Skip to main content
SpringerLink
Log in

General direction of development of the theory of multilayered shells

  • Published:
Mechanics of Composite Materials 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. É. I. Grigolyuk and F. A. Kogan, ″Current state of the theory of multilayered shells,″ Prikl. Mekh.,8, No. 6, 3–17 (1972).

    Google Scholar 

  2. A. A. Dudchenko, S. A. Lur'e, and I. F. Obraztsov, ″Anisotropic multilayered plates and shells,″ Itogi Nauki Tekh. Mekh. Deform. Tverd. Tela,15, 3–68 (1983).

    Google Scholar 

  3. V. V. Bolotin and Yu. N. Novichkov, Mechanics of Multilaminate Structures [in Russian], Moscow (1980).

  4. É. I. Grigolyuk, ″Equations of three-layer shells with a lightweight filler,″ Izv. Akad. Nauk SSSR, Otd. Tekh. Nauk, No. 1, 77–84 (1957).

    Google Scholar 

  5. É. I. Grigolyuk, ″Finite deflections of three-layer shells with a stiff filler,″ Izv. Akad. Nauk SSSR, Otd. Tekh. Nauk, No. 1, 26–34 (1958).

    Google Scholar 

  6. É. I. Grigolyuk and P. P. Chulkov, ″Theory of viscoelastic multilayered shells with stiff fillers in the case of finite deflections,″ Zh. Prikl. Mekh. Tekh. Fiz., No. 5, 109–117 (1964).

    Google Scholar 

  7. É. I. Grigolyuk and P. P. Chulkov, ″Nonlinear equations of thin elastic laminated anisotropic shallow shells with a stiff filler,″ Izv. Akad. Nauk SSSR, Mekh. Tverd. Tela, No. 5, 68–80 (1965).

    Google Scholar 

  8. É. I. Grigolyuk and P. P. Chulkov, ″Nonlinear equations of shallow multilayered shells of regular structure,″ Inzh. Zh. Mekh. Tverd. Tela, No. 1, 163–169 (1967).

    Google Scholar 

  9. É. I. Grigolyuk and P. P. Chulkov, ″On the theory of multilayered shells,″ in: Contributions to the Theory of Aircraft Structures, Delft (1972), pp. 171–183.

  10. L. Libresku, ″Nonlinear theory of elastic anisotropic multilayered shells,″ in: Selected Problems of Applied Mechanics [in Russian], Moscow (1974), pp. 453–466.

  11. V. E. Chepiga, ″Linearized equations of stability of thick multilayered shells,″ Izv. Akad. Nauk SSSR, Mekh. Tverd. Tela, No. 2, 33–41 (1971).

    Google Scholar 

  12. M. Epstein and P. G. Glockner, ″Nonlinear analysis of multilayered shells,″ Int. J. Solids Struct.,13, No. 11, 1081–1089 (1977).

    Google Scholar 

  13. P. P. Chulkov, ″Equations of the vibration of elastic laminated shells,″ Din. Sploshnoi Sredy,4, 19–29 (1970).

    Google Scholar 

  14. L. V. Baev, ″Application of an approximate theory of multilayered plates which accounts for transverse shear,″ Din. Sploshnoi Sredy,4, 11–18 (1970).

    Google Scholar 

  15. L. V. Baev and P. P. Chulkov, ″Design of laminated plates,″ Mekh. Polim., No. 6, 1135 (1969).

    Google Scholar 

  16. Yu. D. Nasonkin, ″Finding a particular solution for an equation describing the bending of a multilayered plate,″ Mekh. Polim., No. 6, 1131 (1975).

    Google Scholar 

  17. S. S. Kokhmanyuk and A. N. Shupikov, ″Deformation of multilayered plates under nonsteady loading,″ Probl. Mashinostr.,10, 20–22 (1980).

    Google Scholar 

  18. A. E. Bogdanovich, ″Equations of multilayered composite cylindrical shells on the basis of the straight-line hypothesis,″ Second International Conference of Young Specialists in the Mechanics of Composite Materials. Summary of Documents. Riga (1979), pp. 68–69.

  19. A. E. Bogdanovich and É. V. Yarve, ″Analysis of stresses in multilayerd beams in transverse dynamic bending,″ Mekh. Kompozitn. Mater., No. 5, 824–837 (1983).

