Hostname: page-component-78c5997874-v9fdk Total loading time: 0 Render date: 2024-11-12T19:41:29.843Z Has data issue: false hasContentIssue false
  • English
  • Français

On the Generalized Thermoelasticity Problem for an Infinite Fibre-Reinforced Thick Plate under Initial Stress

Published online by Cambridge University Press:  03 June 2015

Ahmed E. Abouelregal  and
Ashraf M. Zenkour
Ahmed E. Abouelregal
Affiliation:
Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, Egypt Department of Mathematics, College of Science and Arts, University of Aljouf, El-Qurayat, Saudi Arabia
Ashraf M. Zenkour*
Affiliation:
Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia Department of Mathematics, Faculty of Science, Kafrelsheikh University, Kafr El-Sheikh 33516, Egypt
*
*Corresponding author. Email: [email protected]
Get access

Abstract

In this paper, the generalized thermoelasticity problem for an infinite fiber-reinforced transversely-isotropic thick plate subjected to initial stress is solved. The lower surface of the plate rests on a rigid foundation and temperature while the upper surface is thermally insulated with prescribed surface loading. The normal mode analysis is used to obtain the analytical expressions for the displacements, stresses and temperature distributions. The problem has been solved analytically using the generalized thermoelasticity theory of dual-phase-lags. Effect of phase-lags, reinforcement and initial stress on the field quantities is shown graphically. The results due to the coupled thermoelasticity theory, Lord and Shulman’s theory, and Green and Naghdi’s theory have been derived as limiting cases. The graphs illustrated that the initial stress, the reinforcement and phase-lags have great effects on the distributions of the field quantities.

Keywords

73B73C73KDual-phase-lag theoryfiber-reinforcedinitial stressnormal mode analysisthick plate
Type
Research Article
Information
Advances in Applied Mathematics and Mechanics , Volume 6 , Issue 6 , December 2014 , pp. 783 - 796
Copyright
Copyright © Global-Science Press 2014

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

[1]Belfield, A. J., Rogers, T. G. and Spencer, A. J. M., Stress in elastic plates reinforced by fibres lying in concentric circles, J. Mech. Phys. Solids, 31 (1983), pp. 25–54.Google Scholar
[2]Verma, P. D. S. and Rana, O. H., Rotation of a circular cylindrical tube reinforced by fibres lying along helices, Mech. Mater., 2 (1983), pp. 353–359.Google Scholar
[3]Sengupta, P. R. and Nath, S., Surface waves in fibre-reinforced anisotropic elastic media, Sadhana, 26 (2001), pp. 363–370.Google Scholar
[4]Zenkour, A. M., Thermal effects on the bending response of fiber-reinforced viscoelastic composite plates using a sinusoidal shear deformation theory, Acta. Mech., 171 (2004), pp. 171–187.Google Scholar
[5]Abbas, I. A. and Abd-Alla, A. N., Effect of initial stress on a fiber-reinforced anisotropic thermoelastic thickplate, Int. J. Thermophys., 32 (2011), pp. 1098–1110.Google Scholar
[6]Abouelregal, A. E. and Zenkour, A. M., Effect of fractional thermoelasticity on a two-dimensional problem of a mode I crack in a rotating fibre-reinforced thermoelastic medium, Chinese Phys. B, 22 (2013), 108–102.Google Scholar
[7]Abbas, I. A. and Zenkour, A. M., The effect of rotation and initial stress on thermal shock problem for a fiber-reinforced anisotropic half-space using Green-Naghdi theory, J. Comput. Theor. Nanosci., 11 (2014), pp. 331–338.Google Scholar
[8]Nowacki, W., Dynamic Problems of Thermoelasticity, Noordhoff, Leyden, The Netherlands, 1975.Google Scholar
[9]Nowacki, W., Thermoelasticity, 2nd edition, Pergamon Press, Oxford, 1986.Google Scholar
[10]Biot, M. A., Thermoelasticity and irreversible thermodynamics, J. Appl. Phys., 27 (1956), pp. 240–253.Google Scholar
[11]Lord, H. W. and Shulman, Y., A generalized dynamical theory of thermoelasticity, J. Mech. Phys. Solids, 15 (1967), pp. 299–309.Google Scholar
[12]Green, A. E. and Lindsay, K. A., Thermoelasticity, J. Elast., 2 (1972), pp. 1–7.Google Scholar
[13]Green, A. E. and Naghdi, P. M., Thermoelasticity without energy dissipation, J. Elast., 31 (1993), pp. 189–209.Google Scholar
[14]Tzou, D. Y., Macro-to-Microscale Heat Transfer: the Lagging Behavior, Washington, DC, Taylor & Francis, 1996.Google Scholar
[15]Tzou, D. Y., A unified approach for heat conduction from macro-to-micro scales, J. Heat Trans., 117 (1995), pp. 8–16.Google Scholar
[16]Tzou, D. Y., Experimental support for the lagging behavior in heat propagation, J. Thermophys. Heat Trans., 9 (1995), pp. 686–693.Google Scholar
[17]Quintanilla, R. and Jordan, P. M., A note on the two temperature theory with dual-phase-lag delay: some exact solutions, Mech. Res. Commun., 36 (2009), pp. 796–803.Google Scholar
[18]Abouelregal, A. E., Generalized thermoelasticity for an isotropic solid sphere in dual-phase-lag of heat transfer with surface heat flux, Int. J. Comput. Meth. Eng. Sci. Mech., 12 (2011), pp. 96–105.Google Scholar
[19]Zenkour, A. M., Mashat, D. S. and Abouelregal, A. E., The effect of dual-phase-lag model on reflection of thermoelastic waves in a solid half space with variable material properties, Acta. Mech. Solida Sinica, 26 (2013), pp. 659–670.CrossRefGoogle Scholar
[20]Abbas, I. A. and Zenkour, A. M., Dual-phase-lag model on thermoelastic interactions in a semi-infinite medium subjected to a ramp-type heating, J. Comput. Theoretical Nanosci., 11 (2014), pp. 642–645.Google Scholar
[21]Singh, B., Effect of hydrostatic initial stresses on waves in a thermoelastic solid half-space, Appl. Math. Comput., 198 (2008), pp. 494–505.Google Scholar
[22]Cheng, J. C. and Zhang, S. Y., Normal mode expansion method for laser generated ultrasonic Lamb waves in orthotropic thin plates, Appl. Phys. B, 70 (2000), pp. 57–63.Google Scholar
[23]Hetnarski, R. B. and Ignaczak, J., Generalized thermoelasticity, J. Thermal Stresses, 22 (1999), pp. 451–476.Google Scholar