979).

    Google Scholar 

  85. Yu. V. Skosarenko, “The stress–strain state of a frame-reinforced conic shell under a dynamic load,” Prikl. Mekh., 16, No. 3, 122–126 (1980).

    Google Scholar 

  86. Yu. V. Skosarenko, “Study of the effect of ring ribs on the natural frequencies of conic shells,” Prikl. Mekh., 19, No. 9, 121–124 (1983).

    Google Scholar 

  87. Yu. V. Skosarenko, “Stress–strain analysis of shells of revolution reinforced with a regular system of meridional ribs,” Prikl. Mekh., 21, No. 5, 68–73 (1985).

    Google Scholar 

  88. Yu. V. Skosarenko, “The influence of the position of a mass and the tapering angle on the natural frequencies of ribbed conic shells,” Prikl. Mekh., 23, No. 2, 119–122 (1987).

    Google Scholar 

  89. Yu. V. Skosarenko, “The influence of the number of regularly added masses on the natural vibrations of ribbed cylindrical and conic shells,” Prikl. Mekh., 26, No. 5, 119–123 (1990).

    Google Scholar 

  90. Yu. V. Skosarenko, “The influence of the rigidity of a cantilever on the natural frequencies of a ribbed cylindrical shell,” in: Studies on Design of Plates and Shells [in Russian], Rostov-on-Don (1986), pp. 42–47.

  91. Yu. V. Skosarenko and I. V. Sluchak, “The stress–strain state of a ribbed conic shell at resonance,” Prikl. Mekh., 27, No. 4, 25–28 (1991).

    Google Scholar 

  92. S. P. Timoshenko, Plates and Shells [in Russian], Gostekhizdat, Moscow (1937).

    Google Scholar 

  93. S. Yu. Fialko, “Study of the influence of an initial deflection on the natural frequencies of ribbed conic shells,” Prikl. Mekh., 18, No. 11, 118–122 (1982).

    Google Scholar 

  94. S. Yu. Fialko, “The modes of natural vibrations of imperfect conic shells,” Prikl. Mekh., 20, No. 12, 109–112 (1984).

    Google Scholar 

  95. S. Yu. Fialko, “The modes of natural vibrations of ribbed conic shells,” Prikl. Mekh., 20, No. 11, 51–55 (1984).

    Google Scholar 

  96. S. Yu. Fialko, “The unsteady vibrations of ribbed conic shells under local loads,” Prikl. Mekh., 23, No. 6, 43–48 (1987).

    Google Scholar 

  97. V. N. Khitrov, “Determination of strains and forces in a shell reinforced with ribs in two directions,” Prikl. Mekh., 7, No. 1, 49–54 (1971).

    Google Scholar 

  98. V. N. Khitrov, “The elastic equilibrium of ribbed shells,” Prikl. Mekh., 7, No. 4, 110–115 (1971).

    Google Scholar 

  99. V. N. Khitrov, “The action of a local load on a reinforced cylindrical shell,” Probl. Prochn., No. 6, 77–81 (1971).

    Google Scholar 

  100. V. N. Khitrov, “Influence of reinforcements on strain under local actions,” Soprot. Mater. Teor. Sooruzh., No. 16, 38–40 (1972).

    Google Scholar 

  101. V. N. Khitrov, “The stress–strain state of reinforced shallow shells with a rectangular planform,” Prikl. Mekh., 9, No. 5, 31–37 (1973).

    Google Scholar 

  102. Yu. A. Shimanskii, The Structural Mechanics of Submarines [in Russian], Sudnopromgiz, Leningrad (1948).

    Google Scholar 

  103. A. N. Guz', V. A. Zarutskii, I. Ya. Amiro, et al., Experimental Investigations of Thin-Walled Structures [in Russian], Naukova Dumka, Kiev (1984).

    Google Scholar 

  104. I. Ya. Amiro and V. A. Zarutskii, “Taking the discrete rib spacing into account when studying the stressed–strained vibrations and stability of ribbed shells (review),” Int. Appl. Mech., 34, No. 4, 299–314 (1998).

    Google Scholar 

  105. W. Flugge, “Die Stabilitat der Kreizylinder Schale,” Ing. Arch., 111, No. 5, 463–506 (1932).

    Google Scholar 

  106. V. A. Zarutsky, “Dynamics of ribbed cylindrical shell,” in: Proc. 9th Symp. on the Dynamics of Structures [in Polish], (Rzeszow-Jawor, 9-11, October 1996), Zeszyty naykowe Politechniki rzeszowskiej n. 151, Mechanika, 1, No. 48 (1996), pp. 129–138.

    Google Scholar 

  107. V. A. Zarutsky, “Effect of discrete placement of ribs on the stress–strain state of cylindrical shells,” in: Abstracts of Papers Read at 6th Conf. on Shell Structures: Theory and Applications (Gdansk-Yurata (Poland), October 12–14, 1998) (1998), pp. 287–288.

    Google Scholar 

  108. V. A. Zarutsky, “General theory of reinforced shells. Stress–strain state of reinforced cylindrical shells under static loading,” in: Proc. 27th Israel Conf. on Mechanical Engineering (Technion City, Haifa (Israel), 19–20 May, 1998) (1998), pp. 598–560.

    Google Scholar 

  109. V. A. Zarutsky and Yu. V. Skosarenko, “Vibrations of ribbed cylindrical shells,” in: Proc. Seminar on Computers and the Future of Structural Mechanics (Cracow University of Technology, May 15–17, 1995), p. 81.

  110. V. A. Zarutskii and V. F. Sivak, “Experimental investigation of the dynamics of shells of revolution (review),” Int. Appl. Mech., 35, No. 3, 217–224 (1999).

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Zarutskii, V.A. The Theory and Methods of the Stress–Strain Analysis of Ribbed Shells. International Applied Mechanics 36, 1259–1283 (2000). https://doi.org/10.1023/A:1009408415517

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1009408415517

Keywords

Navigation