    Google Scholar 

  20. V. L. Narusberg and L. A. Pazhe, ″Effect of kinematic nonuniformity on the critical stability parameters of laminated cylindrical shells,″ Mekh. Kompozitn. Mater., No. 2, 271–278 (1982).

    Google Scholar 

  21. I. A. Buryakov, ″Nonlinear equations of a Timoshenko-type theory of multilayered anisotropic shells,″ Mekh. Kompozitn. Mater., No. 2, 271–278 (1982).

    Google Scholar 

  22. É. I. Grigolyuk and G. M. Kulikov, ″Toward a theory of elastic laminated anisotropic shells,″ Dokl. Akad. Nauk SSSR,275, No. 5, 1077–1073 (1984).

    Google Scholar 

  23. É. I. Grigolyuk and G. M. Kulikov, ″Theory and numerical solution of problems of the statics of multilayered reinforced shells,″ Mekh. Kompozitn. Mater., No. 4, 643–650 (1986).

    Google Scholar 

  24. G. M. Kulikov, ″Effect of anisotropy on the stress state of multilayered reinforced shells,″ Prikl. Mekh.,22, No. 12, 66–72 (1986).

    Google Scholar 

  25. É. I. Grigolyuk and G. M. Kulikov, ″Variant of the nonlinear theory of elastic multilayered shallow shells,″ Prikl. Mekh.,22, No. 12, 66–72 (1986).

    Google Scholar 

  26. G. W. Swift and R. A. Heller, ″Layered beam analysis,″ Proc. Am. Soc. Civ. Eng. J. Eng. Mech. Division,100, No. 2, 267–282 (1974).

    Google Scholar 

  27. S. V. Filitov, ″Stability of laminated shell structures,″ Raschety na Prochn. Zhestkost',4, 139–152 (1982).

    Google Scholar 

  28. S. V. Filitov, ″Calculation of the stiffness matrix of a laminated shell,″ Rasche'ty na Prochn. Zhestkost',5, 123–219 (1983).

    Google Scholar 

  29. É. I. Grigolyuk and G. M. Kulikov, ″Effect of shear stress nonuniformity in modern tires,″ Mekh. Kompozitn. Mater., No. 5, 870–877 (1986).

    Google Scholar 

  30. É. I. Grigolyuk and G. M. Kulikov, ″Axisymmetric deformation of anisotropic laminated shells of revolution of complex form,″ Mekh. Kompozitn. Mater., No. 4, 637–645 (1981).

    Google Scholar 

  31. V. G. Bazhenov and E. A. Zhuravlev, ″Variational-difference method of solving nonlinear axisymmetric problems of the dynamics of laminated shells,″ Prikl. Probl. Prochn. Plastichn.,13, 36–45 (1979).

    Google Scholar 

  32. V. N. Paimushin and V. G. Demidov, ″Variant of relations of the theory of central bending of multilayered shells of complex geometry,″ Stat. Dinam. Obolochek,12, 53–60 (1979).

    Google Scholar 

  33. N. Alam and N. T. Asnani, ″Vibration and damping analysis of a multilayered cylindrical shell. Pt. 1: Theoretical analysis,″ AIAA J.,22, No. 6, 803–810 (1984).

    Google Scholar 

  34. N. Alam and N. T. Asnani, ″Vibration and damping analysis of a multilayered cylindrical shell. Pt. 2: Numerical results,″ AIAA J.,22, No. 7, 975–981 (1984).

    Google Scholar 

  35. N. Alam and N. T. Asnani, ″Vibration and damping analysis of a multilayered rectangular plate with constrained viscoelastic layers,″ J. Sound Vib.,97, No. 4, 597–614 (1984).

    Google Scholar 

  36. P. Seide, ″An improved approximate theory for the bending of laminated plates,″ Mechanics Today,5, 451–466 (1980).

    Google Scholar 

  37. M. Gotteland, ″On a theory for anisotropic and laminated plates,″ in: 3rd Intern. Conf. on Structural Mechanics in Reactor Technology. Pt. M, Amsterdam; Oxford (1975), Vol. 5, M 5/4.

  38. C. -T. Sun and J. M. Whitney, ″Theories for the dynamic response of laminated plates,″ AIAAJ.,11, No. 2, 178–183 (1973).

    Google Scholar 

  39. S. T. Mau, ″A refined laminated plate theory,″ Trans. ASME,E40, No. 2, 606–607 (1973).

    Google Scholar 

  40. T. L. Waltz and J. R. Vinson, ″Interlaminar stresses in laminated cylindrical shells of composite materials,″ AIAA J.,14, No. 9, 1213–1218 (1976).

