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Literature cited
É. I. Grigolyuk and F. A. Kogan, ″Current state of the theory of multilayered shells,″ Prikl. Mekh.,8, No. 6, 3–17 (1972).
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).
V. V. Bolotin and Yu. N. Novichkov, Mechanics of Multilaminate Structures [in Russian], Moscow (1980).
É. I. Grigolyuk, ″Equations of three-layer shells with a lightweight filler,″ Izv. Akad. Nauk SSSR, Otd. Tekh. Nauk, No. 1, 77–84 (1957).
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).
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).
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).
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).
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.
L. Libresku, ″Nonlinear theory of elastic anisotropic multilayered shells,″ in: Selected Problems of Applied Mechanics [in Russian], Moscow (1974), pp. 453–466.
V. E. Chepiga, ″Linearized equations of stability of thick multilayered shells,″ Izv. Akad. Nauk SSSR, Mekh. Tverd. Tela, No. 2, 33–41 (1971).
M. Epstein and P. G. Glockner, ″Nonlinear analysis of multilayered shells,″ Int. J. Solids Struct.,13, No. 11, 1081–1089 (1977).
P. P. Chulkov, ″Equations of the vibration of elastic laminated shells,″ Din. Sploshnoi Sredy,4, 19–29 (1970).
L. V. Baev, ″Application of an approximate theory of multilayered plates which accounts for transverse shear,″ Din. Sploshnoi Sredy,4, 11–18 (1970).
L. V. Baev and P. P. Chulkov, ″Design of laminated plates,″ Mekh. Polim., No. 6, 1135 (1969).
Yu. D. Nasonkin, ″Finding a particular solution for an equation describing the bending of a multilayered plate,″ Mekh. Polim., No. 6, 1131 (1975).
S. S. Kokhmanyuk and A. N. Shupikov, ″Deformation of multilayered plates under nonsteady loading,″ Probl. Mashinostr.,10, 20–22 (1980).
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.
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).
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).
I. A. Buryakov, ″Nonlinear equations of a Timoshenko-type theory of multilayered anisotropic shells,″ Mekh. Kompozitn. Mater., No. 2, 271–278 (1982).
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).
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).
G. M. Kulikov, ″Effect of anisotropy on the stress state of multilayered reinforced shells,″ Prikl. Mekh.,22, No. 12, 66–72 (1986).
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).
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).
S. V. Filitov, ″Stability of laminated shell structures,″ Raschety na Prochn. Zhestkost',4, 139–152 (1982).
S. V. Filitov, ″Calculation of the stiffness matrix of a laminated shell,″ Rasche'ty na Prochn. Zhestkost',5, 123–219 (1983).
É. I. Grigolyuk and G. M. Kulikov, ″Effect of shear stress nonuniformity in modern tires,″ Mekh. Kompozitn. Mater., No. 5, 870–877 (1986).
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).
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).
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).
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).
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).
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).
P. Seide, ″An improved approximate theory for the bending of laminated plates,″ Mechanics Today,5, 451–466 (1980).
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.
C. -T. Sun and J. M. Whitney, ″Theories for the dynamic response of laminated plates,″ AIAAJ.,11, No. 2, 178–183 (1973).
S. T. Mau, ″A refined laminated plate theory,″ Trans. ASME,E40, No. 2, 606–607 (1973).
T. L. Waltz and J. R. Vinson, ″Interlaminar stresses in laminated cylindrical shells of composite materials,″ AIAA J.,14, No. 9, 1213–1218 (1976).
J. A. Zukas and J. R. Vinson, ″Laminated transversely isotropic cylindrical shells,″ Trans. ASME,E38, No. 2, 109–115 (1971).
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).
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).
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.
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).
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).
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.
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).
L. V. Baev, ″Calculation of multilayered plates with allowance for transverse shear and compression,″ Din. Sploshnoi Sredy,6, 92–104 (1970).
L. V. Baev, ″Design of regular plates composed of an arbitrary number of layers,″ Din. Sploshnoi Sredy,25, 10–17 (1976).
L. Libresku, ″Refined linear theory of elastic anisotropic multilayered shells,″ Pt. 1, Mekh. Polim., No. 6, 1038–1050 (1975).
L. Libresku, ″Refined linear theory of elastic anisotropic multilayered shells,″ Pt. 2, Mekh. Polim., No. 1, 100–109 (1976).
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).
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).
M. Epstein and P. G. Glockner, ″Multilayered shells and directed surfaces,″ Int. J. Eng. Sci.,17, No. 5, 553–562 (1979).
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).
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).
P. P. Chulkov and V. N. Paimushin, ″Problem of the design of multilayered shells of complex geometry,″ Statica Sooruzh., Kiev (1978), pp. 69–72.
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.
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).
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.
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).
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).
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).
V. E. Chepiga, ″Refined theory of laminated shells,″ Prikl. Mekh.,12, No. 11, 45–49 (1976).
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).
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).
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).
B. L. Pelekh and V. A. Laz'ko, Laminated Anisotropic Plates and Shell with Stress Concentrators [in Russian], Kiev (1982).
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).
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).
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).
Ya. M. Grigorenko, A. T. Vasilenko, and N. D. Pankratova, Statics of Anisotropic Thick-Walled Shells [in Russian], Kiev (1985).
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Translated from Mekhanika Kompozitnykh Materialov, No. 2, pp. 287–298, March–April, 1988.
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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
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DOI: https://doi.org/10.1007/BF00608158