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4 International Journal of Applied Mechanics and Engineering

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Eigenvalue approach to two dimensional problem of generalized thermoelasticity for a half - space with body-force

Lahiri A., Das B.

International Journal of Applied Mechanics and Engineering

2012

Vol. 17, no. 2

419-437

The theory of generalized thermoelasticity is applied to a two-dimensional problem for a half-space under the action of body forces. The surface is stress free with thermal shock. Double integral transforms (Laplace transform for time variable and Fourier transform for space variable) are used and the resulting equations are written in the form of a vector-matrix differential equation. The solution of the vector-matrix differential equation in the transformed domain are obtained by eigenvalue approach. The inversion of the Laplace transform is carried out numerically by the Bellman method and computations are done by Mathematica software. Finally, numerical computations of the temperature distribution, displacement and stress components are made and represented graphically.

Response due to mechanical and thermal sources in micropolar generalized thermoelastic medium

Singh R., Singh K., Kumar V.

International Journal of Applied Mechanics and Engineering

2011

Vol. 16, no 1

107-128

The eigen value approach, following the Laplace and Fourier transformation, is employed to find the general solution of the field equation in a micropolar generalized thermoelastic medium for a plane strain problem. An application of an infinite space with an impulsive mechanical source and thermal source is taken to illustrate the utility of the approach. The integral transformation is inverted by using a numerical inversion technique to get a result in the physical domain. The result in the form of normal displacement, normal force stress, tangential force stress, tangential couple stress and temperature field components is obtained numerically and illustrated graphically. A special case of a thermoelastic solid also deduced.

Elastodynamic response of various sources in micropolar thermodiffusive elastic medium

Kumar R., Kaushal S., Miglani A.

International Journal of Applied Mechanics and Engineering

2010

Vol. 15, no 1

63-98

A general solution to the field equations of a micropolar thermodiffusive elastic solid are obtained in the transformed form, using the Laplace and Fourier transform techniques. The deformation due to various sources has been investigated. As an application, concentrated and distributed sources are taken to show the utility of the approach. The transformed solutions are inverted using a numerical inversion technique to invert the Laplace and Fourier transforms. The components of stress, temperature distribution and chemical potential distribution are obtained numerically and discussed graphically to depict the effects of micropolarity and diffusion.

Eigenvalue approach to study the effect of rotation in three dimensional problem of generalized thermoelasticity

Lahiri A., Das B., Datta B.

International Journal of Applied Mechanics and Engineering

2010

Vol. 15, no 1

99-120

This paper deals with the thermoelastic interactions due to heat source in a homogeneous isotropic and unbounded rotating elastic medium in the context of generalized thermoelasticity. Integral transform techniques are adopted, namely: the Laplace transform for the time variable and the exponential Fourier transform for two of the space variables to the basic equations of the generalized thermoelasticity and finally the resulting equations are written in the form of a vector-matrix differential equation which is then solved by the eigenvalue approach. Exact expressions for the temperature distribution, thermal stresses and displacement components are obtained in the Laplace-double Fourier transform domain. A numerical approach is implemented for the inversion of the Laplace transform and double Fourier transforms in order to obtain the solution in physical domain. Finally, numerical computations of the stresses and temperature have been made and presented graphically.