DOI QR코드

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Analytical solution of a two-dimensional thermoelastic problem subjected to laser pulse

  • Abbas, Ibrahim A. (Department of Mathematics, Faculty of Science and Arts - Khulais, University Of Jeddah) ;
  • Alzahrani, Faris S. (Nonlinear Analysis and Applied Mathematics Research Group (NAAM), Department of Mathematics, King Abdulaziz University)
  • 투고 : 2015.12.29
  • 심사 : 2016.06.10
  • 발행 : 2016.07.20

초록

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.

키워드

참고문헌

  1. Abbas, I.A. (2014a), "Eigenvalue approach for an unbounded medium with a spherical cavity based upon two-temperature generalized thermoelastic theory", J. Mech. Sci. Technol., 28(10), 4193-4198. https://doi.org/10.1007/s12206-014-0932-6
  2. Abbas, I.A. (2014b), "Eigenvalue approach in a three-dimensional generalized thermoelastic interactions with temperature-dependent material properties", Comput. Math. Appl., 68(12), 2036-2056. https://doi.org/10.1016/j.camwa.2014.09.016
  3. Abbas, I.A. (2014c), "The effects of relaxation times and moving heat source on a two-temperature generalized thermoelastic thin slim strip", Can. J. Phys., 93(5), 585-590.
  4. Abbas, I.A. (2015a), "A dual phase lag model on thermoelastic interaction in an infinite fiber-reinforced anisotropic medium with a circular hole", Mech. Based Des. Struct. Mach., 43(4), 501-513. https://doi.org/10.1080/15397734.2015.1029589
  5. Abbas, I.A. (2015b), "Eigenvalue approach to fractional order generalized magneto-thermoelastic medium subjected to moving heat source", J. Magnet. Magnet. Mater., 377, 452-459. https://doi.org/10.1016/j.jmmm.2014.10.159
  6. Abbas, I.A. (2015c), "The effects of relaxation times and a moving heat source on a two-temperature generalized thermoelastic thin slim strip", Can. J. Phys., 93(5), 585-590.
  7. Abbas, I.A. and Kumar, R. (2016), "2D deformation in initially stressed thermoelastic half-space with voids", Steel Compos. Struct., Int. J., 20(5), 1103-1117. https://doi.org/10.12989/scs.2016.20.5.1103
  8. Abbas, I.A. and Youssef, H.M. (2015), "Two-dimensional fractional order generalized thermoelastic porous material", Latin Am. J. Solid. Struct., 12(7), 1415-1431. https://doi.org/10.1590/1679-78251584
  9. Abbas, I.A. and Zenkour, A.M. (2013), "LS model on electro-magneto-thermoelastic response of an infinite functionally graded cylinder", Compos. Struct., 96, 89-96. https://doi.org/10.1016/j.compstruct.2012.08.046
  10. Abbas, I.A. and Zenkour, A.M. (2014), "Dual-ohase-lag model on thermoelastic interactions in a semiinfinite medium subjected to a ramp-type heating", J. Computat. Theor. Nanosci., 11(3), 642-645. https://doi.org/10.1166/jctn.2014.3407
  11. Agarwal, V.K. (1978), "On surface waves in generalized thermoelasticity", J. Elast., 8(2), 171-177. https://doi.org/10.1007/BF00052480
  12. Agarwal, V.K. (1979a), "On electromagneto-thermoelastic plane waves", Acta Mechanica, 34(3-4), 181-191. https://doi.org/10.1007/BF01227983
  13. Agarwal, V.K. (1979b), "On plane waves in generalized thermoelasticity", Acta Mechanica, 31(3-4), 185-198. https://doi.org/10.1007/BF01176847
  14. Al-Qahtani, H.M. and Datta, S.K. (2008), "Laser-generated thermoelastic waves in an anisotropic infinite plate: Exact analysis", J. Therm. Stress., 31(6), 569-583. https://doi.org/10.1080/01495730801978380
  15. Biot, M.A. (1956), "Thermoelasticity and irreversible thermodynamics", J. Appl. Phys., 27(3), 240-253. https://doi.org/10.1063/1.1722351
  16. Bouchafa, A., Bouiadjra, M.B., Houari, M.S.A. and Tounsi, A. (2015), "Thermal stresses and deflections of functionally graded sandwich plates using a new refined hyperbolic shear deformation theory", Steel Compos. Struct., Int. J., 18(6), 1493-1515. https://doi.org/10.12989/scs.2015.18.6.1493
  17. Das, N.C., Lahiri, A. and Giri, R.R. (1997), "Eigenvalue approach to generalized thermoelasticity", Ind. J. Pure Appl. Math., 28(12), 1573-1594.
