Advertisement

Contact mechanics of shell structures under local loading

  • V. S. Hudramovych
Article

The results of theoretical and experimental studies of contact interaction in frame-and-shell structures under local loading are analyzed. Contact problems for elements of frame-and-shell structures and structures with various foundations such as supports are solved. Critical states (local instability and ultimate plasticity) of frame-and-shell structures under local loading are examined. Numerous experimental results are presented

Keywords

contact interaction frame-and-shell structure contact problem local loading local instability limiting plasticity experimental data 

References

  1. 1.
    A. V. Aksenenko, V. S. Hudramovych, and A. K. Kozlov, Performance of Shell Structures under Local Impact Loading [in Russian], Dnepr. Univ., Dnepropetrovsk (2006).Google Scholar
  2. 2.
    V. M. Aleksandrov and S. M. Mkhitaryan, Contact Problems for Bodies with Thin Coatings and Interlayers [in Russian], Nauka, Moscow (1983).Google Scholar
  3. 3.
    V. M. Aleksandrov and B. L. Romalis, Contact Problems in Mechanical Engineering [in Russian], Mashinostroenie, Moscow (1986).Google Scholar
  4. 4.
    L. I. Balabukh and L. I. Shapovalov, “Contact problems for momentless shells of revolution with an elastic ring,” Izv. AN SSSR, OTN Mekh. Mashinostr., No. 1, 61–66 (1962).Google Scholar
  5. 5.
    N. V. Banichuk, V. M. Petrov, and F. L. Chernous’ko, “Algorithm and convergence of the local variation method in problems with partial derivatives,” Zh. Vych. Mat. Mat. Fiz., 13, No. 1, 47–57 (1973).Google Scholar
  6. 6.
    I. A. Birger, “General algorithms for solving problems of elasticity, plasticity, and creep,” in: Advances in Solid Mechanics [in Russian], Nauka, Moscow (1975), pp. 51–73.Google Scholar
  7. 7.
    G. I. Bogomaz, V. S. Hudramovych, M. B. Sobolevskaya, et al., “Testing of sacrificial elements for protecting passenger cars in emergencies,” Visn. Dnepr. Univ., No. 2/2, 19–28 (2007).Google Scholar
  8. 8.
    V. N. Vedernikov, V. S. Hudramovych, V. G. Zubchaninov, and V. N. Lotov, “Influence of local heating of a circular hole on the load-bearing capacity of cylindrical shells under axial compression,” Dokl. AN SSSR, Ser. A, No. 5, 29–31 (1988).Google Scholar
  9. 9.
    V. N. Vedernikov, V. S. Hudramovych, and V. N. Lotov, “Experimental investigation of the elastoplastic stability of compressed shells with a locally heated circular opening,” in: Proc. 14th Conf. on Theory of Shells and Plates [in Russian], Metsniereba, Tbilisi (1987), pp. 42–46.Google Scholar
  10. 10.
    V. A. Velichkin, V. S. Hudramovych, V. Ya. Konovalenko, et al., “Vibrations of a physically nonlinear system under impulsive loading,” in: Strength and Reliability of Engineering Devices (Collected Papers) [in Russian], Naukova Dumka, Kyiv (1981), pp. 3–10.Google Scholar
  11. 11.
    V. Z. Vlasov, “Contact problems for shells and bars,” Izv. AN SSSR, OTN, No. 6, 68–82 (1949).Google Scholar
  12. 12.
    V. Z. Vlasov and N. N. Leont’ev, Beams and Plates on Elastic Foundation [in Russian], Fismatgiz, Moscow (1960).Google Scholar
  13. 13.
    E. L. Gart and V. S. Hudramovych, “Projective-iterative modifications of the local variation method and aspects of their use in local-instability problems for shells,” in: Modern Problems of Mechanics and Mathematics [in Ukrainian], IPPMM NANU, L’viv, No. 6 (2008), pp. 18–20.Google Scholar
  14. 14.
    A. A. Gvozdev, Limit Equilibrium Design of Structures [in Russian], Stroiizdat, Moscow (1949).Google Scholar
  15. 15.
    A. A. Gvozdev and A. M. Protsenko, “Trends in the application of limit equilibrium theory for shells,” in: Proc. 7 th All-Union Conf. on Theory of Shells and Plates [in Russian], Nauka, Dnepropetrovsk–Moscow (1970), pp. 736–748.Google Scholar
  16. 16.
