Skip to main content
SpringerLink
Log in

Determination of Viscoelastic Stresses in Plates with Inclusions

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

We describe an approach to the determination of viscoelastic stresses in plates with inclusions. It is based on the method of boundary integral equations and the Laplace integral transformation. The formal solution of the problem of elasticity theory in which the differential operators are replaced with constants is constructed by the method of boundary integral equations and reduced to the solution of a system of algebraic equations. The corresponding system for the viscoelasticity problem is solved with the help of the Laplace integral transformation and a refined numerical-analytic formula for its inversion.

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. S. A. Kaloerov and A. B. Mironenko, “Analyzing the viscoelastic state of a plate with elliptic or linear elastic inclusions,” Prikl. Mekh., 43, No. 2, 88–98 (2007); English translation: Int. Appl. Mech., 43, No. 2, 198–208 (2007).

  2. R. M. Kushnir, V. M. Maksymovych, and T. Ya. Solyar, “Determination of nonstationary temperatures with the help of improved formulas of the inverse Laplace transformation,” Fiz.-Khim. Mekh. Mater., 38, No. 2, 18–26 (2002); English translation: Mater. Sci., 38, No. 2, 172–184 (2002).

  3. V. M. Maksymovych, O. S. Prykhod’ko, and T. Ya. Solyar, “Determination of stresses near elastic inclusions in plates of complex shape,” Mat. Met. Fiz.-Mekh. Polya, 57, No. 3, 109–118 (2014) ; English translation: J. Math. Sci., 217, No. 3, 271–282 (2016).

  4. M. P. Savruk and V. M. Zelenyak, Two-Dimensional Problems of Thermoelasticity for Piecewise Homogeneous Bodies with Cracks [in Ukrainian], Rastr-7, Lviv (2009).

  5. M. P. Savruk, P. N. Osiv, and I. V. Prokopchuk, Numerical Analysis in Plane Problems of the Theory of Cracks [in Russian], Naukova Dumka, Kiev (1989).

    Google Scholar 

  6. E. Riande, R. Diaz-Calleja, M. Prolongo, R. Masegosa, and C. Salom, Polymer Viscoelasticity: Stress and Strain in Practice, Marcel Dekker, New York (2000).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Luts’k National Technical University, Luts’k, Ukraine

    V. M. Maksymovych

  2. Pidstryhach Institute for Applied Problems in Mechanics and Mathematics, Ukrainian National Academy of Sciences, Lviv, Ukraine

    T. Ya. Solyar

Authors
  1. V. M. Maksymovych
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. T. Ya. Solyar
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Translated from Matematychni Metody ta Fizyko-Mekhanichni Polya, Vol. 58, No. 3, pp. 91–96, July–September, 2015.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Maksymovych, V.M., Solyar, T.Y. Determination of Viscoelastic Stresses in Plates with Inclusions. J Math Sci 226, 114–122 (2017). https://doi.org/10.1007/s10958-017-3523-0

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10958-017-3523-0

Search

Navigation