  18. Deresiewicz, H. (1975), "Thermal coupling of waves in a plate", Acta Mechanica, 21(4), 329-342. https://doi.org/10.1007/BF01303074
  19. Dhaliwal, R.S. and Sherief, H.H. (1980), "Generalized thermoelasticity for anisotropic media", Quart. Appl. Math., 38(1), 1-8. https://doi.org/10.1090/qam/575828
  20. Ezzat, M.A. (2011), "Magneto-thermoelasticity with thermoelectric properties and fractional derivative heat transfer", Physica B: Condensed Matter, 406(1), 30-35. https://doi.org/10.1016/j.physb.2010.10.005
  21. Ezzat, M. and Awad, E. (2010), "Analytical aspects in the theory of thermoelastic bodies with microstructure and two temperatures", J. Therm. Stress., 33(7), 674-693. https://doi.org/10.1080/01495731003776069
  22. Ezzat, M.A. and El-Karamany, A.S. (2003), "The relaxation effects of the volume properties of viscoelastic material in generalized thermoelasticity", Int. J. Eng. Sci., 41(19), 2281-2298. https://doi.org/10.1016/S0020-7225(03)00108-3
  23. Ezzat, M.A. and Youssef, H.M. (2005), "Generalized magneto-thermoelasticity in a perfectly conducting medium", Int. J. Solid. Struct., 42(24-25), 6319-6334. https://doi.org/10.1016/j.ijsolstr.2005.03.065
  24. Green, A.E. and Lindsay, K.A. (1972), "Thermoelasticity", J. Elastic., 2(1), 1-7. https://doi.org/10.1007/BF00045689
  25. Isavand, S., Shakeri, B.M. and Mohandesi, J.A. (2015), "Dynamic response of functionally gradient austenitic-ferritic steel composite panels under thermo-mechanical loadings", Steel Compos. Struct., Int. J., 18(1), 1-28. https://doi.org/10.12989/scs.2015.18.1.001
  26. Kakar, S. and Kakar, R. (2014), "Electro-magneto-thermoelastic surface waves in non-homogeneous orthotropic granular half space", Geomech. Eng., Int. J., 7(1), 1-36. https://doi.org/10.12989/gae.2014.7.1.001
  27. Kumar, R. and Rupender (2010), "The effect of rotation in a magneto-micropolar thermoelastic layer with one relaxation time", Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, 224(3), 661-673. https://doi.org/10.1243/09544062JMES1725
  28. Lord, H.W. and Shulman, Y. (1967), "A generalized dynamical theory of thermoelasticity", J. Mech. Phys. Solid., 15(5), 299-309. https://doi.org/10.1016/0022-5096(67)90024-5
  29. Mallik, S.H. and Kanoria, M. (2008), "A two dimensional problem for a transversely isotropic generalized thermoelastic thick plate with spatially varying heat source", Euro. J. Mech., A/Solids, 27(4), 607-621. https://doi.org/10.1016/j.euromechsol.2007.09.002
  30. Othman, M.I.A. and Abbas, I.A. (2012), "Generalized thermoelasticity of thermal-shock problem in a nonhomogeneous isotropic hollow cylinder with energy dissipation", Int. J. Thermophys., 33(5), 913-923. https://doi.org/10.1007/s10765-012-1202-4
  31. Othman, M.I. and Abbas, I.A. (2014), "Effect of rotation on plane waves in generalized thermomicrostretch elastic solid: Comparison of different theories using finite element method", Can. J. Phys., 92(10), 1269-1277. https://doi.org/10.1139/cjp-2013-0482
  32. Saadatfar, M. and Aghaie-Khafri, M. (2015), "Electromagnetothermoelastic behavior of a rotating imperfect hybrid functionally graded hollow cylinder", Smart Struct. Syst., Int. J., 15(6), 1411-1437. https://doi.org/10.12989/sss.2015.15.6.1411
  33. Verma, K. and Hasebe, N. (1999), "On the propagation of generalized thermoelastic vibrations in plates", Eng. Transact., 47(3), 300-319.
  34. Zenkour, A.M. and Abbas, I.A. (2015a), "Electro-magneto-thermo-elastic response of infinite functionally graded cylinders without energy dissipation", J. Magnet. Magnet. Mater., 395, 123-129. https://doi.org/10.1016/j.jmmm.2015.07.038
  35. Zenkour, A.M. and Abouelregal, A.E. (2015b), "Thermoelastic interaction in functionally graded nanobeams subjected to time-dependent heat flux", Steel Compos. Struct., Int. J., 18(4), 909-924. https://doi.org/10.12989/scs.2015.18.4.909

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