Skip to main content Accessibility help
×
Home

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
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
E-mail address:

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.


Type
Research Article
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.

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. 2554.CrossRefGoogle 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. 353359.CrossRefGoogle Scholar
[3]Sengupta, P. R. and Nath, S., Surface waves in fibre-reinforced anisotropic elastic media, Sadhana, 26 (2001), pp. 363370.CrossRefGoogle 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. 171187.CrossRefGoogle 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. 10981110.CrossRefGoogle 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), 108102.CrossRefGoogle 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. 331338.CrossRefGoogle 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. 240253.CrossRefGoogle Scholar
[11]Lord, H. W. and Shulman, Y., A generalized dynamical theory of thermoelasticity, J. Mech. Phys. Solids, 15 (1967), pp. 299309.CrossRefGoogle Scholar
[12]Green, A. E. and Lindsay, K. A., Thermoelasticity, J. Elast., 2 (1972), pp. 17.CrossRefGoogle Scholar
[13]Green, A. E. and Naghdi, P. M., Thermoelasticity without energy dissipation, J. Elast., 31 (1993), pp. 189209.CrossRefGoogle 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. 816.CrossRefGoogle Scholar
[16]Tzou, D. Y., Experimental support for the lagging behavior in heat propagation, J. Thermophys. Heat Trans., 9 (1995), pp. 686693.CrossRefGoogle 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. 796803.CrossRefGoogle 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. 96105.CrossRefGoogle 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. 659670.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. 642645.CrossRefGoogle Scholar
[21]Singh, B., Effect of hydrostatic initial stresses on waves in a thermoelastic solid half-space, Appl. Math. Comput., 198 (2008), pp. 494505.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. 5763.CrossRefGoogle Scholar
[23]Hetnarski, R. B. and Ignaczak, J., Generalized thermoelasticity, J. Thermal Stresses, 22 (1999), pp. 451476.Google Scholar

Full text views

Full text views reflects PDF downloads, PDFs sent to Google Drive, Dropbox and Kindle and HTML full text views.

Total number of HTML views: 0
Total number of PDF views: 14 *
View data table for this chart

* Views captured on Cambridge Core between September 2016 - 4th December 2020. This data will be updated every 24 hours.

Hostname: page-component-b4dcdd7-z76xg Total loading time: 0.461 Render date: 2020-12-04T09:15:45.829Z Query parameters: { "hasAccess": "0", "openAccess": "0", "isLogged": "0", "lang": "en" } Feature Flags last update: Fri Dec 04 2020 08:59:57 GMT+0000 (Coordinated Universal Time) Feature Flags: { "metrics": true, "metricsAbstractViews": false, "peerReview": true, "crossMark": true, "comments": true, "relatedCommentaries": true, "subject": true, "clr": false, "languageSwitch": true }

Send article to Kindle

To send this article to your Kindle, first ensure no-reply@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about sending to your Kindle. Find out more about sending to your Kindle.

Note you can select to send to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be sent to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

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

Send article to Dropbox

To send this article to your Dropbox account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Dropbox.

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

Send article to Google Drive

To send this article to your Google Drive account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Google Drive.

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

Reply to: Submit a response


Your details


Conflicting interests

Do you have any conflicting interests? *