The Stressed State of the “Boundary Layer” Type in Cylindrical Shells Investigated according to a Nonclassical Theory

  • V. V. Firsanov
Reliability, Strength, and Wear Resistance of Machines and Structures


Two variants of a refined theory for calculating the stress–strain state in the boundary zones of cylindrical shells are presented. The relevant mathematical models are based on equations of the three-dimensional elasticity theory and the increase over the thickness of the shell in the orders of the polynomials that approximate the sought displacements. The Lagrange variational principle is applied to the value of the shell’s total energy functional defined more exactly with respect to the classical Kirchhoff–Love theory. The formulated boundary problems allow determination with different degrees of accuracy of additional stressed states of the “boundary layer” type. The calculated results obtained in this work are compared with the results obtained according to the classical theory. It has been established that the above stresses make a significant contribution to the total stressed state of the shell and should be considered when designing and testing machine structures for strength and longevity.


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  1. 1.
    Firsanov, V.V., Some refining of classic theory of rectangular plates made from composite materials, Mekh. Kompoz. Mater. Konstrukts., 2002, vol. 8, no. 1, pp. 20–64.Google Scholar
  2. 2.
    Firsanov, V.V. and Doan, Ch.N., Energy-consistent theory of cylindrical shells, J. Mach. Manuf. Reliab., 2011, vol. 40, no. 6, pp. 543–548.CrossRefGoogle Scholar
  3. 3.
    Firsanov, V.V., Doan, T.N., and Hieu, L.T., Investigation of the stress-strain state of cylindrical shells on the basis of three-dimensional equations of the theory of elasticity, Probl. Mashinostr. Avtomatiz., 2012, no. 2, pp. 98–105.Google Scholar
  4. 4.
    Firsanov, V.V. and Doan, T.N., Investigation of the statics and free vibrations of cylindrical shells on the basis of a nonclassical theory, Compos.: Mech., Comput., Appl., 2014, vol. 6, no. 2, pp. 135–166.Google Scholar
  5. 5.
    Firsanov, V.V., Study of stress-deformed state of rectangular plates based on nonclassical theory, J. Mach. Manuf. Reliab., 2016, vol. 45, no. 6, pp. 515–522.CrossRefGoogle Scholar
  6. 6.
    Firsanov, V.V. and Doan, T.N., Energy concerted the approach to research of elastic arbitrary shells, Vestn. MAI, 2011, vol. 18, no. 1, pp. 194–207.Google Scholar
  7. 7.
    Firsanov, V.V., Doan, T.N., and Le, T.H., Research stress strain state of cylindrical shell under the refined theory, Vestn. MAI, 2012, vol. 19, no. 5, pp. 158–171.Google Scholar

Copyright information

© Allerton Press, Inc. 2018

Authors and Affiliations

  1. 1.Moscow Aviation Institute (National Research University)MoscowRussia

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