    I. G. Goryacheva, Mechanics of Frictional Interaction [in Russian], Nauka, Moscow (2001).Google Scholar
  17. 17.
    E. I. Grigolyuk and V. M. Tolkachev, Contact Problems for Plates and Shells [in Russian], Mashinostroenie, Moscow (1980).Google Scholar
  18. 18.
    Ya. M. Grigorenko, G. G. Vlaikov, and A. Ya. Grigorenko, Numerical-Analytic Solution of Problems in the Mechanics of Shells Based on Different Models [in Russian], Akademperiodika, Kyiv (2007).Google Scholar
  19. 19.
    V. S. Hudramovych, “Strength of space engineering structures under extreme service conditions,” Tekhn. Mekh., No. 2, 74–87 (2001).Google Scholar
  20. 20.
    V. S. Hudramovych, “Collimation mirrors of compact antenna polygon,” Tekhn. Mekh., No. 2, 131–136 (2005).Google Scholar
  21. 21.
    V. S. Hudramovych, “Contact problems for systems of shallow shells and rings under arbitrary loading,” in: Contact Strength of Spatial Structures (Collected Papers) [in Russian], Naukova Dumka, Kyiv (1976), pp. 56–66.Google Scholar
  22. 22.
    V. S. Hudramovych, “Contact problems for frame-and-shell structures in the mechanics of space engineering structures,” Tekhn. Mekh., No. 2, 70–84 (2008).Google Scholar
  23. 23.
    V. S. Hudramovych, “Design of cylindrical shells subjected to hydrostatic pressure,” Stroit. Mekh. Rasch. Sooruzh., No. 4, 32–35 (1971).Google Scholar
  24. 24.
    V. S. Hudramovych, “Methods strength design for space engineering shell structures subject to local loads and contact interaction,” Kosmich. Nauka Tekhnol., 8, No. 4, 11–24 (2002).Google Scholar
  25. 25.
    V. S. Hudramovych, “Methods to solve elastoplastic contact problems in the theory of thin-walled structures,” in: Abstracts of Field Session of the AS USSR, Kharkiv [in Russian], Naukova Dumka, Kyiv (1971), pp. 114–115.Google Scholar
  26. 26.
    V. S. Hudramovych, “Load-bearing capacity of rings under concentrated forces,” Izv. VUZov, Aviats. Techn., No. 1, 125–128 (1972).Google Scholar
  27. 27.
    V. S. Hudramovych, “On load-bearing capacity of airrames,” Kosmich. Issled. na Ukraine, Issue 9, 78–85 (1976).Google Scholar
  28. 28.
    V. S. Hudramovych, “On regularity of infinite systems of equations in contact problems of shell theory,” in: Hydroaeromechanics and Theory of Elasticity (All-Union Interuniversity Collection), Issue 15 (1972), pp. 123–131.Google Scholar
  29. 29.
    V. S. Hudramovych, “Plastic buckling of a cylindrical finite-length shell under local impulsive loading,” in: Proc. 8 th All-Union Conf. on Theory of Shells and Plates [in Russian], Nauka, Moscow (1971) pp. 125–130.Google Scholar
  30. 30.
    V. S. Hudramovych, “Limit equilibrium of shell systems under local loads,” in: Proc. 8th Conf. on Metallic Structures [in Russian], 2, Stal’, Kyiv (2004), pp. 211–220.Google Scholar
  31. 31.
    V. S. Hudramovych, “Limit analysis as an efficient method to assess the structural strength of shell systems,” in: V. V. Panasyuk (ed.), Fracture Mechanics of Materials and Strength of Structures [in Ukrainian], FMI im. G. V. Karpenka NANU, Lviv (2004), pp. 583–588.Google Scholar
  32. 32.
    V. S. Hudramovych, Creep Theory and Its Applications in Design of Thin-Walled Structural Members [in Russian], Naukova Dumka, Kyiv (2005).Google Scholar
  33. 33.
    V. S. Hudramovych, “Manufacturing technologies for antennas, waveguides, and solar devices with high optical and mechanical characteristics,” in: System Technologies (Collected Papers) [in Russian], Dnepropetrovsk, No. 2(13) (2001), pp. 3–6.Google Scholar
  34. 34.
