Abstract
A unified generalized thermoelasticity solution for the transient thermal shock problem in the context of three different generalized theories of the coupled thermoelasticity, namely: the extended thermoelasticity, the temperature-rate-dependent thermoelasticity and the thermoelasticity without energy dissipation is proposed in this paper. First, a unified form of the governing equations is presented by introducing the unifier parameters. Second, the unified equations are derived for the thermoelastic problem of the isotropic and homogeneous materials subjected to a transient thermal shock. The Laplace transform and inverse transform are used to solve these equations, and the unified analytical solutions in the transform domain and the short-time approximated solutions in the time domain of displacement, temperature and stresses are obtained. Finally, the numerical results for copper material are displayed in graphical forms to compare the characteristic features of the above three generalized theories for dealing with the transient thermal shock problem.
Similar content being viewed by others
References
Peshkov V.: Second sound in helium II. J. Phys. 8, 381–386 (1944)
Landau L.D.: The theory of superfluidity of helium II. J. Phys. 5, 71–90 (1941)
Lord H.W., Shulman Y.: A generalized dynamical theory of thermoelasticity. J. Mech. Phys. Solids 15, 299–309 (1967)
Green A.E., Lindsay K.A.: Thermoelasticity. J. Elast. 2, 1–7 (1972)
Green A.E., Naghdi P.M.: Thermoelasticity without energy dissipation. J. Elast. 31, 189–208 (1993)
Balla M., Hungary B.: Analytical study of the thermal shock problem of a half-space with various thermoelasticity models. Acta Mech. 89, 73–92 (1991)
Chen J., Dargush G.F.: Boundary element method for dynamic poroelastic and thermoelastic analysis. Int. J. Solids Struct. 32, 2257–2278 (1995)
Bagri A., Eslami M.R.: Generalized coupled thermoelasticity of disks based on the Lord-Shulman model. J. Therm. Stress. 27, 691–704 (2004)
Hosseini T.P., Eslami M.R.: Boundary element analysis of finite domains under thermal and mechanical shock with the Lord-Shulman theory. J. Strain. Anal. Eng. 38, 53–64 (2003)
Zamani A., Hetnarski R.B., Eslami M.R.: Second sound in a cracked layer based on Lord-Shulman theory. J. Therm. Stress. 34, 181–200 (2011)
Chandrasekharaiah D.S.: One-dimensional wave propagation in the linear theory of thermoelasticity without energy dissipation. J. Therm. Stress. 19, 695–710 (1996)
Taheri H., Fariborz S., Eslami M.R.: Thermoelasticity solution of a layer using the Green-Naghdi model. J. Therm. Stress. 27, 795–809 (2004)
Chattopadhyay N.C., Biswas M.: Study of thermal stress generalized in an elastic half-space in the context of generalized thermoelasticity theory. J. Therm. Stress. 30, 107–204 (2007)
Furukawa T., Noda N., Ashida F.: Generalized thermoelasticity for an infinite solid cylinder. JSME Int. J. A-Solid M. 34, 281–286 (1991)
EI-Karamany A.S.: Uniqueness and reciprocity theorems in generalized linear micropolar thermoviscoelasticity. Int. J. Eng. Sci. 40, 2097–2117 (2002)
Bagri A., Eslami M.R.: A unified generalized thermoelasticity solution for cylinders and spheres. Int. J. Mech. Sci. 49, 1325–1335 (2007)
Bagri A., Eslami M.R.: A unified generalized thermoelasticity formulation: application to thick functionally graded cylinders. J. Therm. Stress. 30, 911–930 (2007)
Kumar R., Devi S.: Thermomechanical deformation in porous generalized thermoelastic body with variable material properties. Struct. Eng. Mech. 34, 285–300 (2010)
Tzou D.Y.: A unified approach for heat conduction from macro to micro-scales. J. Heat. Trans-T. ASME 117, 8–16 (1995)
Chandrasekharaiah D.S., Srinath K.S.: One-dimensional waves in a thermoelastic half-space without energy dissipation. Int. J. Eng. Sci. 34, 1447–1455 (1996)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Wang, YZ., Zhang, XB. & Song, XN. A unified generalized thermoelasticity solution for the transient thermal shock problem. Acta Mech 223, 735–743 (2012). https://doi.org/10.1007/s00707-011-0597-5
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00707-011-0597-5