    Google Scholar 

  41. J. A. Zukas and J. R. Vinson, ″Laminated transversely isotropic cylindrical shells,″ Trans. ASME,E38, No. 2, 109–115 (1971).

    Google Scholar 

  42. B. L. Pelekh, A. V. Maksimuk, and N. N. Shcherbina, ″Contact stiffness of laminated cylindrical shells. 2. Matrix method of solving contact problems for multilayered cylindrical shells,″ Mekh. Kompozitn. Mater., No. 2, 276–280 (1986).

    Google Scholar 

  43. B. L. Pelekh, M. A. Sukhorol'skii, and F. P. Yakimov, ″Contact problems for laminated plates subjected to mechanical and thermal loads,″ Prikl. Mekh.,14, No. 5, 79–84 (1978).

    Google Scholar 

  44. B. L. Pelekh and N. N. Shcherbina, ″Deformation of multilayered cylindrical shells in the case of imperfect contact between the layers,″ in: Summary of Documents of the II All-Union Scientific-Technical Seminar: Nonclassical Problems of the Mechanics of Composite Materials and Structures, Kiev (1984), pp. 35–36.

  45. T.-M. Hsu and J. T.-S. Wang, ″A theory of laminated cylindrical shells consisting of layers of orthotopic laminae,″ AIAA J.,8, No. 12, 2141–2146 (1970).

    Google Scholar 

  46. T.-M. Hsu and J. T.-S. Wang, ″Rotationally symmetric vibrations of orthotopic layered cylindrical shells,″ J. Sound Vib.,16, No. 4, 473–487 (1971).

    Google Scholar 

  47. A. M. Krochak, ″Determination of stress concentration in a transversely isotropic multilayered plate,″ in: Basalt-Fiber Composite Materials and Structures [in Russian], Kiev (1980), pp. 191–195.

  48. A. V. Ivanov and P. P. Chulkov, ″Allowance for transverse strains of the filler in problems of the stability of three-layered plates with different load-bearing layers,″ Izv. Akad. Nauk SSSR, Mekh. Tverd. Tela, No. 6, 101–107 (1969).

    Google Scholar 

  49. L. V. Baev, ″Calculation of multilayered plates with allowance for transverse shear and compression,″ Din. Sploshnoi Sredy,6, 92–104 (1970).

    Google Scholar 

  50. L. V. Baev, ″Design of regular plates composed of an arbitrary number of layers,″ Din. Sploshnoi Sredy,25, 10–17 (1976).

    Google Scholar 

  51. L. Libresku, ″Refined linear theory of elastic anisotropic multilayered shells,″ Pt. 1, Mekh. Polim., No. 6, 1038–1050 (1975).

    Google Scholar 

  52. L. Libresku, ″Refined linear theory of elastic anisotropic multilayered shells,″ Pt. 2, Mekh. Polim., No. 1, 100–109 (1976).

    Google Scholar 

  53. L. I. Librescu, ″Some results concerning the refined theory of elastic multilayered shells. Pt. I. The physically nonlinear theory,″ Rev. Roumaine Sci. Tech. Ser. de Mecanique Appl.,20, No. 1, 93–105 (1975).

    Google Scholar 

  54. L. I. Librescu, ″Some results concerning the refined theory of elastic multilayered shells. Pt. 1. The physically nonlinear theory,″ Rev. Roumaine Sci. Tech. Ser. de Mecanique Appl.,20, No. 1, 93–105 (1975).

    Google Scholar 

  55. M. Epstein and P. G. Glockner, ″Multilayered shells and directed surfaces,″ Int. J. Eng. Sci.,17, No. 5, 553–562 (1979).

    Google Scholar 

  56. I. A. Buyakov, ″Allowance for strains in the normal direction in a nonlinear Timoshenko-type theory of multilayered shells,″ Mekh. Kompozitn. Mater., No. 2, 358–359 (1980).

    Google Scholar 

  57. V. L. Narusberg and L. A. Pazhe, ″Calculation of the natural spectra of vibration of laminated shells of moderate thickness,″ Mekh. Kompozitn. Mater., No. 2, 298–304 (1985).

    Google Scholar 

  58. P. P. Chulkov and V. N. Paimushin, ″Problem of the design of multilayered shells of complex geometry,″ Statica Sooruzh., Kiev (1978), pp. 69–72.

