Abstract
In this paper, we constructed the equations of generalized magneto-thermoelasticity in a perfectly conducting medium. The formulation is applied to generalizations, the Lord–Shulman theory with one relaxation time, and the Green–Lindsay theory with two relaxation times, as well as to the coupled theory. The material of the cylinder is supposed to be nonhomogeneous isotropic both mechanically and thermally. The problem has been solved numerically using a finite element method. Numerical results for the temperature distribution, displacement, radial stress, and hoop stress are represented graphically. The results indicate that the effects of nonhomogeneity, magnetic field, and thermal relaxation times are very pronounced. In the absence of the magnetic field or relaxation times, our results reduce to those of generalized thermoelasticity and/or classical dynamical thermoelasticity, respectively. Results carried out in this paper can be used to design various nonhomogeneous magneto-thermoelastic elements under magnetothermal load to meet special engineering requirements.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Bargmann H. (1974). Recent developments in the field of thermally induced waves and vibrations. Nrecl. Eng. Des. 27: 372
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
Boley, B.A.: In: Thermal Stresses: Hasselman, D.P.H., Heller, R.A. (eds.), pp. 1-ll. Plenum, New York (1980)
Qiu T.Q. and Tien C.L. (1993). Heat transfer mechanism during short-pulse laser heating of metals. ASME J. Heat Transf. 115: 835–841
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
Chandrasekhariah D.S. (1986). Thermoelasticity with second sound a-review. Appl. Mech. Rev. 39: 355
Lord H. and Shulman Y. (1967). A generalized dynamical theory of thermoelasticity. J. Mech. Phys. Solids 15: 299–309
Green A.E. and Lindsay K.A. (1972). Thermoelasticity. J. Elast. 2: 1–7
Erbay S. and Suhubi E.S. (1986). Longitudinal wave propagation in a generalized thermo-elastic cylinder. J. Therm. Stresses 9: 279
Furukawa T., Noda N. and Ashida F. (1990). Generalized thermoelasticity for an infinite bode with cylindrical hole. JSME Int. J. 31: 26
Nowinski, J.L.: Theory of Thermoelasticity with Applications. Sijthoff & Noordhoff International, Alphen Aan Den Rijn (1978)
Bahar, L., Hetnarski, R.: State space approach to thermoelasticity. In: Proceedings of 6th Canadian Congress on Applied Mechanics, pp. 17–18. University of British Columbia, Vancouver (1977)
Bahar, L., Hetnarski, R.: Transfer matrix approach to thermoelasticity. In: Proceedings of the 15th Midwest Mechanic Conference, pp. 161–163. University of Illinois, Chicago (1977)
Furukawa T., Noda N. and Ashida F. (1990). Generalized thermoelasticity for an infinite bode with cylindrical hole. JSME Int. J. 31: 26
Sharma J.N. and Chand D. (1992). On the axisymmetrical and plane strain problems of generalized thermoelasticity. Int J. Eng. Sci. 30: 223–230
Chandrasekharaiah D.S. and Murthy H.N. (1993). Thermoelastic interactions in an unbounded body with a spherical cavity. J. Therm. Stresses 16: 55–71
Misra J.C., Chattopadhyay N.C. and Samanta S.C. (1994). Thermoviscoelastic waves in an infinite aeolotropic body with a cylindrical cavity-a study under the review of generalized theory of thermoelasticity. Comp. Struc. 52(4): 705–717
Chandrasekharaiah D.S. (1996). One-dimensional wave propagation in the linear theory of thermoelasticity with energy dissipation. J. Therm. Stresses 19: 695–710
Abd-alla A.N. and Abbas I.A. (2002). A problem of generalized magnetothermoelasticity for an infinitely long, perfectly conducting cylinder. J. Therm. Stresses 25: 1009–1025
Misra J.C., Samanta S.C., Chakraborty A.K. and Misra S.C. (1991). Magnetothermoelastic interaction in an infinite elastic continuum with a cylindrical hole subjected to ramp-type heating. Int. J. Eng. Sci. 29(12): 1505–1514
Misra J.C., Samanta S.C. and Chakraborty A.K. (1991). Magnetothermoelastic interaction in an aeolotropic solid cylinder subjected to a ramp-type heating. Int. J. Eng. Sci. 29(9): 1065–1075
Zienkiewicz O.C. and Taylor R.L. (2000). The Finite Element Method Fluid Dynamics, 5th edn. Butterworth-Heinemann, London
Reddy J.N. (1993). An Introduction to the Finite Element Method, 2nd edn. McGraw-Hill, New York
Cook R.D., Malkus D.S. and Plesha M.E. (1989). Concepts and Applications of Finite Element Analysis, 3rd edn. Wiley, New York
Author information
Authors and Affiliations
Corresponding author
Additional information
An erratum to this article can be found at http://dx.doi.org/10.1007/s00419-009-0301-6
Rights and permissions
About this article
Cite this article
Abbas, I.A. Generalized magneto-thermoelasticity in a nonhomogeneous isotropic hollow cylinder using the finite element method. Arch Appl Mech 79, 41–50 (2009). https://doi.org/10.1007/s00419-008-0206-9
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00419-008-0206-9