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.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
S. A. Ambartsumyan, Theory of Anisotropic Plates, Technomic, Stanford (1970).
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.
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).
A. D. Kovalenko, Foundations of Thermoelasticity [in Russian], Naukova Dumka, Kiev (1970).
L. S. Leibenzon, A Course on Elasticity Theory [in Russian], Gostekhteorizdat, Moscow–Leningrad (1947).
Ya. S. Podstrigach, Ya. I. Burak, A. R. Gachkevich, and L. V. Chernyavskaya, Thermoelasticity of Electrically Conducting Bodies [in Russian], Naukova Dumka, Kiev (1977).
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).
S. K. Bhullar and J. L. Wegner, “Some transient thermoelastic plate problems,” J. Therm. Stresses, 32, No. 8, 768–790 (2009).
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).
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).
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).
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).
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).
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).
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).
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).
J. Masinda, “Application of the boundary element method to elasticity and thermoelasticity problems,” Monogr. Mem., Nat. Res. Inst. Mach. Des., No. 36 (1986).
Yu. A. Melnikov, Influence Function and Matrices, Marcel Dekker, New York–Basel (1999).
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).
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).
N. Noda, “Thermal stresses in materials with temperature-dependent properties,” in: R. B. Hetnarski (Ed.), Thermal Stresses I, Elsevier, Amsterdam (1986), pp. 391–483.
K. Santaoja, “Gradient theory from the thermomechanics point of view,” Eng. Fract. Mech., 71, No. 4–6, 557–566 (2004).
M. Schanz and O. Steinbach (Eds.), “Boundary Element Analysis. Mathematical Aspects and Applications,” Lect. Notes in Appl. Comput. Mech., Springer, Berlin, Vol. 29 (2007).
M. M. Selim, “Orthotropic elastic medium under the effect of initial and couple stresses,” Appl. Math. Comput., 181, No. 1, 185–192 (2006).
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
About this article
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). https://doi.org/10.1007/s10958-015-2456-8
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10958-015-2456-8