A variational principle for the dynamic problem of linear coupled thermoelasticity

Summary A functional is constructed by whose stationarity the mixed problem for linear and dynamic thermoelasticity is obtained. In contrast with previous results[2], [4], [8], neither constrained variations nor previous transformations upon the equations of the problem are used. The unrestricted variational formulation is made possible by means of a convolutive bilinear form.

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Sommario Si costruisce un funzionale dalla cui stazionarietà si ricava il problema misto della termoelasticità lineare accoppiata. A differenza di precedenti risultati[2], [4], [8] non si ricorre né a variazioni bloccate né a preliminari trasformazioni del problema. La formulazione variazionale non ristretta è resa possibile dall'uso di una forma bilineare convolutiva.

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Work done in the sphere of activity of the Group for Mathematical Research of the (Italian) C.N.R.     

On the plane problem of orthotropic quasi-static thermoelasticity

The plane displacement boundary value problem of quasi-static linear orthotropic thermoelasticity is discussed. The thermoelastic system on a bounded simply-connected domain is decoupled. The decoupled temperature equation is investigated by using an accurate estimate and the contractive mapping principle. Representation of solution of the field equation is obtained, and some solvability results are proved. The results are of both theoretical and numerical interest.     

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.     

Analysis of dispersion relations of a coupled thermoelasticity problem with regard to heat flux relaxation

Dispersion relations for a coupled thermoelasticity problem including a hyperbolic heat conduction equation are derived, and their asymptotic analysis is performed. Dependences of the wave number and characteristics of the vibration damping rate on frequency are obtained and compared with similar diagrams in the classical model.     

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.