State-space approach of two-temperature generalized thermoelasticity of one-dimensional problem

In this paper, we will consider a half-space filled with an elastic material, which has constant elastic parameters. The governing equations are taken in the context of the two-temperature generalized thermoelasticity theory [Youssef, H., 2005a. The dependence of the modulus of elasticity and the thermal conductivity on the reference temperature in generalized thermoelasticity for an infinite material with a spherical cavity, J. Appl. Math. Mech., 26(4), 4827; Youssef, H., 2005b. Theory of two-temperature generalized thermoelasticity, IMA J. Appl. Math., 1–8]. The medium is assumed initially quiescent. Laplace transform and state space techniques are used to obtain the general solution for any set of boundary conditions. The general solution obtained is applied to a specific problem of a half-space subjected to thermal shock and traction free. The inverse Laplace transforms are computed numerically using a method based on Fourier expansion techniques. Some comparisons have been shown in figures to estimate the effect of the two-temperature parameter.     

Comparative asymptotic analysis of coupled and uncoupled thermoelasticity

The asymptotic solution of the three-dimensional dynamic of coupled thermoelasticity problem (with the mutual influence of the strain and temperature fields taken into account) for an isotropic rectangular plate is used to perform a comparative analysis of the results obtained according to this theory and the theory of temperature stresses. The parameters whose values affect the applicability of these theories and of the applied theory used to solve quasistatic problems of thermoelasticity are obtained.     

Uniqueness in linear coupled thermoelasticity

It is shown that the boundary-initial-value problem of linear coupled thermoelasticity has at most one regular solution on unbounded domains in a very large function class.     

On surface waves in generalized thermoelasticity

Knowles' representation theorem for harmonically time-dependent free surface waves on a homogeneous, isotropic elastic half-space is extended to include harmonically time-dependent free processes for thermoelastic surface waves in generalized thermoelasticity of Lord and Shulman and of Green and Lindsay.r , , r , , .This work was done when author was unemployed.     

A reciprocal theorem in generalized thermoelasticity

A reciprocal theorem for initial mixed boundary value problems is obtained in the context of the linearized anisotropic thermoelasticity theory of Green and Lindsay.     

On formation of singularities in one-dimensional nonlinear thermoelasticity

Dedicated to Bernard D. Coleman on the occasion of his 60^th birthday     

A generalized variational principle in micromorphic thermoelasticity

Recently Nappa obtains a Gurtin-type variational principle for micromorphic thermoelasticity. However, the use of convolutions is of course restricted to the linear case, which sets a limit to the rang of applicability. This paper establishes a classic variational principles for the discussed problem by the semi-inverse method.     

Global smooth solutions and asymptotic stability in one-dimensional nonlinear thermoelasticity

The global existence of smooth solutions to the equations of nonlinear thermoelasticity is shown for a one-dimensional homogeneous reference configuration. Dirichlet boundary conditions are studied and the asymptotic behaviour of the solutions as t is described.Dedicated to Professor Rolf Leis and to Proffessor Mutsuhide Matsumura on the occasion of their sixtieth birthdays in 1991     

The method of subregions in coupled thermoelasticity

Summary There are at present only a few exact solutions of rather simple problems in coupled thermoelasticity. For many problems important from a practical point of view no exact solutions are known. The present paper deals with a convenient method of approximate solutions of these problems. As guideline in the use of this method for the solutions of quasistatic, thermoelastic-coupled problems a numerical example is presented, where the effect of coupling is demonstrated.

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Übersicht Bisher sind nur wenige und relativ einfache thermoelastische Probleme unter Berücksichtigung der Verkopplung von Wärmeleitungsgleichung und der Gleichung für die elastischen Verschiebungen gelöst worden. Viele praktisch interessierende Probleme konnten noch nicht exakt gelöst werden. Zu ihrer näherungsweisen Lösung wird hier ein geeignetes und einfaches Verfahren angegeben. An einem numerisch ausgerechneten Beispiel wird der Einfluß der Verkopplung der beiden Ausgangsgleichungen untersucht.

     

Propagation of discontinuities in electromagneto generalized thermoelasticity in cylindrical regions

In this work we study wave propagation for a problem of an infinitely long solid conducting circular cylinder whose lateral surface is traction free and subjected to known surrounding temperatures in the presence of a uniform magnetic field in the direction of the axis. The problem is in the context of generalized magneto-thermo-elasticity theory with one relaxation time. Laplace transform techniques are used to derive the solution in the Laplace transform domain. The inversion process is carried out using a numerical method based on Fourier series expansions. Wave propagation in the elastic medium and in the free space, bounding it, is investigated.     

Explicit finite-difference procedures for elastodynamic analysis of layered media

Summary Explicit finite-difference procedures are proposed to simulate the elastodynamic response of layered media. To avoid large numerical dispersion and dissipation, different grid sizes are used for different material layers so that the CFL number in each layer can be set to one in the limit. The master-slave technique is applied to deal with the mismatch of grids along the material interface. The interface can be either bonded or unbonded. The dynamic contact between two layers along an unbonded interface is also considered. Numerical examples are presented. Received 4 August 1997; accepted for publication 24 April 1998