    V. S. Hudramovych, “Stability and load-bearing capacity of plastic shells,” in: Strength and Life of Structures (Collected Papers) [in Russian], Naukova Dumka, Kyiv (1980), pp. 15–31.Google Scholar
  35. 35.
    V. S. Hudramovych, Stability of Elastoplastic Shells [in Russian], Naukova Dumka, Kyiv (1987).Google Scholar
  36. 36.
    V. S. Hudramovych, “Description of plastic deformations in determining the contact pressure in reinforced shells on a lodgment,” [in Russian], in: Strength of Materials and Structural Theory, Issue 16, Budivel’nik (1972), pp. 47–48.Google Scholar
  37. 37.
    V. S. Hudramovych, “Efficient production processes for high-precision waveguide systems,” in: Important Aspects of Physical and Mechanical Studies. Acoustics and Waves [in Russian], Naukova Dumka, Kyiv (2007), pp. 94–99.Google Scholar
  38. 38.
    V. S. Hudramovych, V. G. Baranov, N. A. Konovalov, and I. M. Maitala, “Vibrations of the shells of reflecting antennas during vibrational excitation,” Int. Appl. Mech., 27, No. 1, 56–61 (1991).Google Scholar
  39. 39.
    V. S. Hudramovych, V. A. Blazhko, and E. L. Gart, “Contact interactions of main pipelines and saddle supports with defects in the contact zone,” in: Proc. Int. Conf. on Strength and Reliability of Main Pipelines, IPM NANU (2008), pp. 35–36.Google Scholar
  40. 40.
    V. S. Hudramovych and I. M. Volkova, “Shape optimization for curvilinear rods and shells of revolution undergonig natural vibrations,” in: Proc. All-Union Sci. School on Optimization and Dynamics, Tartu Univ., Tartu (1982), p. 16.Google Scholar
  41. 41.
    V. S. Hudramovych, A. P. Gaiduchenko, and A. I. Kovalenko, “Electroforming production technologies for antennas, waveguidess and solar devices,” Kosmich. Nauka Technol., 7, No. 2/3, 66–77 (2001).Google Scholar
  42. 42.
    V. S. Hudramovych and E. L. Gart, “Influence of the shape of a finite element on the computational efficiency of projective-iterative methods when applied to solve a plane problem of elasticity,” Visn. Kyiv. Univ., Ser. Fiz.-Mat. Nauki, No. 4, 53–58 (2008).Google Scholar
  43. 43.
    V. S. Hudramovych, E. L. Gart, and O. M. Rubinchik, “Linear and bilinear approximations in the projective-iterative modification of the finite-element method for a plane problem of elasticity,” Tekhn. Mekh., No. 9, 84–96 (2009).Google Scholar
  44. 44.
    V. S. Hudramovych and V. P. Gerasimov, “Load-bearing capacity of reiforcement rings under local loading,” in: Contact Strength of Spatial Structures (Collected Papers) [in Russian], Naukova Dumka, Kyiv (1976), pp. 163–172.Google Scholar
  45. 45.
    V. S. Hudramovych and V. P. Gerasimov, “Plastic failure of a cylindrical shell under local loading,” in: Mechanics of Deformable Bodies (Interuniversity Collection) [in Russian], Issue 4, Kuibyshev. Univ., Kuibyshev (1979), pp. 36–39.Google Scholar
  46. 46.
    V. S. Hudramovych and V. P. Gerasimov, “Limit analysis of cylindrical elements of tower structures with inhomogeneous stress state,” in: Design and Building of Engineering Structures of Cast-in-Place Ferroconcrete (Collected Papers) [in Russian], LPSNIIP, Leningrad (1989), pp. 87–92.Google Scholar
  47. 47.
    V. S. Hudramovych and V. P. Gerasimov, “Statics and dynamics of rigid–plastic cylindrical shells under local loading,” in: Proc. 12th All-Union Conf. on Theory of Shells and Plates [in Russian], No. 2, Erevan. Univ., Erevan (1980), pp. 50–56.Google Scholar
  48. 48.
    V. S. Hudramovych, V. P. Gerasimov, and A. F. Demenkov, Limit Analysis of Structural Members [in Russian], Naukova Dumka, Kyiv (1990).Google Scholar
  49. 49.
