Skip to main content
SpringerLink
Log in

The Problem of the Location of an Inclusion in a Two-Dimensional Elastic Body with Two Thin Rigid Inclusions

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

We study the optimal control problem for nonlinear mathematical models describing the equilibrium state of an inhomogeneous body, where the nonlinearity is caused by the Signorini contact condition. We establish the solvability of the optimal control problem and prove that the equilibrium problem for an elastic body with two joined rigid inclusions is the limit for a family of equilibrium problems for bodies with two separate inclusions.

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. A. Khludnev and G. Leugering, “On elastic bodies with thin rigid inclusions and cracks,” Math. Meth. Appl. Sci. 33, No. 16, 1955–1967 (2010).

    MathSciNet  MATH  Google Scholar 

  2. A. M. Khludnev, L. Faella, and C. Perugia, “Optimal control of rigidity parameters of thin inclusions in composite materials,” Z. Angew. Math. Phys. 68, No. 2, Paper No. 47 (2017).

  3. N. Lazarev and E. Rudoy, “Optimal location of a finite set of rigid inclusions in contact problems for inhomogeneous two-dimensional bodies,” J. Comput. Appl. Math. 403, No. 10, Article ID 113710 (2022).

  4. A. M. Khludnev, A. A. Novotny, J. Sokolowski, and A. Zochowski, “Shape and topology sensitivity analysis for cracks in elastic bodies on boundaries of rigid inclusions,” J. Mech. Phys. Solids 57, No. 10, 1718–1732 (2009).

    Article  MathSciNet  MATH  Google Scholar 

  5. I. Hlaváček, J. Haslinger, J. Nečas, and J. Lovíšek, Solution of Variational Inequalities in Mechanics, Springer, New York etc. (1988).

  6. G. Duvaut, J.-L. Lions, Inequalities in Mechanics and Physics, Springer, Berlin etc. (1976).

  7. C. Baiocchi, A. Capello, Variational and Quasivariational Inequalities. Application to Free Boundary Problems, John Wiley and Sons, Chichester etc. (1984).

Download references

Author information

Authors and Affiliations

  1. Nord-Easten Federal University, 48, Kulkovskogo St., Yakutsk, 677000, Russia

    N. P. Lazarev & G. M. Semenova

Authors
  1. N. P. Lazarev
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. G. M. Semenova
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to N. P. Lazarev.

Additional information

Translated from Problemy Matematicheskogo Analiza 122, 2023, pp. 61-67.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Lazarev, N.P., Semenova, G.M. The Problem of the Location of an Inclusion in a Two-Dimensional Elastic Body with Two Thin Rigid Inclusions. J Math Sci 270, 571–578 (2023). https://doi.org/10.1007/s10958-023-06368-3

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10958-023-06368-3

Search

Navigation