Thermoelastic Problem for An Infinitely Long Annular Cylinder Without Energy Dissipation (GN Theory)

infinitely long annular cylinder without energy dissipation

  • Shaaban Khader Department of Mathematical and Theoretical Physics Atomic Energy Authority, EGYPT
Keywords: annular cylinder, thermoelasticity without energy dissipation, Laplace transforms


In this paper we consider the problem of an infinitely long annular cylinder whose inner and outer surfaces are subjected to known surrounding temperatures and are traction free. The problem is in the context of the theory of thermoelasticity without energy dissipation. The Laplace transform with respect to time is used. The inversion process is carried out using a numerical method based on a Fourier series expansion. Numerical results are computed for the temperature, displacement and stress distributions. The numerical results are represented graphically. Comparison is made between the predictions here and those of the theory of thermoelasticity with one relaxation time.


H. Lord and Y. Shulman, A Generalized Dynamical Theory of Thermo- elasticity,

J.Mech. Phys. Solid. 15 (1967) 299 309.

Green, A. E., Lindsay, K. A.: Thermoelasticity. J. Elasticity 2 (1972) 1-7.

H. Sherief, N. M. El-Maghraby, An Internal Penny-Shaped Crack in an Infinite Thermoelastic Solid, J. Thermal Stresses. 26 (2003) 333-352.

H. Sherief, F. Hamza, Generalized Two-Dimensional Thermoelastic Problems in Spherical Regions Under Axisymmetric Distributions, J. Thermal Stresses. 19 (1996) 55-76.

H. Sherief, M. Anwar, A Problem in Generalized Thermoelasticity for an Infinitely Long Annular Cylinder Composed of Two Different Materials, Acta Mechanica. 80 (1989) 137-149.

M. Anwar, H. Sherief, Boundary Integral Equation formulation for Generalized Thermoelasticity in a Laplace Transform Domain, Appl. Math. Model.12 (1988) 161-166.

H. Sherief, M. A. Ezzat, Solution of the Generalized Problem of Thermoelasticity in the form of Series of Functions, J. Thermal Stresses. 17 (1994) 75-95.

H. Sherief, Problem in Electromagneto Thermoelasticity for an Infinitely Long Solid Conducting Circular Cylinder with Thermal Relaxation, Int. J. Eng. Sci. 32 (1994) 435-452.

A. E. Green, P. M. Naghdi, Thermoelasticity without energy dissipation, J. Elasticity. 31(1993)189–208.

D. Iesan, on the theory of thermoelasticity without energy dissipation, J. Thermal Stresses. 21(1998) 295–307.

R. Quintanilla, on existence in thermoelasticity without energy dissipation, J. Thermal Stresses. 25(2002) 195–202.

K.L. Verma, N. Hasebe, Dispersion of thermoelastic waves in a plate with and without energy dissipation. International Journal of Thermophysics. 22(2001) 957-978.

R. Quintanilla, On the spatial behavior in thermoelasticity without energy dissipation, J. Thermal Stresses. 22(1999) 213–224.

K. L. Verma, Generalized Thermoelastic Vibrations in Heat Conducting Plates without Energy Dissipation, Tamkang Journal of Science and Engineering. 10(2007) 1-9.

Hamdy M. Youssef, Variational Principle of Two-Temperature Thermoelasticity without Energy Dissipation, Journal of Thermoelasticity. 1(2013) 42-44.

R. V. Churchill, Operational Mathematics, Third edition, McGraw-Hill Book Company, New York, 1972.

G. Honig and U. Hirdes, A Method For The Numerical Inversion of the Laplace Transform, J. Comp. Appl. Math. 10 (1984) 113-132.

Research Articles