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2 International Journal of Applied Mechanics and Engineering

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Eigenvalue approach to generalized thermoelastic interactions in an unbounded body with spherical cavity

Lahiri A., Kar T. K.

International Journal of Applied Mechanics and Engineering

2007

Vol. 12, no 4

1027-1037

Exact expressions for the temperature distribution stress and displacement component are obtained in the Laplace transform domain in the case of an infinite medium with a spherical cavity by using the eigenvalue approach in the context of the theory of thermoelasticity with two relaxation time parameters. The surface of the spherical cavity is stress free and suddenly subjected to a thermal shock. A numerical approach is implemented for the inversion of the Laplace transform in order to obtain the solution in a physical domain. Finally numerical computations of the stress and temperature have been made and represented graphically.

Eigenvalue approach to gerneralized thermoelasticity in an isotropic medium with an instantaneous heat source

Kar T. K., Lahiri A.

International Journal of Applied Mechanics and Engineering

2004

Vol. 9, no 1

147-160

The fundamental equations of plane strain problems in generalised thermoelasticity with one relaxation time parameter including the heat source have been written in the form of a vector matrix differential equation. Integral transform techniques are adopted, namely: the Laplace transform for the time variable and the exponential Fourier transform for one of the space variables. Exact expressions for the temperature distribution, thermal stresses and displacement components are obtained in the Laplace-Fourier transform domain. A numerical approach is implemented for the inversion of both transforms in order to obtain the solution in physical domain. Finally, numerical computations of the stresses and temperature have been made and represented graphically (for different values of time t and relaxation time parameter t as shown in the figures).