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1

Eigen value approach to generalized thermoelastic interactions in an unbounded body with circular cylindrical cavity without energy dissipation

Chakraborty S.

International Journal of Applied Mechanics and Engineering

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2017

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Vol. 22, no. 4

811--825

EN

The theory of generalized thermoelasticity in the context of the Green-Naghdi model -II (thermoelasticity without energy dissipation) is studied for an infinite circular cylindrical cavity subjected to two different cases of thermoelastic interactions when the radial stress is zero for (a) maintaining constant temperature and (b) temperature is varying exponentially with time. The Laplace transform from time variable is used to the governing equations to formulate a vector matrix differential equation which is then solved by the eigen value approach. Numerical computations for the displacement component, temperature distribution and components of thermal stress have been made and presented graphically.

2

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

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2012

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Vol. 17, no. 2

419-437

EN

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.

3

Eigenvalue approach to study generalized thermoelastic problem for an infinitely long circular cylinder

Lahiri A., Sarkar N.

International Journal of Applied Mechanics and Engineering

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2011

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Vol. 16, no 3

731-745

EN

In this work, a one-dimensional problem for an infinitely long circular cylinder is solved by an eigenvalue approach. The outer surface of this cylinder is traction free and subjected to a thermal shock. The problem is in the context of the theory of generalized thermoelasticity with one relaxation time parameter. The Laplace transform technuiqe is used. The solution in the transformed domain is obtained by a direct eigenvalue approach. The inversion of the Laplace transform solution is evaluated numerically. Numerical results are obtained and represented graphically for two cases and finally compared with the current results available in the literature.

4

Eigenvalue approach to coupled thermoelasticity with temperature dependent modulus of elasticity in an isotropic elastic medium with a cylindrical hole

Lahiri A., Das B.

International Journal of Applied Mechanics and Engineering

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2011

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Vol. 16, no 2

411-423

EN

The fundamental equations of coupled thermoelasticity in an isotropic elastic medium with a cylindrical cavity under the dependence of the modulus of elasticity on the reference temperature have been written in the form of a vector-matrix differential equation and solved by the eigenvalue approach. The normal mode analysis is used to obtain the expressions for stresses and temperature when the lateral surface of the cylinder is kept at ambient temperature. Finally, numerical computations of the stresses and temperature have been made and presented graphically. Comparisons are made with the results obtained in the case of temperature independent modulus of elasticity.

5

Eigenvalue approach to generalized thermoelastic interactions in an unbounded body with circular cylindrical hole without energy dissipation

Lahiri A., Das B.

International Journal of Applied Mechanics and Engineering

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2008

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Vol. 13, no 4

939-953

EN

The fundamental equations of the problems of generalized thermoelasticity based on the Green and Naghdi theory have been written in the form of a vector- matrix differential equation in the Laplace transform domain and solved by the eigenvalue approach. Two problems arising in the study of wave propagation in infinite medium studied in details by examining of the nature of the solution in space time domain for different conditions of the boundary. Finally, numerical computations of the stresses and temperature have been made and presented graphically.

6

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

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2004

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Vol. 9, no 1

147-160

EN

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).