Skip to main content
SpringerLink
Log in

Solution of two-dimensional problems of the statics of flexible shallow shells by spline approximation

  • Published:
International Applied Mechanics Aims and scope

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

References

  1. R. Bellman and R. Kalaba, Quasi-Linearization and Nonlinear Boundary-Value Problems [Russian translation], Mir, Moscow (1968).

    Google Scholar 

  2. Ya. M. Grigorenko, "Solution of the problem of the deformation of a long cylindrical shell with variable parameters," Dopov. Akad. Nauk Ukr. RSR Ser. A, 418–422 (1977).

  3. Ya. M. Grigorenko and M. N. Berenov, "Solution of two-dimensional problems of the bending of rectangular plates on the basis of spline approximation," Dopov. Akad. Nauk Ukr. RSR Ser. A, No. 8, 22–25 (1987).

  4. Ya. M. Grigorenko and M. N. Berenov, "Numerical solution of problems of the statics of shallow shells on the basis of the spline-collocation method," Prikl. Mekh.,24, No. 5, 32–36 (1988).

    Google Scholar 

  5. Ya. M. Grigorenko and N. N. Kryukov, Numerical Solution of Problems of the Statics of Flexible Shells with Variable Parameters [in Russian], Nauk. Dumka, Kiev (1988).

    Google Scholar 

  6. Ya. M. Grigorenko and N. N. Kryukov, "Certain approaches to the solution of problems of the theory of shells and plates based on spline approximation," Transactions of the XI All-Union Conference on the Theory of Plates and Shells (Kazan, August 28 – September 2, 1990). Izd-vo Kazan. Un-ta, Kazan (1990), Vol. 1, pp. 31–36.

    Google Scholar 

  7. Ya. M. Grigorenko and N. N. Kryukov, "Solution of linear and nonlinear boundary-value problems of the theory of plates and shells on the basis of the method of lines," Prikl. Mekh.,29, No. 4, 3–11 (1993).

    Google Scholar 

  8. Ya. M. Grigorenko, N. N. Kryukov, and V. S. Demyanchuk, "Solution of the problem of the deformation of shallow shells in a temperature field by the spline-collocation method," Dopov. Akad. Nauk Ukr. RSR, No. 3, 45–48 (1990).

  9. Ya. M. Grigorenko, N. N. Kryukov, and Yu. I. Ivanov, "One approach to solving nonlinear problems of the bending of rectangular plates on the basis of spline approximation," Dopov. Akad. Nauk Ukr. RSR, No. 5, 54–57 (1992).

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

    Google Scholar 

  11. P. C. Dumir and A. Bhaskar, "Nonlinear static analysis of rectangular plates on elastic foundations by the orthogonal point collocation method," Comput. Meth. Appl. Mech. Eng.,67, 111–124 (1988).

    Google Scholar 

  12. Ya. M. Grigorenko, N. N. Kryukov, and J. J. Ivanova, "The analysis of geometrically nonlinear deformation of shallow shells using spline functions," Dopov. Akad. Nauk Ukr. RSR, No. 11, 40–43 (1992).

Download references

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

  3. Yu. I. Ivanova
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

S. P. Timoshenko Institute of Mechanics, National Academy of Sciences of the Ukraine, Kiev. Translated from Prikladnaya Mekhanika, Vol. 31, No. 4, pp. 10–16, April, 1995.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Grigorenko, Y.M., Kryukov, N.N. & Ivanova, Y.I. Solution of two-dimensional problems of the statics of flexible shallow shells by spline approximation. Int Appl Mech 31, 255–260 (1995). https://doi.org/10.1007/BF00846771

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00846771

Keywords

Search

Navigation