Eur. Phys. J. Plus (2016) 131: 424
https://doi.org/10.1140/epjp/i2016-16424-8

Regular Article

Analytical solution of magnetothermoelastic interaction in a fiber-reinforced anisotropic material

¹ Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box. 80203, 21589, Jeddah, Saudi Arabia
² Department of Mathematics, Faculty of Science and Arts - Khulais, University of Jeddah, Jeddah, Saudi Arabia
³ Nonlinear Analysis and Applied Mathematics Research Group (NAAM), Department of Mathematics, King Abdulaziz University, Jeddah, Saudi Arabia
⁴ Department of mathematics, Faculty of Science, Sohag University, Sohag, Egypt

^* e-mail: ibrabbas7@yahoo.com

Received: 26 September 2016
Accepted: 1 November 2016
Published online: 8 December 2016

Abstract

The present paper is concerned with the investigation of the analytical solution of a fiber-reinforced anisotropic material under generalized magnetothermoelastic theory using the eigenvalue approach. Based on the Lord-Shulman theory, the formulation is applied to generalized magnetothermoelasticity with one relaxation time. Based on eigenvalue approach, exponential Fourier transform and Laplace techniques, the analytical solutions has been obtained. The inverses of Fourier transforms are obtained analytically. Numerical computations for a fiber-reinforced-like material have been performed and the results are presented graphically. The results of the temperature, displacement components and stress components have been verified numerically and are represented graphically. Comparisons are made with the results predicted by the presence and absence of reinforcement.