Skip to main content
SpringerLink
Log in

Application of Discrete Fourier Series in the Stress Analysis of Cylindrical Shells of Variable Thickness with Arbitrary End Conditions

  • Published:
International Applied Mechanics Aims and scope

Abstract

An approach is proposed to solve boundary-value stress—strain problems for cylindrical shells with thickness varying in two coordinate directions. The approach employs discrete Fourier series to separate circumferential variables. This makes it possible to reduce the problem to a one-dimensional one, which can be solved by the stable discrete-orthogonalization method. Examples are given

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

Similar content being viewed by others

REFERENCES

  1. V. Z. Vlasov, General Theory of Shells and Its Application in Engineering [in Russian], Gostekhizdat, Moscow-Leningrad (1949).

    Google Scholar 

  2. A. L. Gol'denveizer, Theory of Elastic Thin Shells [in Russian], Nauka, Moscow (1976).

    Google Scholar 

  3. Ya. M. Grigorenko, Isotropic and Anisotropic Laminated Shells of Revolution with Variable Stiffness [in Russian], Naukova Dumka, Kiev (1973).

    Google Scholar 

  4. Ya. M. Grigorenko and A. T. Vasilenko, Theory of Variable Stiffness, Vol. 4 of the five-volume series Methods of Shell Design [in Russian], Naukova Dumka, Kiev (1981).

    Google Scholar 

  5. Ya. M. Grigorenko, A. T. Vasilenko, E. I. Bespalova, et al., Numerical Solution of Static Problems for Orthotropic Shells with Variable Characteristics [in Russian], Naukova Dumka, Kiev (1975).

    Google Scholar 

  6. L. H. Donnell, Beams, Plates, and Shells, McGraw Hill, New York (1976).

    Google Scholar 

  7. N. V. Kolkunov, Fundamentals of the Design of Elastic Shells: A College Textbook [in Russian], Vyssh. Shk., Moscow (1987).

    Google Scholar 

  8. V. V. Novozhilov, Theory of Thin Shells [in Russian], Sudostroenie, Leningrad (1962).

    Google Scholar 

  9. G. M. Fikhtengol'ts, Differential and Integral Calculus [in Russian], Vol. 3, Fizmatgiz, Moscow (1966).

    Google Scholar 

  10. Ya. M. Grigorenko and L. I. Zakhariichenko, “Solution of the problem of the stress state of noncircular cylindrical shells of variable thickness,” Int. Appl. Mech., 34, No.12, 1196–1203 (1998).

    Google Scholar 

  11. Ya. M. Grigorenko and L. I. Zakhariichenko, “Studying the effect of the spatial frequency and amplitude of corrugation on the stress-strain state of cylindrical shells,” Int. Appl. Mech., 39, No.12, 1429–1435 (2003).

    Article  Google Scholar 

  12. V. G. Piskunov and A. O. Rasskasov, “Evolution of the theory of laminated plates and shells,” Int. Appl. Mech., 38, No.2, 135–166 (2002).

    Article  Google Scholar 

  13. N. D. Semenyuk, “Stability of axially compressed noncircular cylindrical shells consisting of panels of constant curvature,” Int. Appl. Mech., 39, No.6, 726–735 (2003).

    Article  Google Scholar 

  14. A. T. Vasilenko and G. K. Sudavtsova, “Analysis of stresses and displacements in orthotropic noncircular cylindrical shells under centrifugal loads,” Int. Appl. Mech., 40, No.1, 91–96 (2004).

    Article  Google Scholar 

  15. K. P. Soldatos, “Mechanics of cylindrical shells with noncircular cross section. A survey,” Appl. Mech. Rev., 52, No.8, 237–274 (1999).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. S. P. Timoshenko Institute of Mechanics, National Academy of Sciences of Ukraine, Kiev, Ukraine

    Ya. M. Grigorenko & V. A. Tsybul'nik

Authors
  1. Ya. M. Grigorenko
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. V. A. Tsybul'nik
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

__________

Translated from Prikladnaya Mekhanika, Vol. 41, No. 6, pp. 85–94, June 2005.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Grigorenko, Y.M., Tsybul'nik, V.A. Application of Discrete Fourier Series in the Stress Analysis of Cylindrical Shells of Variable Thickness with Arbitrary End Conditions. Int Appl Mech 41, 657–665 (2005). https://doi.org/10.1007/s10778-005-0133-1

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10778-005-0133-1

Keywords

Search

Navigation