Abstract
A two-dimensional problem for an infinite thermoelastic half-space with a permeating substance in contact with the bounding plane is developed. The formulation is applied to the generalized thermoelastic diffusion based on Lord–Shulman theory. The bounding surface is traction free and subjected to a known axisymmetric temperature distribution, and the chemical potential is assumed to be a known function of time. Integral transform technique is used to find the analytic solution in the transform domain by using a direct approach. Inversion of transforms is done employing a numerical scheme. The mathematical model is prepared for copper material, and numerical results for temperature, stress, displacement, chemical potential and concentration are obtained and illustrated graphically.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Biot M.: Thermoelasticity and irreversible thermodynamics. J. Appl. Phys. 27, 249–253 (1956)
Lord H., Shulman Y.: A generalized dynamical theory of thermo-elasticity. J. Mech. Phys. Solids 15, 299–309 (1967)
Hetnarski R.B., Ignaczak J.: Generalized thermoelasticity. J. Therm. Stress. 22, 451–476 (1999)
Nowacki W.: Dynamical problems of thermodiffusion in solids I. Bull. Acad. Pol. Sci. Ser. Sci. Technol. 22, 55–64 (1974)
Nowacki W.: Dynamical problems of thermodiffusion in solids II. Bull. Acad. Pol. Sci. Ser. Sci. Technol. 22, 129–135 (1974)
Nowacki W.: Dynamical problems of thermodiffusion in solids III. Bull. Acad. Pol. Sci. Ser. Sci. Technol. 22, 257–266 (1974)
Nowacki W.: Dynamical problems of thermo diffusion in elastic solids. Proc. Vib. Probl. 15, 105–128 (1974)
Olesiak Z.S., Pyryev Y.A.: A coupled quasi-stationary problem of thermo-diffusion for an elastic cylinder. Int. J. Eng. Sci. 33, 773–780 (1995)
Sherief H.H., Hamza F.A., Saleh H.A.: The theory of generalized thermoelastic diffusion. Int. J. Eng. Sci. 42, 591–608 (2004)
Sherief H.H., Saleh H.A.: A half space problem in the theory of generalized thermoelastic diffusion. Int. J. Solid Struct. 42, 4484–4493 (2005)
El-Maghraby N.M.: A two-dimensional generalized thermoelasticity problem for a half-space under the action of a body force. J. Therm. Stress. 31, 557–568 (2008)
Aouadi M.: Generalized theory of thermoelastic diffusion for an anisotropic media. J. Therm. Stress. 31, 270–285 (2008)
Sharma N., Ram P., Kumar R.: Plane strain deformation in generalized thermoelastic diffusion. Int. J. Thermophys. 29, 1503–1522 (2008)
Kumar R., Kansal T.: Propagation of Lamb waves in transversely isotropic thermoelastic diffusive plate. Int. J. Solids Struct. 45, 5890–5913 (2008)
Kumar R., Kothari S., Mukhopadhyay S.: Some theorems on generalized thermoelastic diffusion. Acta Mech. 217, 287–296 (2011)
Elhagary M.: Generalized thermoelastic diffusion problem for an infinitely long hollow cylinder for short times. Acta Mech. 218, 205–215 (2011)
Kothari S., Mukhopadhyay S.: On the representations of solutions in the theory of generalized thermoelastic diffusion. Math. Solids 17, 120–130 (2011)
Elhagary M.: A two-dimensional generalized thermoelastic diffusion problem for a half-space subjected to harmonically varying heating. Acta Mech. 224, 4711–4722 (2013)
El-Sayed, A.M.: A two-dimensional generalized thermoelastic diffusion problem for a half-space. Math. Mech. Solids (2014). doi:10.1177/1081286514549877
Gaver D.P.: Observing Stochastic processes and approximate transform inversion. Op. Res. 14, 444–459 (1996)
Stehfast H.: Algorithm 368, Numerical inversion of Laplace transforms. Comm. Ass’n. Comp. Mach. 13, 47–49 (1970)
Stehfast H.: Remark on algorithm 368, Numerical inversion of Laplace transforms. Comm. Ass’n. Comp. 3, 624 (1970)
Knight J.H., Raiche A.D.: Transient electromagnetic calculations using Gaver–Stehfast inverse Laplace transform method. Geophysics 47, 47–50 (1982)
Villinger H.: Solving cylindrical geothermal problems using the Gaver–Stehfast inverse Laplace transform. Geophysics 50, 1581–1587 (1985)
Kuznetsov A.: On the convergence of the Gaver–Stehfast Algorithm. SIAM J. Numer. Anal. 51, 2984–2998 (2013)
Press, W.H., Flannery, B.P., Teukolsky, S.A., Vetterling, W.A.: Numerical Recipes, Cambridge University Press, Cambridge (1986)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Tripathi, J.J., Kedar, G.D. & Deshmukh, K.C. Two-dimensional generalized thermoelastic diffusion in a half-space under axisymmetric distributions. Acta Mech 226, 3263–3274 (2015). https://doi.org/10.1007/s00707-015-1383-6
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00707-015-1383-6