Generalized Thermoelasticity Problem of Material Subjected to Thermal Loading Due to Laser Pulse


This work is devoted to a study of the induced temperature and stress fields in an elastic half space in context of clas-sical coupled thermoelasticity and generalized thermoelasticity in a unified system of equations. The half space is con-sidered to be made of an isotropic homogeneous thermoelastic material. The bounding plane surface is heated by a non-Gaussian laser beam with pulse duration of 2 ps. An exact solution of the problem is first obtained in Laplace transform space. Since the response is of more interest in the transient state, the inversion of Laplace transforms have been carried numerically. The derived expressions are computed numerically for copper and the results are presented in graphical form.

Share and Cite:

H. Youssef and A. Al-Felali, "Generalized Thermoelasticity Problem of Material Subjected to Thermal Loading Due to Laser Pulse," Applied Mathematics, Vol. 3 No. 2, 2012, pp. 142-146. doi: 10.4236/am.2012.32022.

Conflicts of Interest

The authors declare no conflicts of interest.


[1] M. Boit, “Thermoelasticity and Irreversible Thermo-Dynamics,” Journal of Applied Physics, Vol. 27, 1956, pp. 240-251.
[2] H. Bargmann, “Recent Developments in the Field of Thermally Induced Waves and Vibrations,” Nuclear Engineering and Design, Vol. 27, No. 3, 1974, pp. 372-381.
[3] B. Boley, “In Thermal Stresses,” In: D. P. H. Hasselman and R. A. Heller, Eds., 1-ll. Plenum Press, New York, 1980. doi:10.1007/978-1-4613-3156-8_1
[4] D. S. Chandrasekharaiah, “Thermoelasticity with Second Sound: A Review,” Applied Mechanics Review, Vol. 39 No. 3, 1986, pp. 355-376. doi:10.1115/1.3143705
[5] H. Lord and Y. Shulman, “A Generalized Dynamical Theory of Thermoelasticity,” Journal of the Mechanics and Physics of Solids, Vol. 15, No. 5, 1967, pp. 299-307. doi:10.1016/0022-5096(67)90024-5
[6] A. E. Green and K. A. Lindsay, “Thermoelasticity,” Journal of Elasticity, Vol. 2, No. 1, 1972, pp. 1-7. doi:10.1007/BF00045689
[7] Y. Sun, D. Fang, M. Saka and A. K. Soh, “Laser-Induced Vibrations of Micro-Beams under Different Boundary Conditions,” International Journal of Solids and Structures, Vol. 45, No. 7-8, 2008, pp. 1993-2013. doi:10.1016/j.ijsolstr.2007.11.006
[8] D. Tzou, “Macro-to-Micro Heat Transfer,” Taylor & Francis, Washington DC, 1996.
[9] H. Sherief and M. Anwar, “Two-Dimensional Problem of a Moving Heated Punch in Generalized Thermoelasticity,” Journal of Thermal Stresses, Vol. 9, No. 4, 1986, 325-335. doi:10.1080/01495738608961910
[10] X. Wang and X. Xu, “Thermoelastic Wave Induced by Pulsed Laser Heating,” Applied Physics A: Materials Science & Processing, Vol. 73, No. 1, 2001, pp. 107-114. doi:10.1007/s003390000593
[11] F. A. McDonald, “On the Precursor in Laser-Generated Ultrasound Waveforms in Metals,” Applied Physics Letters, Vol. 56, No. 3, 1990, pp. 230-232. doi:10.1063/1.102839
[12] A. Bagri and M. R. Eslami, “A Unified Generalized Thermoelasticity; Solution for Cylinders and Spheres,” International Journal of Mechanical Sciences, Vol. 49, No. 12, 2007, pp. 1325-1338.
[13] H. M. Youssef, “Two-Dimensional Generalized Thermoelasticity Problem for a Half-Space Subjected to RampType Heating,” European Journal of Mechanics—A/Solids, Vol. 25, No. 5, 2006, pp. 745-763.
[14] H. M. Youssef and A. El-Bary, “Generalized Thermoelastic Infinite Layer Subjected to Ramp-Type Thermal and Mechanical Loading under Three Theories—State Space Approach,” Journal of Thermal Stresses, Vol. 32, No. 12, 2009, pp. 1293-1310. doi:10.1080/01495730903249276

Copyright © 2023 by authors and Scientific Research Publishing Inc.

Creative Commons License

This work and the related PDF file are licensed under a Creative Commons Attribution 4.0 International License.