State-space approach of two-temperature generalized thermoelasticity of infinite body with a spherical cavity subjected to different types of thermal loading

Archive of Applied Mechanics

Volumn 77, Issue 9, 2007, Pages 675-687

  Youssef, Hamdy M ^a,b   Al Harby, Amnah H ^c  

^a Alexandria University   (Egypt)

^b UMM AL QURA UNIVERSITY   (Saudi Arabia)

^c Faculty of Education   (Saudi Arabia)

Author keywords

Generalized thermoelasticity; State space approach; Two temperature

Indexed keywords

BOUNDARY CONDITIONS; LAPLACE TRANSFORMS; NUMERICAL METHODS; PROBLEM SOLVING; THERMAL LOAD;

GENERALIZED THERMOELASTICITY; STATE-SPACE APPROACH;

THERMOELASTICITY;

EID: 34547163883     PISSN: 09391533     EISSN: 14320681     Source Type: Journal    
DOI: 10.1007/s00419-007-0120-6     Document Type: Article

References (41)

1. Abd-Alla A.N. and Maugin G.A. (1990). Nonlinear equations for thermoelastic magnetizable conductors. Int. J. Eng. Sci. 28: 589
2. Anisimov S.I., Kapeliovich B.L. and Perelman T.L. (1974). Electron emission from metal surfaces exposed to ultra-short llaser pulses. Sov. Phys. JETP 39: 375-377
3. Anwar M. and Sherief H. (1988). State space approach to generalized thermoelasticity. J. Therm. Stresses 11: 353-365
4. Anwar M. and Sherief H. (1988). Boundary integral equation formulation of generalized thermoelasticity in a Laplace transform domain. Appl. Math. Model. 12: 161-166
5. Bahar, L.Y., Hetnarski, R.B.: In: Proceedings of 6th Canadian Congress Applied Mechanic Conference pp. 17-18. University of British Columbia, Vancouver, British Columbia, Canada (1977)
6. Bahar, L.Y., Hetnarski, R.B.: In: Proceedings of 15th Midwest Mechanic Conference pp. 161-163. University of Illinois, Chicago (1977)
7. Bahar L.Y. and Hetnarski R.B. (1978). State space approach to thermoelasticity. J. Therm. Stresses 1: 135
8. Bargmann H. (1974). Recent developments in the field of thermally induced waves and vibrations. Nrecl. Eng. Des. 27: 372
9. Boley, B.A.: In thermal stresses. Hasselman, D.P.H., Heller, R.A. (eds.) pp. 1-ll. Plenum Press, New York (1980)
10. Boley B.A. and Tolins I.S. (1962). Transient coupled thermoelastic boundary value problems in the half-space. J. Appl. Mech. 29: 637-646
11. Chandrasekaraiah D.S. and Murthy H.N. (1993). Thermoelasticity of infinite elastic material with spherical cavity. J. Therm. Stresses 16: 55
12. Chandrasekhariah D.S. (1986). Thermoelasticity with second sound a-review. Appl. Mech. Rev. 39: 355
13. Charles G.C. (1972). Matrices and linear transformations, 2nd edn. Addison-Wesley Publishing Company, USA
14. Chen P.J. and Gurtin M.E. (1968). On a theory of heat conduction involving two temperatures. Zamp 19: 614-627
15. Chen P.J., Gurtin M.E. and Williams W.O. (1969). On the thermodynamics of non-simple elastic materials with two temperatures. Zamp 20: 107-112
16. Chen P.J., Gurtin M.E. and Williams W.O. (1968). A note on non-simple heat conduction. Zamp 19: 969-970
17. Chen J.K., Beraun J.E. and Tham C.L. (2004). Ultrafast thermoelasticity for short-pulse laser heating. Int. J. Eng. Sci. 42: 793-807
18. El-Maghraby N.M. and Youssef H.M. (2004). State space approach to generalized thermoelastic problem with thermo-mechanical shock. J. Appl. Math. Comput. 156: 577
19. Erbay S. and Suhubi E.S. (1986). Longitudinal wave propagation in a generalized thermo-elastic cylinder. J. Therm. Stresses 9: 279
20. Eringen, A.C., Maugin, G.A.: Electrodynamics of continua, vol 2. Springer, New York (1989)
21. Furukawa T., Noda N. and Ashida F. (1990). Generalized thermoelasticity for an infinite bode with cylindrical hole. Jsme Int. J. 31: 26
22. Green A.E. and Lindsay K.A. (1972). Thermoelasticity. J. Elasticity 2: 1
23. Hanig G. and Hirdes U. (1984). A method for the numerical inversion of laplace transform. J. Comp. Appl. Math. 10: 113-132
24. Ignaczak J. (1979). Uniqueness in generalized thermoelasticity. J. Therm. Stresses 2: 171
25. Ignaczak J. (1982). A note on uniqueness in thermoelasticity with one relaxation time. J. Therm. Stresses 5: 257-263
26. Lord H. and Shulman Y. (1967). A generalized dynamical theory of thermo-elasticity. J. Mech. Phys. Solids 15: 299
27. Maugin, G.A.: Continuum mechanics of electromagnetic solids. North-Holland, Amsterdam (1988)
28. Misra J.C., Kar S.B. and Samanta S.C. (1987). The effects of mechanical and thermal relaxations in a heated viscoelastic medium containing a cylindrical hole. Trans. CSME 11: 151
29. Qiu T.Q. and Tien C.L. (1993). Heat transfer mechanism during short-pulse laser heating of metals. ASME J. Heat Trans. 115: 835-841
30. Sherief H. and Youssef H. (2004). Short time solution for a problem in magneto-thermoelasticity with thermal relaxation. J. Therm. Stresses 27(6): 537
31. Sherief H. and Anwar M. (1986). Two-dimensional problem of a moving heated punch in generalized thermoelasticity. J. Therm. Stresses 9: 325-343
32. Sherief H. and Anwar M. (1994). A two dimensional generalized thermoelasticity problem for an infinitely long cylinder. J. Therm. Stresses 17: 213-227
33. Sherief H. and Hamza F. (1994). Generalized thermoelastic problem of a thick plate under axisymmetric temperature distribution. J. Therm. Stresses 17: 435-453
34. Sherief H. (1986). Fundamental solution of the generalized thermoelastic problem for short times. J. Therm. Stresses 9: 151-164
35. Sherief H. (1987). On uniqueness and stability in generalized thermoelasticity. Quart. Appl. Math. 45: 773-778
36. Sherief H. (1993). J. State space formulation for generalized thermoelasticity with one relaxation time including heat sources. J. Therm. Stresses 16: 163
37. Tzou, D.Y.: Macro- to microscale heat transfer: the lagging behavior. Taylor & Francis, Washington, DC (1997)
38. Warren W.E. and Chen P.J. (1973). Wave Propagation in the Two-Temperature Theory of Thermoelasticity. Acta Mech. 16: 21-33
39. Youssef H. (2005). The dependence of the modulus of elasticity and the thermal conductivity on the reference temperature in generalized thermoelasticity for an infinite material with a spherical cavity. J. Appl. Math. Mech. 26(4): 470-475
40. Youssef, H.: Theory of two-temperature generalized thermoelasticity. IMA J. Appl. Math. 1-8 (2005)
41. Youssef, H.: Problem of generalized thermoelastic infinite medium with cylindrical cavity subjected to a ramp-type heating and loading. J. Arch. App. Mech. 75, 8-9, 553-565 (2006)