The effect of magnetic field on a thermoelastic fiber-reinforced material under GN-III theory

Faris S. Alzahrani and Ibrahim A. Abbas

Abstract

In this work, the two-dimensional generalized magneto-thermoelastic problem of a fiber-reinforced anisotropic material is investigated under Green and Naghdi theory of type III. The solution will be obtained for a certain model when the half space subjected to ramp-type heating and traction free surface. Laplace and exponential Fourier transform techniques are used to obtain the analytical solutions in the transformed domain by the eigenvalue approach. The inverses of Fourier transforms are obtained analytically. The results have been verified numerically and are represented graphically. Comparisons are made with the results predicted by the presence and absence of reinforcement and magnetic field.

Key Words

analytical solution; magnetothermoelasticity; fiber-reinforced material; eigenvalue approach; Green and Naghdi theory

Address

(1) Faris S. Alzahrani: Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box. 80203, Jeddah 21589, Saudi Arabia;<br>(2) Ibrahim A. Abbas: Department of Mathematics, Faculty of Science and Arts - Khulais, University Of Jeddah, Saudi Arabia;<br>(3) Faris S. Alzahrani, Ibrahim A. Abbas: Nonlinear Analysis and Applied Mathematics Research Group (NAAM), Department of Mathematics, King Abdulaziz University, Jeddah, Saudi Arabia;<br>(4) Ibrahim A. Abbas: Department of Mathematics, Faculty of Science, Sohag University, Sohag, Egypt.

← Back to Volume 22, No. 2