Skip to main content
SpringerLink
Log in

Unilateral contact problem for two plates with a rigid inclusion in the lower plate

  • Published:
Journal of Mathematical Sciences Aims and scope Submit manuscript

We study the unilateral contact problem for two elastic plates arranged at a given angle to each other, with a rigid inclusion in the lower plate. For a smooth solution the problem is equivalent to a variational problem. We analyze configurations of the rigid inclusion and show that the problem under consideration can be regarded as the limit problem for a family of problems of the theory of elasticity. Bibliography: 10 titles. Illustrations: 3 figures.

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. G. Fichera, The Existence Theorems in the Theory of Elasticity [Russian translation], Nauka, Moscow (1974).

    Google Scholar 

  2. A. M. Khludnev, K.-H. Hoffmann, and N. D. Botkin, “The variational contact problem for elastic objects of different dimensions” [in Russian], Sib. Mat. Zh. 47, No. 3, 707–719 (2006); English transl.: Sib. Math. J. 47, No. 3, 584–593 (2006).

  3. T. A. Stekina, “Variational problem on unilateral contact of an elastic plate with a beam” [in Russian], Vestn. Novosib. Gos. Univ., Ser. Mat. Mekh. Inform. 9, No. 1, 46–56 (2009).

    Google Scholar 

  4. A. M. Khludnev, “On unilateral contact of two plates aligned at an angle to each other” [in Russian], Prikl. Mekh. Tekhn. Fiz. 49, No. 4, 42–58 (2008); English transl.: J. Appl. Mech. Techn. Phys. 49, No. 4, 553–567 (2008).

  5. N. V. Neustroeva, “A rigid inclusion in the contact problem for elastic plates” [in Russian], [in Russian], Sib. Zh. Ind. Mat. 12, No. 4, 92–105 (2009); English transl.: J. Appl. Ind. Math. 4, No. 4, 526–538 (2010).

  6. N. V. Neustroeva, “Unilateral contact of elastic plates with a rigid inclusion” [in Russian], Vestn. Novosib. Gos. Univ., Ser. Mat. Mekh. Inform. 9, No. 4, 51–64 (2009).

    MathSciNet  MATH  Google Scholar 

  7. A. Morrassi and E. Rosset, “Detecting rigid inclusions, or cavities, in an elastic body,” J. Elasticity 73, 101–126 (2003).

    Article  MathSciNet  Google Scholar 

  8. A. M. Khludnev, The Problem about a Crack on the Interface of a Rigid Inclusion in an Elastic Plate, [in Russian], Preprint, Lavrent’ev Institute of Hydrodynamics SB RAS, Novosibirsk, No. 1, 1–18 (2009).

  9. A. M. Khludnev and V. A. Kovtunenko, Analysis of Cracks in Solids,WIT Press, Southampton etc. (2000).

    Google Scholar 

  10. R. Temam, Problèmes Mathématiques en Plasticité, Gauthier-Villars, Paris (1983).

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Lavrent’ev Institute of Hydrodynamics SB RAS 15, pr. Akad. Lavrent’eva, Novosibirsk, 630090, Russia

    T. A. Rotanova

Authors
  1. T. A. Rotanova
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to T. A. Rotanova.

Additional information

Translated from Vestnik Novosibirskogo Gosudarstvennogo Universiteta: Seriya Matematika, Mekhanika, Informatika 11, No. 1, 2011, pp. 87-98

Rights and permissions

Reprints and permissions

About this article

Cite this article

Rotanova, T.A. Unilateral contact problem for two plates with a rigid inclusion in the lower plate. J Math Sci 188, 452–462 (2013). https://doi.org/10.1007/s10958-012-1142-3

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10958-012-1142-3

Keywords

Search

Navigation