Skip to main content
SpringerLink
Log in

Nonstationary axisymmetric problem of the impact of a spherical shell on an elastic half-space (initial stage of interaction)

  • Published:
Mechanics of Solids Aims and scope Submit manuscript

Abstract

The supersonic stage of interaction (where the rate of expansion of the contact region is no less than the speed of compression waves) between a Timoshenko-type spherical shell (indenter) and an elastic half-space (foundation) is studied. The expansion of the desired functions in series in Legendre polynomials and their derivatives are used to construct a system of resolving equations. An analytical-numerical algorithm for solving this system is developed. A similar problem was considered in [1], where the original problem was replaced by a problem with a periodic system of indenters.

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. D. Kubenko and V. R. Bogdanov, “Axisymmetric Impact of a Shell on an Elastic Halfspace,” Prikl. Mekh. 31(10), 56–63 (1995) [Int. Appl.Mech. (Engl. Transl.) 31 (10), 829–835 (1995)].

    Google Scholar 

  2. A. G. Gorshkov, A. L. Medvedskii, L. N. Rabinskii, and D. V. Tarlakovskii, Waves in Continuous Media (Fizmatlit, Moscow, 2004) [in Russian].

    Google Scholar 

  3. A. G. Gorshkov and D. V. Tarlakovskii, Dynamic Contact Problems with Moving Boundaries (Nauka, Fizmatlit, Moscow, 1995) [in Russian].

    MATH  Google Scholar 

  4. M. Abramowitz and I. A. Stegun (Editors) Handbook of Mathematical Functions, with Formulas, Graphs, and Mathematical Tables, Ed. by M. Abramowitz and I. Stegun (Dover, New York, 1972; Nauka, Moscow, 1979).

    MATH  Google Scholar 

  5. N. S. Bakhvalov, Numerical Methods: Analysis, Algebra, Ordinary Differential Equations (Nauka, Moscow, 1975; Central Books, 1978).

    Google Scholar 

  6. I. M. Gelfand and G. E. Shilov, Generalized Functions and Operations over Them (Fizmatgiz, Moscow, 1959) [in Russian].

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Moscow Aviation Institute (State University of Aerospace Technologies), Volokolamskoe sh. 4, GSP-3, A-80, Moscow, 125993, Russia

    E. Yu. Mikhailova & G. V. Fedotenkov

Authors
  1. E. Yu. Mikhailova
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. G. V. Fedotenkov
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to E. Yu. Mikhailova.

Additional information

Original Russian Text © E.Yu. Mikhailova, G.V. Fedotenkov, 2011, published in Izvestiya Akademii Nauk. Mekhanika Tverdogo Tela, 2011, No. 2, pp. 98–108.

About this article

Cite this article

Mikhailova, E.Y., Fedotenkov, G.V. Nonstationary axisymmetric problem of the impact of a spherical shell on an elastic half-space (initial stage of interaction). Mech. Solids 46, 239–247 (2011). https://doi.org/10.3103/S0025654411020129

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.3103/S0025654411020129

Keywords

Search

Navigation