Volume 6, Issue 6
On the Generalized Thermoelasticity Problem for an Infinite Fibre-Reinforced Thick Plate under Initial Stress

Ahmed E. Abouelregal & Ashraf M. Zenkour

Adv. Appl. Math. Mech., 6 (2014), pp. 783-796.

Published online: 2014-06

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  • 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

Dual-phase-lag theory, fiber-reinforced, initial stress, normal mode analysis, thick plate.

  • AMS Subject Headings

73B, 73C, 73K

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{AAMM-6-783, author = {E. Abouelregal , Ahmed and M. Zenkour , Ashraf}, title = {On the Generalized Thermoelasticity Problem for an Infinite Fibre-Reinforced Thick Plate under Initial Stress}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2014}, volume = {6}, number = {6}, pages = {783--796}, 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.

}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.2013.m206}, url = {http://global-sci.org/intro/article_detail/aamm/48.html} }
TY - JOUR T1 - On the Generalized Thermoelasticity Problem for an Infinite Fibre-Reinforced Thick Plate under Initial Stress AU - E. Abouelregal , Ahmed AU - M. Zenkour , Ashraf JO - Advances in Applied Mathematics and Mechanics VL - 6 SP - 783 EP - 796 PY - 2014 DA - 2014/06 SN - 6 DO - http://doi.org/10.4208/aamm.2013.m206 UR - https://global-sci.org/intro/article_detail/aamm/48.html KW - Dual-phase-lag theory, fiber-reinforced, initial stress, normal mode analysis, thick plate. AB -

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.

Ahmed E. Abouelregal & Ashraf M. Zenkour. (1970). On the Generalized Thermoelasticity Problem for an Infinite Fibre-Reinforced Thick Plate under Initial Stress. Advances in Applied Mathematics and Mechanics. 6 (6). 783-796. doi:10.4208/aamm.2013.m206
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