Skip to main content
Log in

Application of the Spline-Collocation Method to Solve Problems of Statics and Dynamics for Multilayer Cylindrical Shells with Design and Manufacturing Features

  • Published:
International Applied Mechanics Aims and scope

We propose a spline-collocation technique for the analysis of the static stress–strain state and the free vibrations of ribbed multilayer orthotropic cylindrical shells with attached masses. Numerical examples are used to test the solution and analyze its practical convergence depending on the number of collocation points. The stress–strain state of nuclear steam generator tubes is designed taking into account the operating conditions. It was found that with increase in the stiffness of the sludge, the internal forces on which the load-bearing capacity of the tubes strongly depends peak in the load-bearing cross-section. The bending moment and the shearing force significantly exceed the maximum bending moment in the tube without sludge.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. S. A. Ambartsumyan, General Theory of Anisotropic Shells [in Russian], Nauka, Moscow (1974).

  2. I. Ya. Amiro and V. A. Zarutskii, Theory of Ribbed Shells, Vol. 2 of the five-volume series Methods of Shell Design [in Russian], Naukova Dumka, Kyiv (1980).

  3. I. Ya. Amiro, V. A. Zarutskii, and P. S. Polyakov, Ribbed Cylindrical Shells [in Russian], Naukova Dumka, Kyiv (1973).

  4. I. Ya. Amiro, V. A. Zarutskii, V. N. Revutskii, Yu. V. Skosarenko, A. I. Telalov, and S. Yu. Fialko, Vibrations of Ribbed Shells of Revolution [in Russian], Naukova Dumka, Kyiv (1988).

  5. Ya. M. Grigorenko, Yu. N. Shevchenko, Numerical Methods, Vol. 11 of the 12-volume series Mechanics of Composite Materials [in Russian], A.S.K., Kyiv (2002).

  6. Yu. S. Zav’yalov, Yu. I. Kvasov, and V. L. Miroshnichenko, Spline-Function Methods [in Russian], Nauka, Moscow (1980).

  7. J. R. Banerjee, C. W. Cheung, R. Morisima, M. Perera, and J. Njuguna, “Free vibration of a three-layered sandwich beam using the dynamic stiffness method and experiment,” Int. J. Solids Struct., 44, No. 22–23, 7543–7563 (2007).

    Article  Google Scholar 

  8. K. G. Golovko, P. Z. Lugovoi, and V. F. Meish, “Solution of axisymmetric dynamic problems for cylindrical shells on elastic foundation,” Int. Appl. Mech., 43, No. 12, 1390–1395 (2007).

    Article  ADS  Google Scholar 

  9. A. Ya. Grigorenko, S. A. Pankrat’ev, and S. N. Yaremchenko, “Solution of stress–strain problems for complex-shaped plates in a refined formulation,” Int. Appl. Mech., 53, No. 3, 326–333 (2017).

    Article  ADS  MathSciNet  Google Scholar 

  10. A. Ya. Grigorenko, S. A. Pankrat’ev, and S. N. Yaremchenko, “Analysis of the stress–strain state of complex-shaped plates,” Int. Appl. Mech., 54, No. 6, 695–701 (2018).

    Article  ADS  MathSciNet  Google Scholar 

  11. P. Z. Lugovoi and V. F. Meish, “Dynamics of inhomogeneous shell systems under non-stationary loading (survey),” Int. Appl. Mech., 53, No. 5, 481–537 (2017).

    Article  ADS  Google Scholar 

  12. P. Z. Lugovoi, V. N. Sirenko, N. Ya. Prokopenko, and K. V. Klimenko, “Influence of the parameters of a non-constant disturbing load on the transient process of vibration of a ribbed cylindrical shell,” Int. Appl. Mech., 53, No. 6, 680–687 (2017).

    Article  ADS  MathSciNet  Google Scholar 

  13. P. Z. Lugovoi, V. N. Sirenko, Yu. V. Skosarenko, and T. Ya. Batutina, “Dynamics of a discretely reinforced shell under a local impulsive load,” Int. Appl. Mech., 53, No. 2, 173–180 (2017).

  14. V. F. Meish, Yu. A. Meish, and À. V. Pavlyuk, “Dynamics of a three-layer elliptic cylindrical shell reinforced with discrete rings,” Int. Appl. Mech., 54, No. 2, 172–179 (2018).

    Article  ADS  MathSciNet  Google Scholar 

  15. M. S. Qatu, Vibration of Laminated Shells and Plates, Academic Press, New-York (2004).

  16. M. S. Qatu, E. Asadi, and W. Wang, “Review of recent literature on static analyses of composite shells: 2000–2010,” Open J. Compos. Mater., No. 2, 61–86 (2012).

    Article  Google Scholar 

  17. S. Timoshenko, D. H. Young, and W. Weaver, Vibration Problems in Engineering, Wiley, New York (1974).

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to A. P. Shugailo.

Additional information

Translated from Prikladnaya Mekhanika, Vol. 55, No. 5, pp. 78–88, September–October 2019.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Lugovoi, P.Z., Skosarenko, Y.V., Orlenko, S.P. et al. Application of the Spline-Collocation Method to Solve Problems of Statics and Dynamics for Multilayer Cylindrical Shells with Design and Manufacturing Features. Int Appl Mech 55, 524–533 (2019). https://doi.org/10.1007/s10778-019-00974-y

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10778-019-00974-y

Keywords

Navigation