    V. S. Hudramovych and A. V. Gladkii, “Load-bearing capacity of cylindrical shells with geometrical and physical nonlinearity under nonuniform loading,” Techn. Mekh., No. 5, 121–126 (1997).Google Scholar
  50. 50.
    V. S. Hudramovych and A. F. Demenkov, Elastoplastic Structures with Geometrical Imperfections and Residual Stresses [in Russian], Naukova Dumka, Kyiv (1991).Google Scholar
  51. 51.
    V. S. Hudramovych, A. F. Demenkov, M. F. Demeshko, and E. V. Samarskaya, “Experimental investigation of the deformation and bearing capacity of elastoplastic cylindrical shells with initial shape imperfections of different configuration under axial compression,” Strength of Materials, 21, No. 5, 731–735 (1990).CrossRefGoogle Scholar
  52. 52.
    V. S. Hudramovych, A. F. Demenkov, A. I. Kovalenko, et al., “Residual stresses in thin-walled structural elements of antennas, waveguides, and solar devices produced by electroforming,” Tekhn. Mekh., No. 1, 135–140 (2004).Google Scholar
  53. 53.
    V. S. Hudramovych, A. F. Demenkov, and E. V. Samarskaya, “Effect of process-induced defects (initial deflections and residual stresses) on the deformation and limiting state of trussed structures,” in: Proc. Int. Conf. on Evaluation and Justification for Extending the Service Life of Structural Members [in Russian], IPP NANU, Kyiv (2000), pp. 455–460.Google Scholar
  54. 54.
    V. S. Hudramovych and A. P. Dzyuba, “Contact interactions and optimization of shell systems under local loading,” Mat. Met. Fiz.-Mekh. Polya, 51, No. 2, 188–201 (2008).MATHGoogle Scholar
  55. 55.
    V. S. Hudramovych, A. P. Dzyuba, and Yu. M. Selivanov, “Interference study of the properties of optimized locally loaded structures,” in: Proc. Int. Conf. on Important Problems of Continuum Mechanics and Structural Strength [in Russian], Dnepropetrovsk Univ., Dnepropetrovsk (2007), p. 182.Google Scholar
  56. 56.
    V. S. Hudramovych and I. A. Diskovskii, “Dynamical stability of a finite-length cylindrical shell under impulsive local loading,” in: Hydroaeromechanics and Elastic Theory (All-Union Interuniversity Collection) [in Russian], Issue 16 (1973), pp. 90–96.Google Scholar
  57. 57.
    V. S. Hudramovych and I. A. Diskovskii, “On local instability of spherical shells,” Dokl. AN SSSR, 232, No. 6, 1283–1285 (1977).Google Scholar
  58. 58.
    V. S. Hudramovych and I. A. Diskovskii, “Parabolic shells subjected to solar radiation,” Int. Appl. Mech., 23, No. 11, 1043–1049 (1987).Google Scholar
  59. 59.
    V. S. Hudramovych and I. A. Diskovskii, “Theoretical and experimental research of spherical shells with strongly inhomogeneous stress states,” in: Solid Mechanics (Interuniversity Collection) [in Russian], Issue 3, Kuibyshev. Univ., Kuibyshev (1978), pp. 142–148.Google Scholar
  60. 60.
    V. S. Hudramovych and I. A. Diskovskii, “A setup for strength and buckling studies of shell systems under local loads,” in: Strength and Reliability of Structures (Collected Papers) [in Russian], Naukova Dumka, Kyiv (1978), pp. 30–36.Google Scholar
  61. 61.
    V. S. Hudramovych and I. A. Diskovskii, “Experimental study of the local instability of spherical segments,” in: Proc. 4th All-Union Conf. on Statics and Dynamics of Space Structures [in Russian], Kyiv. Inzh.-Stroit Inst., Kyiv (1978), pp. 54–57.Google Scholar
  62. 62.
    V. S. Hudramovych, I. A. Diskovskii, and N. A. Konovalov, “High-speed photography in experimental study of local loss of stability,” Zh. Nauchn. Prikl. Fotogr. Kinematogr. AN SSSR, 24, No. 1, 14–20 (1979).Google Scholar
  63. 63.
    V. S. Hudramovych, I. A. Diskovskii, N. A. Konovalov, and I. M. Maitala, “Experimental study of dynamic characteristics of a thin-walled mirror antenna with two-position high-speed photography,” Zh. Nauchn. Prikl. Fotogr. Kinematogr. AN SSSR, 34, No. 5, 321–326 (1989).Google Scholar
  64. 64.
