Hany H. Sherief

FUNDAMENTAL SOLUTION OF THE GENERALIZED THERMOELASTIC PROBLEM FOR SHORT TIMES

Abstract The solution of the problem of determining stress and temperature distributions with a continuous source of heat in an infinite elastic body governed by the equations of generalized thermoelasticity are obtained by using the Laplace transform technique. Inverse transforms are obtained in an approximate manner for small values of time. Numerical computations for some particular cases are carried out and the results are compared with the corresponding solutions of the coupled case and the uncoupled classical case.

STATE SPACE APPROACH TO GENERALIZED THERMOELASTICITY

The state space approach developed in [1–4] for the solution of coupled thermo-elastic problems is adopted for the solution of one-dimensional problems in generalized thermoelasticity with one relaxation time. The technique is applied to a thermal shock half-space problem and to a problem pertaining to a layered medium. Some numerical results are given.

STATE SPACE FORMULATION FOR GENERALIZED THERMOELASTICITY WITH ONE RELAXATION TIME INCLUDING HEAT SOURCES

The equations of generalized thermoelasticity with one relaxation time for one-dimensional problems including heat sources are cast into matrix form using the state space and Laplace transform techniques. The resulting formulation is applied to a problem for the whole space with a plane distribution of heat sources. It is also applied to a semispace problem with a traction-free surface and plane distribution of heat sources located inside the medium. The inversion of the Laplace transforms is carried out using a numerical approach. Numerical results for the temperature, displacement, and stress distributions are given and illustrated graphically for both problems.

A thermal-shock problem in magneto-thermoelasticity with thermal relaxation

Abstract The one-dimensional problem of distribution of thermal stresses and temperature is considered in a generalized thermoelastic electrically conducting half-space permeated by a primary uniform magnetic field when the bounding plane is suddenly heated to a constant temperature. The Laplace transform technique is used to solve the problem. Inverse transforms are obtained in an approximate manner using asymptotic expansions valid for small values of time. Nurnerical computations for two particular cases are carried out.

A two-dimensional problem for a half-space in magneto-thermoelasticity with thermal relaxation

In this work we study a two-dimensional problem in electromagneto-thermoelasticity for a half-space whose surface is subjected to a non-uniform thermal shock and is stress free in the presence of a transverse magnetic field. The problem is in the context of the theory of generalized thermoelasticity with one relaxation time. Laplace and exponential Fourier transform techniques are used to obtain the solution by a direct approach. The solution of the problem in the physical domain is obtained by using a numerical method for the inversion of the Laplace transforms based on Fourier series expansions. The distributions of the temperature, the displacement, the stress and the induced magnetic and electric fields are obtained. The numerical values of these functions are represented graphically.

GENERALIZED THERMOELASTIC PROBLEM OF A THICK PLATE UNDER AXISYMMETRIC TEMPERATURE DISTRIBUTION

The two-dimensional problem of a thick plate whose lower and upper surfaces are traction free and subjected to a given axisymmetric temperature distribution is considered within the context of the theory of generalized thermoelasticity with one relaxation time. Potential functions together with Laplace and Hankel transform techniques are used to derive the solution in the transformed domain. The Hankel transforms are inverted analytically. The inversion of the Laplace transforms are carried out using the inversion formula of the transform together with Fourier expansion techniques. Numerical methods are used to accelerate the convergence of the resulting series and to evaluate the improper integrals involved to obtain the temperature and stress distributions in the physical domain. Analysis of wave propagation in the medium is presented. Numerical results are represented graphically and discussed. A comparison is made with the solution of the corresponding coupled problem.

PROBLEM IN GENERALIZED THERMOELASTICITY

Abstract The distributions of thermal stresses and temperature for a problem in generalized thermoelasticity have been obtained for an infinite elastic space under the influence of a continuous line source of heat located along the z axis. The solution of the problem is obtained by applying the Hankel and Laplace integral transforms successively. Numerical results for a particular case are given.

An internal penny-shaped crack in an infinite thermoelastic solid

In this work, we solve a dynamical problem for an infinite thermoelastic solid with an internal penny-shaped crack, which is subjected to prescribed temperature and stress distributions. The problem is solved using the Laplace and Hankel transforms. The boundary conditions of the problem give a set of four dual integral equations. The operators of fractional calculus are used to transform the dual integral equations into a Fredholm integral equation of the second kind, which is solved numerically. The inverse Hankel and Laplace transforms are obtained using a numerical technique. Numerical results for the temperature, stress, and displacement distributions, as well as for the stress intensity factor, are shown graphically.

THEORY OF GENERALIZED MICROPOLAR THERMOELASTICITY AND AN AXISYMMETRIC HALF-SPACE PROBLEM

ABSTRACT The general equations of motion and constitutive equations are derived for a general homogeneous anisotropic medium with a microstructure, taking into account the effects of heat and allowing for second sound effects. A uniqueness theorem is also derived. As an illustration of the obtained equations, we solve a problem for a half-space whose boundary is rigidly fixed and subjected to an axisymmetric thermal shock. There are no body forces, body couples, or heat sources affecting the medium. Laplace and Hankel transform techniques are used. Numerical results are obtained and graphically illustrated.

GENERALIZED TWO-DIMENSIONAL THERMOELASTIC PROBLEMS IN SPHERICAL REGIONS UNDER AXISYMMETRIC DISTRIBUTIONS

Two-dimensional thermoelastic problems under axisymmetric temperature distributions are considered within the context of the theory of generalized thermoelasticity with one relaxation time. The general solution is obtained in the Laplace transform domain by using a direct approach without the customary use of potential functions. The resulting formulation is used to solve two problems of a solid sphere and of an infinite space with a spherical cavity. The surface in each case is taken to be tractionfree and subjected to a given axisymmetric temperature distribution. The inversion of the Laplace transforms are carried out using the inversion formula of the transform together with Fourier expansion techniques. Numerical methods are used to accelerate the convergence of the resulting series to obtain the temperature, displacement, and stress distributions in the physical domain. Numerical results are represented graphically and discussed. A comparison is made with the solution of the corresponding coupled pr...