Abstract
This paper presents an investigation of temperature, displacement, stress, and induced magnetic field in a half space perfectly-conductive plate. Finite element equations regarding generalized magneto-thermoelasticity problems with two relaxation times (i.e., the G-L theory) are derived using the principle of virtual work. For avoiding numerical complication involved in inverse Laplace and Fourier transformation and low precision thereof, the equations are solved directly in time-domain. As a numerical example, the derived equation is used to investigate the generalized magneto-thermoelastic behavior of a semi-infinite plate under magnetic field and subjecting to a thermal shock loading. The results demonstrate that FEM can faithfully predict the deformation of the plate and the induced magnetic field, and most importantly can reveal the sophisticated second sound effect of heat conduction in two-dimensional generalized thermoelastic solids, which is usually difficult to model by routine transformation methods. A peak can be observed in the distribution of stress and induced magnetic field at the heat wave front and the magnitude of the peak decreases with time, which can not be obtained by transformation methods. The new method can also be used to study generalized piezo-thermoelastic problems.
Similar content being viewed by others
References
Zhu, X., Vileneuve, D.M., Naumov, A.Y., Nikumb, S., Korkum, P.B.: Experimental study of drilling sub-10 μm holes in thin metal foils with femtosecond laser pulses. Appl. Surface Sci. 152, 138–148 (1999)
Bonello, B., Perrin, B., Romatet, E., Jeannet, J.C.: Application of the picosecond ultrasonic technique to the study of the elastic and time-resolved thermal properties of materials. Ultrasonics 35, 223–231 (1999)
Hostetler, J.L., Smith, A.N., Norris, P.M.: Simultaneous measurement of thermophysical and mechanical properties of thin film. Int. J. Thermophys 19, 569–577 (1998)
Lord, H., Shulman, Y.: A generalized dynamical theory of thermoelasticity. J. Mech. Phys. Solids 15, 299–309 (1967)
Dhaliwal, R., Sherief, H.: Generalized thermoelasticity for anisotropic media. Q. Appl. Math. 33, 1–8 (1980)
Green, A.E., Lindsay, K.E.: Thermoelasticity. J. Elasticity 2, 1–7 (1972)
Erbay, S., Suhubi, S.: Longitudinal wave propagation in generalized thermoelastic cylinder. J. Thermal Stresses 9, 279–295 (1986)
Sherief, H.: A thermo-mechanical shock problem for thermoelasticity with two relaxation times. Int. J . Eng. Sci. 32, 313–325 (1994)
Sherief, H.: State space approach to thermoelasticity with two relaxation times. Int J. Eng. Sci. 31, 117–1189 (1993)
Nowinski, J.: Theory of Thermoelasticity with Applications. Sijthoff & Noordhoff International Publishers, Alphenaan den Rij, 1978
Sherief, H.H., Ezzat, M.A.: A problem in generalized magneto-thermoelasticity for an infinitely long annular cylinder. J. Eng. Math. 34, 387–402 (1998)
Ezzat, M.A., Othman, M.I.: Electromagneto-thermoelastic plane waves with thermal relaxation in a medium of perfect conductivity. J. Thermal Stresses 21, 411–432 (2001)
Ezzat, M.A., Othman, M.I.: State-space approach to generalized magneto-thermoelasticity with relaxation in a medium of perfect conductivity. J. Thermal Stresses 25, 409–429 (2002)
Ezzat, M.A., Othman, M.I., Smaan A.A.: State space approach to two-dimensional electromagneto-thermoelastic problems with two relaxation times. Int. J. Eng. Sci. 39, 1383–1404 (2001)
Sherief, H.H., Helmy, K.A.: A two-dimensional problem for a half space in magneto-thermo-elasticity with thermal relaxation. Int. J. Eng. Sci. 40, 587–604 (2002)
Ei-caramany, A.S., Ezzat, M.A.: Thermal shock problem in generalized thermo-viscoelasticity under four theories. Int. J. Eng. Sci. 42, 649-671 (2004)
Chen, T., Weng, C.: Generalized coupled transient thermoelastic plane problems by Laplace transformation/finite element method. J. Appl. Mechanics 55, 377–382 (1988)
Chen, T., Weng, C.: Generalized coupled transient thermoelastic problems of a square cylinder with elliptical hole by Laplace transformation/finite element method. J. Thermal Stresses 12, 305–320 (1989)
Chen, T., Weng, C.: Coupled transient thermoelastic response in an axisymmetric circular cylinder by Laplace transformation-finite element method. Computers & Structures 33, 533–542 (1989)
Prevost, J.H., Tao, D.: Finite element analysis of dynamic coupled thermoelasticity problems with relaxation times. J. Appl. Mechanics 50, 817–822 (1983)
Wang, X.C., Shao, M.: The Fundamental Principle of Finite Element and the Numerical Method, 2nd Ed., Beijing: Tsinghua University Press, 1997
Lee, T.W., Sim, W.J.: Efficient time-domain finite analysis for dynamic coupled thermoelasticity. Computers & Structures 45(4), 785–793 (1992)
Newmark, N.M.: A method for computation for structural dynamics. ASCE J. Eng. Mech. Division 85, 67–94 (1959)
He, T.H., Tian, X.G., Shen, Y.P.: State space approach to one-dimensional thermalshock problem for a semi-infinite piezoelectric rod. Int. J. Eng. Sci. 40, 1081–1097 (2002)
Author information
Authors and Affiliations
Corresponding author
Additional information
The project supported by the National Natural Science Foundation of China (10132010 and 10472089)
The English text was polished by Yunming Chen
Rights and permissions
About this article
Cite this article
Tian, X., Shen, Y. Study on generalized magneto-thermoelastic problems by FEM in time domain. ACTA MECH SINICA 21, 380–387 (2005). https://doi.org/10.1007/s10409-005-0046-6
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10409-005-0046-6