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Steel and Composite Structures Volume 21, Number 4, July20 2016 , pages 791-803 DOI: https://doi.org/10.12989/scs.2016.21.4.791 |
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Analytical solution of a two-dimensional thermoelastic problem subjected to laser pulse |
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Ibrahim A. Abbas and Faris S. Alzahrani
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| Abstract | ||
| In this article, the problem of a two-dimensional thermoelastic half-space are studied using mathematical methods under the purview of the generalized thermoelastic theory with one relaxation time is studied. The surface of the half-space is taken to be thermally insulated and traction free. Accordingly, the variations of physical quantities due to by laser pulse given by the heat input. The nonhomogeneous governing equations have been written in the form of a vector-matrix differential equation, which is then solved by the eigenvalue approach. The analytical solutions are obtained for the temperature, the components of displacement and stresses. The resulting quantities are depicted graphically for different values of thermal relaxation time. The result provides a motivation to investigate the effect of the thermal relaxation time on the physical quantities. | ||
| Key Words | ||
| Eigenvalue approach; exact solution; Lord and Shulman theory; relaxation time; laser pulse | ||
| Address | ||
| (1) Ibrahim A. Abbas: Department of Mathematics, Faculty of Science and Arts - Khulais, University Of Jeddah, Saudi Arabia; (2) Ibrahim A. Abbas: Nonlinear Analysis and Applied Mathematics Research Group (NAAM), Department of Mathematics, King Abdulaziz University, Jeddah, Saudi Arabia; (3) Ibrahim A. Abbas: Department of mathematics, Faculty of Science, Sohag University, Sohag, Egypt; (4) Faris S. Alzahrani: Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box. 80203, Jeddah 21589, Saudi Arabia. | ||