Advertisement

Springer Nature is making Coronavirus research free. View research | View latest news | Sign up for updates

On a representation of the Green's functions for shallow panels supported on the boundary of a rectangular base

  • 14 Accesses

Abstract

To enhance the convergence of double series in the case of a shallow panel supported on a rectangular base and a long closed cylindrical shell we propose an approximate representation of the Green's function as a combination of rapidly convergent expansions and a closed-form analytic component obtained by approximate summation of one particular part of series using the two-dimensional integral Fourier transform and reduction to the Kelvin functions.

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

Literature cited

  1. 1.

    P. M. Velichko and V. P. Shevchenko, “On the action of concentrated forces and moments on a shell of positive Gaussian curvature,”Izv. Akad. Nauk SSSR. Mekh. Tver. Tela, No. 2, 147–151 (1969).

  2. 2.

    V. Z. Vlasov, “On the theory of moment-free shells of revolution,”Izv. Akad. Nauk SSSR. Otd. Tekh. Nauk, No. 5, 55–84 (1955).

  3. 3.

    S. P. Gavelya, A. I. Davidov, and V. P. Skripnik, “On the application of potential representations to the solution of boundary-value problems of the theory of shallow shells,” in:Proc. 10th All-union Conf. Th. Shells and Plates [in Russian], Metsnierba, Tbilisi (1975), pp. 51–58.

  4. 4.

    E. I. Grigolyuk and V. M. Tolkachev,Contact Problems of the Theory of Plates and Shells [in Russian], Mashinostroenie, Moscow (1980).

  5. 5.

    A. I. Danilov and G. N. Chernyshev. “Stiffness and flexibility of shells of negative curvature used in wave transmissions,”Izv. Akad. Nauk SSSR. Mekh. Tver. Tela, No. 5, 163–169 (1978).

  6. 6.

    V. M. Darevskii, “Solution of certain problems of the theory of a cylindrical shell,”Prikl. Mat. i Mekh., No. 2, 159–164 (1952).

  7. 7.

    Yu. P. Zhigalko and L. A. Saitbekova, “Application of a computer to study the stress-strain state of elastic cylindrical shells subjected to the action of concentrated loads,”Studies in the Theory of Plates and Shells, Kazan' University, No. 5 (1967), pp. 93–112.

  8. 8.

    S. Lukasiewicz,Local Loads in Plates and Shells [Russian translation], Mir, Moscow (1982).

  9. 9.

    V. N. Maksimenko and L. A. Fil'shtinskii, “On contact problems in the theory of anisotropic shells,” in:Proc. 10th All-union Conf. Theory Plates and Shells [in Russian], Metsnierba, Tbilisi (1975), pp. 186–195.

  10. 10.

    B. V. Nerubailo,Local Problems of Durability of Cylindrical Shells [in Russian], Mashinostroenie, Moscow (1983).

  11. 11.

    I. F. Obraztsov and B. V. Nerubailo, “On methods of synthesizing the stressed state in the theory of shells,”Dokl. Akad. Nauk SSSR,269, No. 1, 54–56 (1983).

  12. 12.

    V. P. Ol'shanskii, “Fundamental solutions of the equations of shallow shells,”Izv. Vuzov. Matematika, No. 6, 52–56 (1980).

  13. 13.

    G. N. Chernyshev, “Deflection under a concentrated force in shells of positive curvature,”Prikl. Mat. Mekh., No. 5, 883–886 (1967).

  14. 14.

    E. Jahnke, F. Emde, and F. Lösch,Tables of Functions with Formulae and Curves, Dover, New York (1945).

  15. 15.

    M. Fetrua and M. Osamy, “The fundamental solution in the theory of shallow shells,”Int. J. Solids and Structures, No. 12, 971–986 (1978).

  16. 16.

    J. Simmonds and M. Bradley, “The fundamental solution for a shallow shell with an arbitrary quadratic midsurface,”J. Appl. Mech. Trans. ASME. Ser. E, No. 2, 286–290 (1976).

Download references

Additional information

Translated fromMatematicheskie Metody i Fiziko-Mekhanicheskie Polya, Issue 33, 1991, pp. 78–83.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Obraztsov, I.F., Nerubailo, B.V. & Ol'shanskii, V.P. On a representation of the Green's functions for shallow panels supported on the boundary of a rectangular base. J Math Sci 65, 1887–1892 (1993). https://doi.org/10.1007/BF01097311

Download citation

Keywords

  • Fourier
  • Fourier Transform
  • Cylindrical Shell
  • Approximate Representation
  • Double Series