    Google Scholar 

  59. V. N. Paimushin and V. G. Demidov, ″Numerical solution of axisymmetric boundary-value problems of the statics and thermoelasticity of multilayered shells of revolution,″ in: Strength, Stability, and Vibration of Thin-Walled and Monolithic Aircraft Structures [in Russian], Kazan (1981), pp. 79–84.

  60. V. N. Paimushin and V. G. Demidov, ″Equations of the theory of multilayered shells with layers of variable thickness and their application to problems of the theory of elasticity in noncanonical regions,″ Issled. Teor. Plastin. Obolochek, Pt. 2,18, 54–65 (1985).

    Google Scholar 

  61. V. N. Paimushin, Yu. Yu. Petrushenko, and I. Kh. Saitov, ″Generalized model of the mechanical of multilayered shells with layers of variable thickness,″ in: Strength and Vibration of Aircraft Structures [in Russian], Kazan (1984), pp. 37–43.

  62. Yu. N. Novichkov and A. S. Kuz'min, ″Study of the stress-strain state of laminated shells of revolution with application to tire design,″ Mekh. Kompozitn. Mater., No. 6, 1023–1029 (1984).

    Google Scholar 

  63. A. S. Kuz'min, Yu. N. Novichkov, S. L. Sokolov, and O. B. Tret'yakov, ″Statics of laminated elastic composite shells of revolution with application to tire design,″ in: Summary of Documents of the VI Ail-Union Conference on the Mechanics of Polymeric and Composite Materials, Riga (1986).

  64. É. I. Grigolyuk and G. M. Kulikov, ″Modern methods of designing pneumatic tires,″ in: Summary of Documents of the II All-Union Scientific-Technical Conference ″Dynamics and Strength of Automobiles,″ Moscow (1986).

  65. V. E. Chepiga, ″Refined theory of laminated shells,″ Prikl. Mekh.,12, No. 11, 45–49 (1976).

    Google Scholar 

  66. V. E. Chepiga, ″Construction of a theory of multilayered anisotropic shells with a specified conditional accuracy of order hN,″ Izv. Akad. Nauk SSSR, Mekh. Tverd. Tela, No. 4, 113–120 (1977).

    Google Scholar 

  67. V. E. Chepiga, ″Numerical analysis of the equations of a refined theory of laminated shells,″ Submitted to VINITI 14.01.86, No. 290-B, Leningrad (1986).

  68. V. E. Chepiga, ″Study of the stability of multilaminate shells by a refined theory,″ Submitted to VINITI 14.01.86, No. 289-B, Leningrad (1986).

  69. B. L. Pelekh and V. A. Laz'ko, Laminated Anisotropic Plates and Shell with Stress Concentrators [in Russian], Kiev (1982).

  70. B. L. Pelekh, V. A. Laz'ko, and O. S. Machuga, ″Variational method of studying the stress concentration near interlayer defects in laminated anisotropic plates and shells,″ Prikl. Mekh.,21, No. 11, 124–128 (1985).

    Google Scholar 

  71. V. A. Laz'ko, ″Stress-strain state of laminated anisotropic shells in the presence of regions of ideal contact between the layers. 2. Generalization of the equations of orthotopic laminated shells with discontinuous displacements at the interface,″ Mekh. Kompozitn. Mater., No. 1, 77–84 (1982).

    Google Scholar 

  72. L. P. Khoroshun, ″Concept of a mixture in the construction of a theory of laminated plates and shells,″ Prikl. Mekh.,21, No. 4, 110–118 (1985).

    Google Scholar 

  73. Ya. M. Grigorenko, A. T. Vasilenko, and N. D. Pankratova, Statics of Anisotropic Thick-Walled Shells [in Russian], Kiev (1985).

Download references

Author information

Authors and Affiliations

  1. Moscow Automotive Engineering Institute, Tambov Institute of Chemical Machinery Construction, USSR

    É. I. Grigolyuk & G. M. Kulikov

Authors
  1. É. I. Grigolyuk
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. G. M. Kulikov
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Translated from Mekhanika Kompozitnykh Materialov, No. 2, pp. 287–298, March–April, 1988.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Grigolyuk, É.I., Kulikov, G.M. General direction of development of the theory of multilayered shells. Mech Compos Mater 24, 231–241 (1988). https://doi.org/10.1007/BF00608158

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00608158

Keywords

Search

Navigation