Skip to main content

Problem of Thermoelasticity for an Orthotropic Plate-Strip of Variable Thickness with Regard for Transverse Shear

We solve a plane problem of thermoelasticity and a problem of bending for an orthotropic plate-strip with linearly varying thickness under restrained boundary conditions. The results of numerical analyses of displacements, forces, and bending moments in the plate-strip are presented.


  1. S. A. Ambartsumyan, Theory of Anisotropic Plates, Technomic, Stanford (1970).

    Google Scholar 

  2. R. M. Kirakosyan, “On the theory of orthotropic plates with variable thickness with regard for the influence of transverse shears and variations of temperature,” in: Problems of the Mechanics of Deformable Bodies. Collection of Works Dedicated to the 90th Birthday of Academician S. A. Ambartsumyan [in Russian], NAS of Armenia, Yerevan (2012), pp. 177–183.

  3. R. M. Kirakosyan, Applied Theory of Orthotropic Plates with Variable Thickness with Regard for the Influence of Transverse Shear Deformations [in Russian], Gitutyun, Erevan (2000).

    Google Scholar 

  4. A. D. Kovalenko, Foundations of Thermoelasticity [in Russian], Naukova Dumka, Kiev (1970).

    Google Scholar 

  5. L. S. Leibenzon, A Course on Elasticity Theory [in Russian], Gostekhteorizdat, Moscow–Leningrad (1947).

    Google Scholar 

  6. Ya. S. Podstrigach, Ya. I. Burak, A. R. Gachkevich, and L. V. Chernyavskaya, Thermoelasticity of Electrically Conducting Bodies [in Russian], Naukova Dumka, Kiev (1977).

    Google Scholar 

  7. T. Atarashi and S. Minagawa, “Transient coupled-thermoelastic problem of heat conduction in a multilayered composite plate,” Int. J. Eng. Sci., 30, No. 10, 1543–1550 (1992).

    Article  Google Scholar 

  8. S. K. Bhullar and J. L. Wegner, “Some transient thermoelastic plate problems,” J. Therm. Stresses, 32, No. 8, 768–790 (2009).

    Article  Google Scholar 

  9. L. M. Brock, “Transient plane wave solutions to homogeneous equations of orthotropic thermoelasticity with thermal relaxation: Illustration,” Trans. ASME. J. Appl. Mech., 79, No. 6, 1006–1011 (2012).

    Article  Google Scholar 

  10. I. M. Eldesoky, “Mathematical analysis of unsteady MHD blood flow through parallel plate channel with heat source,” World J. Mech., 2, No. 3, 131–137 (2012).

    Article  Google Scholar 

  11. A. Grine, D. Saury, J.-Y. Desmons, and S. Harmand, “Identification models for transient heat transfer on a flat plate,” Exper. Therm. Fluid Sci., 31, No. 7, 701–710 (2007).

    Article  Google Scholar 

  12. R. B. Hetnarski and M. R. Eslami, “Thermal Stresses,” G. M. L. Gladwell (Ed.), Advanced Theory and Applications, Ser. Solid Mechanics and Applications, Vol. 158, Springer, New-York (2008).

    Google Scholar 

  13. S. Kanaun, “An efficient numerical method for calculation of elastic and thermoelastic fields in a homogeneous medium with several heterogeneous inclusions,” World J. Mech., 1, No. 2, 31–43 (2011).

    Article  Google Scholar 

  14. Lei Xiao-Yan and Huang Mao-Guang, “A new boundary element method for Reissner’s plate with new boundary values,” Acta Mech. Sinica, 27, No. 5, 551–559 (1995).

    Google Scholar 

  15. Lü Pin and Huang Mao-Guang, “Calculation of the fundamental solution for the theory of shallow shells considering shear deformation,” Appl. Math. Mech., 13, No. 6, 537–545 (1992).

    MATH  Article  Google Scholar 

  16. M. Misra, N. Ahmad, and Z. Siddiqui, “Unsteady boundary layer flow past a stretching plate and heat transfer with variable thermal conductivity,” World J. Mech., 2, No. 1, 35–41 (2012).

    Article  Google Scholar 

  17. J. Masinda, “Application of the boundary element method to elasticity and thermoelasticity problems,” Monogr. Mem., Nat. Res. Inst. Mach. Des., No. 36 (1986).

  18. Yu. A. Melnikov, Influence Function and Matrices, Marcel Dekker, New York–Basel (1999).

    Google Scholar 

  19. Meng-Cheng Chen, Xue-Cheng Ping, Wan-Hui Liu, and Zheng Xie, “A novel hybrid finite element analysis of two polygonal holes in an infinite elastic plate,” Eng. Fract. Mech., 83, 26–39 (2012).

    Article  Google Scholar 

  20. M. Mochihara and I. Kamiwakida, Numerical solutions of plane stress problems by boundary element method,” Res. Rep. Kagoshima Nat. College Tech., No. 21, 29–35 (1987).

  21. N. Noda, “Thermal stresses in materials with temperature-dependent properties,” in: R. B. Hetnarski (Ed.), Thermal Stresses I, Elsevier, Amsterdam (1986), pp. 391–483.

    Google Scholar 

  22. K. Santaoja, “Gradient theory from the thermomechanics point of view,” Eng. Fract. Mech., 71, No. 4–6, 557–566 (2004).

    Article  Google Scholar 

  23. M. Schanz and O. Steinbach (Eds.), “Boundary Element Analysis. Mathematical Aspects and Applications,” Lect. Notes in Appl. Comput. Mech., Springer, Berlin, Vol. 29 (2007).

  24. M. M. Selim, “Orthotropic elastic medium under the effect of initial and couple stresses,” Appl. Math. Comput., 181, No. 1, 185–192 (2006).

    MATH  MathSciNet  Article  Google Scholar 

Download references

Author information

Authors and Affiliations


Additional information

Translated from Matematychni Metody ta Fizyko-Mekhanichni Polya, Vol. 56, No. 4, pp. 125–130, October–December, 2013.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Kirakosyan, R.M., Stepanyan, S.P. Problem of Thermoelasticity for an Orthotropic Plate-Strip of Variable Thickness with Regard for Transverse Shear. J Math Sci 208, 417–424 (2015).

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI:


  • Plane Problem
  • Boundary Element Method
  • Variable Thickness
  • Transverse Shear
  • Orthotropic Plate