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Chin. Phys. B, 2013, Vol. 22(10): 108102    DOI: 10.1088/1674-1056/22/10/108102

The effect of fractional thermoelasticity on a two-dimensional problem of a mode I crack in a rotating fiber-reinforced thermoelastic medium

Ahmed E. Abouelregala c, Ashraf M. Zenkourb d
a Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, Egypt;
b Department of Mathematics, Faculty of Science, King Abdulaziz University, P. O. Box 80203, Jeddah 21589, Saudi Arabia;
c Department of Mathematics, College of Science and Arts, University of Aljouf, El-Qurayat, Saudi Arabia;
d Department of Mathematics, Faculty of Science, Kafrelsheikh University, Kafr El-Sheikh 33516, Egypt
Abstract  This article is concerned with the effect of rotation on the general model of the equations of the generalized thermoelasticity for a homogeneous isotropic elastic half-space solid, whose surface is subjected to a Mode-I crack problem. The fractional order theory of thermoelasticity is used to obtain the analytical solutions for displacement components, force stresses, and temperature. The boundary of the crack is subjected to a prescribed stress distribution and temperature. The normal mode analysis technique is used to solve the resulting non-dimensional coupled governing equations of the problem. The variations of the considered variables with the horizontal distance are illustrated graphically. Some particular cases are also discussed in the context of the problem. Effects of the fractional parameter, reinforcement, and rotation on the variations of different field quantities inside the elastic medium are analyzed graphically. Comparisons are made between the results in the presence and those in the absence of fiber-reinforcing, rotating and fractional parameters.
Keywords:  fiber-reinforced      mode-I crack      fractional order thermoelasticity theory      rotating medium      normal mode analysis  
Received:  25 February 2013      Revised:  22 April 2013      Published:  30 August 2013
PACS:  81.05.Ni (Dispersion-, fiber-, and platelet-reinforced metal-based composites)  
  46.25.Hf (Thermoelasticity and electromagnetic elasticity (electroelasticity, magnetoelasticity)) (Work functions)  
  46.50.+a (Fracture mechanics, fatigue and cracks)  
Corresponding Authors:  Ashraf M. Zenkour     E-mail:

Cite this article: 

Ahmed E. Abouelregal, Ashraf M. Zenkour The effect of fractional thermoelasticity on a two-dimensional problem of a mode I crack in a rotating fiber-reinforced thermoelastic medium 2013 Chin. Phys. B 22 108102

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