    V. S. Hudramovych, I. A. Diskovskii, and I. A. Makeev, Thin-Walled Elements of Mirror Antennas [in Russian], Naukova Dumka, Kyiv (1986).Google Scholar
  65. 65.
    V. S. Hudramovych and V. S. Konovalenkov, “Deformation and limiting state of inelastic shells with loading history,” Izv. AN SSSR, Mekh. Tverd. Tela, No. 3, 157–163 (1987).Google Scholar
  66. 66.
    V. S. Hudramovych, E. M. Makeev, and V. A. Blazhko, “Influence of process-induced defects on the load-bearing capacity of some antenna, waveguide, and solar structures,” in: Proc. Int. Conf. on Mathematical Problems of Technical Mechanics [in Russian], Dnepropenrovsk (2005), p. 139.Google Scholar
  67. 67.
    V. S. Hudramovych, E. M. Makeev, V. I. Mossakovskii, and P. I. Nikitin, “Contact interaction of shell structures with supporting bases under complex service conditions,” Strength of Materials, 17, No. 10, 1463–1471 (1985).CrossRefGoogle Scholar
  68. 68.
    V. S. Hudramovych, E. M. Makeev, and S. P. Fedii, “Strength of a spherical segment on a lodgment with inhomogeneous contact,” Tekhn. Mekh., No. 1, 141–147(1999).Google Scholar
  69. 69.
    V. S. Hudramovych and V. I. Mossakoskii, “Contact problem for an elastic ring reinforcing a cylindrical shell,” Izv. AN SSSR. Mekh. Mashinostr., No. 2, 153–156 (1961).Google Scholar
  70. 70.
    V. S. Hudramovych and V. I. Mossakoskii, “The general case of the plane contact problem for the ring brace,” Int. Appl. Mech., 2, No. 6, 1–5 (1966).Google Scholar
  71. 71.
    V. S. Hudramovych, A. A. Novopashin, A. A. Purel’, and D. I. Sotnikov, “Contact problem for a reinforced finite-length shell on a circular elastic foundation (lodgment),” in: Hydroaeromechanics and Elastic Theory (All-Union Interuniversity Collection) [in Russian], Issue 8 (1968), pp. 99–107.Google Scholar
  72. 72.
    V. S. Hudramovych and I. V. Pasechnik, “Contact interaction of inhomogeneous shells of revolution and elastic a foundation described by different models,” in: Hydroaeromechanics and Elastic Theory (All-Union Interuniversity Collection) [in Russian], Dnepropetr. Univ., Dnepropentovsk (1987), pp. 98–102.Google Scholar
  73. 73.
    V. S. Hudramovych and I. V. Pasechnik, “Contact interaction of a shell and its base with allowance for their elastoplastic properties,” Int. Appl. Mech., 25, No. 11, 1092–1098 (1989).Google Scholar
  74. 74.
    V. S. Hudramovych and I. V. Pasechnik, “Design of an infinite-length cylindrical shell on a combined foundation,” in: Plasticity and Stability in Solid Mechanics (Collected Papers) [in Russian], Kalininsk. Univ., Kalinin, (1984), pp. 42–46.Google Scholar
  75. 75.
    V. S. Hudramovych and A. A. Purel’, “Contact problems for an arbitrary system of shells of revolution and circular foundation,” in: Proc. 8th All-Union Conf. on Theory of Shells and Plates [in Russian], Nauka, Moscow, (1973), pp. 665–669.Google Scholar
  76. 76.
    V. S. Hudramovych and A. A. Purel’, “Contact problems for an arbitrary system of shells of revolution reinforced with a ring at the joint,” in: Hydroaeromechanics and Elastic Theory (All-Union Interuniversity Collection) [in Russian], Issue 16 (1973), pp. 97–102.Google Scholar
  77. 77.
    A. N. Guz, M. Sh. Dyshel’, G. G. Kuliev, and O. B. Milovanova, Fracture and Stability of Thin Bodies with Cracks [in Russian], Naukova Dumka, Kyiv (1981).Google Scholar
  78. 78.
    A. N. Guz and V. B. Rudnitskii, Fundamentals of the Theory of Contact Interaction of Elastic Bodies with Initial (Residual) Stresses [in Russian], Khmel’nitsk. Univ., Khmel’nitskii (2006).Google Scholar
  79. 79.
