Skip to main content
SpringerLink
Log in

Nonconventional approaches to static problems for noncircular cylindrical shells in different formulations

  • Published:
International Applied Mechanics Aims and scope

Abstract

Stress problems for noncircular cylindrical shells in classical, refined, and spatial statements are solved using nonconventional approaches based on discrete Fourier series and spline functions. Solutions for isotropic and orthotropic shells are presented as plots and tables

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 Applications in Engineering [in Russian], Gostekhizdat, Leningrad (1949).

    Google Scholar 

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

    Google Scholar 

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

    Google Scholar 

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

    Google Scholar 

  5. Ya. M. Grigorenko, G. G. Vlaikov, and A. Ya. Grigorenko, Numerical-and-Analytical Solution of Problems in the Mechanics of Shells Using Various Models [in Russian], Akademperiodika, Kyiv (2006).

    Google Scholar 

  6. Ya. M. Grigorenko and N. N. Kryukov, “Solution of problems of the theory of plates and shells with spline functions (survey),” Int. Appl. Mech., 31, No. 6, 413–434 (1995).

    Article  MATH  MathSciNet  Google Scholar 

  7. Ya. M. Grigorenko and L. S. Rozhok, “Stress analysis of orthotropic hollow noncircular cylinders,” Int. Appl. Mech., 40, No. 6, 679–685 (2004).

    Article  Google Scholar 

  8. Ya. M. Grigorenko and S. N. Yaremchenko, “Stress analysis of orthotropic noncircular cylindrical shells of variable thickness in a refined formulation,” Int. Appl. Mech., 40, No. 3, 266–274 (2004).

    Article  Google Scholar 

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

    MATH  Google Scholar 

  10. Kh. M. Mushtari, “Some generalizations of thin shell theory with application to elastic equilibrium stability problems,” Prikl. Mat. Mekh., 2, No. 14, 439–456 (1939).

    Google Scholar 

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

    Google Scholar 

  12. G. N. Savin, T. V. Putyata, and B. N. Fradlin, Essays on Development of Some Fundamental Problems in Mechanics [in Russian], Naukova Dumka, Kyiv (1964).

    Google Scholar 

  13. G. N. Savin, Stress Distribution around Holes [in Russian], Naukova Dumka, Kyiv (1968).

    Google Scholar 

  14. G. N. Savin, Solid Mechanics (Collected Works) [in Russian], Naukova Dumka, Kyiv (1979).

    Google Scholar 

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

    Google Scholar 

  16. Ya. M. Grigorenko, A. Ya. Grigorenko, and L. I. Zakhariichenro, “Stress analysis of noncircular cylindrical shells with cross section in the form of connected convex half-corrugations,” Int. Appl. Mech., 42, No. 4, 431–438 (2006).

    Article  Google Scholar 

  17. Ya. M. Grigorenko and L. S. Rozhok, “Discrete Fourier-series method in problems of bending of variable-thickness rectangular plates,” J. Eng. Math., 46, No. 3–4, 269–280 (2003).

    Article  MATH  Google Scholar 

  18. Ya. M. Grigorenko and L. S. Rozhok, “Equilibrium of elastic hollow inhomogeneous cylinders of corrugated elliptic cross-section,” J. Eng. Math., 54, No. 2, 145–157 (2006).

    Article  MATH  MathSciNet  Google Scholar 

  19. Ya. M. Grigorenko and L. S. Rozhok, “Stress solution for transversely isotropic corrugated hollow cylinders,” Int. Appl. Mech., 41, No. 3, 277–282 (2005).

    Article  Google Scholar 

  20. Ya. M. Grigorenko and V. A. Tsybul’nik, “Application of discrete Fourier series in the stress analysis of cylindrical shells of variable thickness with arbitrary end conditions,” Int. Appl. Mech., 41, No. 6, 657–665 (2005).

    Article  Google Scholar 

  21. Ya. M. Grigorenko and S. N. Yaremchenko, “Refined design of corrugated noncircular cylindrical shells,” Int. Appl. Mech., 41, No. 1, 7–13 (2005).

    Article  Google Scholar 

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

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

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

    Ya. M. Grigorenko

Authors
  1. Ya. M. Grigorenko
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

__________

Translated from Prikladnaya Mekhanika, Vol. 43, No. 1, pp. 45–65, January, 2007.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Grigorenko, Y.M. Nonconventional approaches to static problems for noncircular cylindrical shells in different formulations. Int Appl Mech 43, 35–53 (2007). https://doi.org/10.1007/s10778-007-0005-y

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10778-007-0005-y

Keywords

Search

Navigation