Skip to main content
SpringerLink
Log in

Solution of Boundary-Value Problems of the Theory of Plates with Variable Parameters Using Periodical B-splines

  • Published:
International Applied Mechanics Aims and scope

An approach to solving static problems for ring plates with parameters varying in two coordinate directions is proposed. The system of equations and boundary conditions are formulated for displacements, forces, and moments. The two-dimensional boundary-value problem is reduced to one-dimensional one using the spline-collocation method. This problem is solved with the stable numerical method of discrete orthogonalization. The numerical results presented as a table are analyzed.

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. 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  ADS  MathSciNet  Google Scholar 

  2. Ya. M. Grigorenko and N. N. Kryukov, Numerical Solution of Static Problems of Flexible Layered Shells with Variable Parameters [in Russian], Naukova Dumka, Kyiv (1998).

    Google Scholar 

  3. Yu. S. Zav’yalov, Yu. I. Kvasov, and V. M. Miroshnichenko, Methods of Spline-Functions [in Russian], Nauka, Moscow (1980).

    MATH  Google Scholar 

  4. M. M. Kryukov and N. S. Yakovenko, “Investigation of the bending of ring and sectorial plates of variable thickness based on spline-approximation,” in: Trans. KUETT, Ser. Transport Systems and Technologies [in Ukrainian], Issue 6, Kyiv (2004), pp. 40–47.

  5. J. H. Alberg, E. N. Nelson, and L. Walsh, The Theory of Splines and Their Application (Mathematics in Science and Engineering, Vol. 8), Academic Press, New York–London (1972).

    Google Scholar 

  6. R. Arcangeli, M. C. L. De Silanes, and J. J. Torrens, Multidimensional Minimizing Splines: Theory and Application, Springer (2004).

  7. E. I. Bespalova and G. P. Urusova, “Stress state of branched shells of revolution subject to transverse shear and reduction,” Int. Appl. Mech., 51, No. 4, 410–419 (2015).

    Article  ADS  Google Scholar 

  8. A. Ya. Grigorenko, W. H. Muller, R. Wille, and S. N. Yaremchenko, “Numerical solution of the problem on the stress-strain state in hollow cylinders using spline-approximation,” J. Math. Sci., 180, No. 2, 135–145 (2012).

    Article  MathSciNet  Google Scholar 

  9. Ya. M. Grigorenko and L. S. Rozhok, “Influence of curvature on the stress state of longitudinally corrugated hollow cylinders,” Int. Appl. Mech., 52, No. 1, 49–55 (2016).

    Article  ADS  MathSciNet  Google Scholar 

  10. A. Ya. Grigorenko and S. N. Yaremchenko, “Analysis of the stress-strain state of inhomogeneous hollow cylinders,” Int. Appl. Mech., 52, No. 4, 342–349 (2016).

    Article  ADS  MathSciNet  Google Scholar 

  11. L. L. Schumaker, Spline Functions: Basic Theory, Cambridge University Press (2007).

Download references

Author information

Authors and Affiliations

  1. S. P. Timoshenko Institute of Mechanics, Ukrainian National Academy of Sciences, 3 Nesterova St., Kyiv, 03057, Ukraine

    Ya. M. Grigorenko

  2. Kyiv State Maritime Academy Named After Hetman Petro Konashevich–Sahaydachiy, 9 Kirillovskaya St., Kyiv, 04071, Ukraine

    N. N. Kryukov

Authors
  1. Ya. M. Grigorenko
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. N. N. Kryukov
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Ya. M. Grigorenko.

Additional information

Translated from Prikladnaya Mekhanika, Vol. 54, No. 4, pp. 3–8, July–August, 2018.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Grigorenko, Y.M., Kryukov, N.N. Solution of Boundary-Value Problems of the Theory of Plates with Variable Parameters Using Periodical B-splines. Int Appl Mech 54, 373–377 (2018). https://doi.org/10.1007/s10778-018-0889-8

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10778-018-0889-8

Keywords

Search

Navigation