    A. N. Guz, I. S. Chernyshenko, V. N. Chekhov, et al., Theory of Shells Weakened by Holes [in Russian], Naukova Dumka, Kyiv (1980).MATHGoogle Scholar
  80. 80.
    M. I. Erkhov, I. A. Monakhov, and V. I. Sebekina, “Method for design of plates and shells with large deflections,” Stroit. Mekh. Rasch. Sooruzh., No. 6, 17–21 (1981).Google Scholar
  81. 81.
    D. D. Ivlev, Perfect Plasticity Theory [in Russian], Nauka, Moscow (1964).Google Scholar
  82. 82.
    B. Ya. Kantor, Contact Problems in the Nonlinear Theory of Shells of Revolution [in Russian], Naukova Dumka, Kyiv (1990).Google Scholar
  83. 83.
    G. K. Klein, Design of Buried Pipes [in Russian], Gostekhizdat, Moscow (1957).Google Scholar
  84. 84.
    M. A. Krasnosel’skii, G. M. Vainikko, P. P. Zabreiko, et al., Approximate Solution of Operator Equations [in Russian], Nauka, Moscow (1969).Google Scholar
  85. 85.
    V. A. Lazaryan, Dynamics of Vehicles (Selected Papers) [in Russian], Naukova Dumka, Kyiv (1985).Google Scholar
  86. 86.
    S. Lukasiewicz, Local Loads in Plates and Shells, Noordhoff, Leyden (1979).MATHGoogle Scholar
  87. 87.
    G. I. L’vov, “Contact creep problems for shallow shells,” Izv. AN SSSR. Mekh. Tverd. Tela, No. 5, 116–124 (1984).Google Scholar
  88. 88.
    A. S. Sakharov and I. Al’tenbakh (eds.), Finite-Element Method in Solid Mechanics [in Russian], Vyshcha Shkola, Kyiv (1982).Google Scholar
  89. 89.
    N. N. Moiseev, “Numerical methods in optimal control theory,” Izv. AN SSSR, Kibernetika, No. 3, 1–29 (1966).Google Scholar
  90. 90.
    V. I. Mossakovskii and V. S. Hudramovych, “Contact problems in shell theory,” in: Contact Strength of Space Structures (Collected Papers) [in Russian], Naukova Dumka, Kyiv (1976), pp. 3–40.Google Scholar
  91. 91.
    V. I. Mossakovskii, V. S. Hudramovych, and E. M. Makeev, Contact Interaction of Elements in Shell Structures [in Russian], Naukova Dumka, Kyiv (1988).Google Scholar
  92. 92.
    V. I. Mossakovskii, V. S. Hudramovych, and E. M. Makeev, Contact Problems for Shells and Bars [in Russian], Mashinostroenie, Moscow (1978).Google Scholar
  93. 93.
    V. I. Mossakovskii, V. S. Hudramovych, A. A. Novopashin, et al., “Contact problem for a reinforced cylindrical shell on a circular foundation (lodgment),” in: Design of Space Structures [in Russian], Issue 11, Stroiizdat, Moscow (1967), pp. 53–72.Google Scholar
  94. 94.
    Sh. A. Mukhamediev, L. V. Nikitin, and S. V. Yunga, “Modified local variation method applied to problems of fracture mechanics,” Izv. AN SSSR. Mekh. Tverd. Tela, No. 1, 76–83 (1976).Google Scholar
  95. 95.
    I. F. Obraztsov, V. V. Nerubailo, and V. P. Ol’shanskii, Shells under Local Loads (Fundamental Results and Research Trends: A Review) [in Russian], Manuscript No. 1222, Dep. at VINITI, MAI, Moscow (1988).Google Scholar
  96. 96.
    B. L. Pelekh and M. A. Sukhorul’skii, Contact Problems for Elastic Anisotropic Shells [in Russian], Naukova Dumka (1980).Google Scholar
  97. 97.
    A. V. Perel’muter and V. I. Slivker, Design Models of Structures and Capabilities for Their Analysis [in Russian], DMK Press, Moscow (2007).Google Scholar
  98. 98.
    G. Ya. Popov, Concentration of Elastic Stresses near Punches, Notches, Thin Inclusions, and Reinforcements [in Russian], Nauka, Moscow (1982).Google Scholar
  99. 99.
