The linear theory of thermoelasticity without energy dissipation is employed to study thermoelastic interactions due to a continuous point heat source in a homogeneous and isotropic unbounded solid. ...The Laplace transform method is employed to solve the problem. Exact expressions, in closed form, for the displacement, temperature and stress fields are obtained. Numerical results for a copper-like material are presented.PUBLICATION ABSTRACT
The linear theory of thermoelasticity without energy dissipation is employed to study thermoelastic interactions in a homogeneous and isotropic unbounded body containing a cylindrical cavity. The ...interactions are supposed to be due to a constant step in radial stress or temperature applied to the boundary of the acvity, which is maintained at a constant temperature or zero radial stress (as the case may be). By using the Laplace transform technique, it is found that the interactions consist of two coupled waves both of which propagate with a finite speed but with no attenuation. The discontinuities that occurs at the wavefronts are computed. Numerical results applicable to a copper-like material are presented.PUBLICATION ABSTRACT
In the context of the linear theory of thermoelasticity without energy dissipation for homogeneous and isotropic materials, variational principles of Biot-and Hamilton-types and a reciprocal ...principle of Betti-Rayleigh-type are presented.
The theory of thermoelasticity with thermal relaxation for homogeneous materials is formulated upon the basis of the law of balance of energy and the law of balance of entropy, proposed by Green and ...Naghdi 5. The non-linear theory is formulated first; then the linearized theory is deduced. The uniqueness of solution of a typical initial, mixed boundary value problem is established.
The linear theory of thermoelasticity without energy dissipation is employed to study waves emanating from the boundary of a spherical cavity in a homogeneous and isotropic unbounded thermoelastic ...body. The waves are supposed to be spherically symmetric and caused by a constant step in temperature applied to the stress-free boundary of the cavity. Small-time solutions for the displacement, temperature, and stress fields are obtained by using the Laplace transform technique. It is found that there exist two coupled waves, of which one is predominantly elastic and the other is predominantly thermal, both propagating with finite speeds but with no exponential attenuation. Exact expressions for discontinuities in the field functions that occur at the wavefronts are computed and analysed. The results are compared with those obtained earlier in the contexts of some other models of thermoelasticity.
The theory of thermoelasticity without energy dissipation is employed to study one-dimensional dimturbances in a half-space with rigid plane boundary. The disturbances are supposed to be due to a ...constant step in temperature applied to the boundary. The Laplace transform method is employed to solve the problem. Exact expressions for displacement, temperature and stress fields are obtained. The characteristic features of the underlying theory are analysed by comparing these expressions with their counterparts in other generalized thermoelasticity theories.
The linear theory of thermoelasticity without energy dissipation for homogeneous and isotropic materials is used to study plane waves in a half-space. The waves are supposed to be caused by a ...time-dependent heating of the stressfree boundary, which includes (i) sudden heating to a constant temperature, (ii) smooth heating for all times, (iii) smooth heating followed by sudden cooling, and (iv) smooth heating that becomes constant after a lapse of time, among its particular cases. The Laplace transform method is used to solve the problem. Exact solutions, in closed form, for the displacement, temperature, and stress fields are obtained and analyzed. Numerical results that illustrate the theoretical analysis are presented
Three general, complete solutions of a coupled hyperbolic or hyperbolicparabolic system of two second-order linear partial differential equations are presented. The system includes among its ...particular cases the governing field equations of the conventional as well as generalized thermoelasticity theories. The solutions obtained are analogous to the Lamé, Papkovitch, and Galerkin solutions in classical elasticity. The interrelationships among the solutions are also exhibited. Some solutions obtained in earlier works are deduced as special cases of the unified solutions obtained here.
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