Journal of Mathematical Sciences

, Volume 171, Issue 5, pp 673–681 | Cite as

Determination of nonstationary temperature fields and stresses in piecewise homogeneous circular plates on the basis of a numerical-analytic Laplace inversion formula

  • T. Ya. Solyar

We investigate nonstationary temperature fields and stresses generated by them in piecewise homogeneous annular plates. An algorithm for the solution of the problem is based on the direct calculation of the Laplace transform and a modified Prudnikov formula for its inversion.


Convective Heat Transfer Inversion Formula Annular Plate Linear Thermal Expansion Coefficient Numerical Inversion 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    H. S. Carslaw and J. C. Jaeger, Conduction of Heat in Solids, Oxford University Press, London (1959).Google Scholar
  2. 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).Google Scholar
  3. 3.
    Ya. S. Podstrigach and Yu. M. Kolyano, Nonstationary Temperature Fields and Stresses in Thin Plates [in Russian], Naukova Dumka, Kiev (1972).Google Scholar
  4. 4.
    R. G. Campos and F. M. Díaz, “Quadrature formulas for the Laplace and Mellin transform analytic-element method for transient porous-media flow,” BIT Numer. Math., 49, No. 3, 477–486 (2009).MATHCrossRefGoogle Scholar
  5. 5.
    B. Davis and B. Martin, “Numerical inversion of the Laplace transform: survey and comparison of methods,” J. Comput. Phys., 33, No. 1, 1–32 (1979).CrossRefMathSciNetGoogle Scholar
  6. 6.
    K. L. Kuhlman and S. P. Neuman, “Laplace-transform analytic-element method for transient porous-media flow,” J. Eng. Math., 64, No. 2, 113–130 (2009).MATHCrossRefMathSciNetGoogle Scholar
  7. 7.
    M. Levesque, M. D. Gilchrist, N. Bouleau, K. Derrien, and D. Baptiste, “Numerical inversion of the Laplace–Carson transform applied to homogenization of randomly reinforced linear viscoelastic media,” Comput. Mech., 40, No. 4, 771–789 (2007).MATHCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, Inc. 2010

Authors and Affiliations

  • T. Ya. Solyar
    • 1
  1. 1.Pidstryhach Institute for Applied Problems in Mechanics and Mathematics, Ukrainian National Academy of SciencesLvivUkraine

Personalised recommendations