    L. A. Galin (ed.), Development of the Theory of Contact Problems in the USSR [in Russian], Nauka, Moscow (1976).Google Scholar
  100. 100.
    M. T. Serebryannikov, Harmonic Analysis [in Russian], Gostekhizdat, Moscow (1948).Google Scholar
  101. 101.
    V. I. Feodos’ev and S. M. Chernyakov, “Transfer of concentrated forces to a thin-walled shell,” Mekh. Tverd. Tela, No. 6, 57–63 (1966).Google Scholar
  102. 102.
    F. L. Chernous’ko and N. V. Banichuk, Variational Problems of Mechanics and Control [in Russian], Nauka, Moscow (1973).Google Scholar
  103. 103.
    J. H. Argyris and D. W. Scharpf, “Methods of elastoplastic analysis,” Rep. No. 105, Stuttgart. Univ., Stuttgart (1971).Google Scholar
  104. 104.
    L. Beskin, “Local stress distribution in cylindrical shells,” J. Appl. Mech., 13, No.2 (1946).Google Scholar
  105. 105.
    G. Galilei, Discourses and Mathematical Demonstrations Relating to Two New Sciences [in Italian], Leiden (1638).Google Scholar
  106. 106.
    P. G. Hodge, “The practical significance of limit analysis,” J. Aerospace Sci., 25, No. 11, 724–726 (1958).Google Scholar
  107. 107.
    V. S. Hudramovich, “Carrying capacity of locally loaded shell structures,” in: V. Krupka and P. Sneider (eds.), Proc. Int. Conf. on Carrying Capacity of Shell Structures, Brno (1997), pp. 145–151.Google Scholar
  108. 108.
    V. S. Hudramovich, “Contact interactions between shell systems and supports (stamps). General solution method. Influence of the structural defects,” in: Proc. Symp. on Important Problems of Mechanics of Inhomogeneous Structures, Lvivsk. Univ., Lviv (2003), pp. 11–12.Google Scholar
  109. 109.
    V. S. Hudramovich, “Features of nonlinear deformation and critical states of shell systems with geometrical imperfections,” Int. Appl. Mech., 42, No. 12, 1323–1355 (2006).CrossRefGoogle Scholar
  110. 110.
    V. S. Hudramovich, “Numerical simulation of nonlinear contact interaction between shell structures and supports (stamps) of different types,” in: J. Emry (ed.), Progress and Trends in Rheology, Springer, Darmstadt (1998), pp. 351–352.Google Scholar
  111. 111.
    V. S. Hudramovych, “Plastic and creep instability of shells with initial imperfections,” in: Wan Reng (ed.), Solid Mechanics and Its Applications, 64, IUTAM Symp. on Rheology of Bodies with Defects, Kluwer Acad. Publ., Dordrecht–Boston–London (1999), pp. 277–289.Google Scholar
  112. 112.
    V. S. Hudramovich, “Strength of locally loaded thin-walled structures of marine vehicles,” in: Proc. 5th Int. Symp. on High Speed Marine Vehicles, Publ. Univ. of Naples Federico II, Capri-Napoli (1999), pp. IV.1.1–IV.1.12.Google Scholar
  113. 113.
    V. S. Hudramovich and A. F. Demenkov, “Influence of damage of the rocket-space girder structures on their deformation and carrying capacity,” in: Proc. 5th Forum on Astronautics and Aeronautis, Publ. Inst. Technol., Harbin (2000), pp. 121–127.Google Scholar
  114. 114.
    W. T. Koiter, “General theorems for elastic-plastic solids,” in: Progress in Solid Mechanics, Vol. 1, Ch. 4, North-Holland, Amsterdam (1960).Google Scholar
  115. 115.
    W. Prager and P. G. Hodge, Theory of Perfectly Plastic Solids, Willey and Sons, London (1951).MATHGoogle Scholar
  116. 116.
    S. P. Timoshenko, History of Strength of Materials, McGraw-Hill, New York (1953).Google Scholar

Copyright information

© Springer Science+Business Media, Inc. 2009

Authors and Affiliations

  1. 1.Institute of Technical MechanicsNational Academy of Sciences of Ukraine, National Space Agency of UkraineDnepropetrovskUkraine

Personalised recommendations