OPTIMIZATION PROBLEMS FOR A THERMOELASTIC FRICTIONAL CONTACT PROBLEM

In the present paper, we analyze and study the control of a static thermoelastic contact problem. We consider a model which describes a frictional contact problem between a thermoelastic body and a deformable heat conductor obstacle. We derive a variational formulation of the model which is in the form of a coupled system of the quasi-variational inequality of elliptic type for the displacement and the nonlinear variational equation for the temperature. Then, under a smallness assumption, we prove the existence of a unique weak solution to the problem. Moreover, we establish the dependence of the solution with respect to the data and prove a convergence result. Finally, we introduce an optimization problem related to the contact model for which we prove the existence of a minimizer and provide a convergence result.

Stress–temperature equations of motion of Ignaczak and Beltrami–Michell types in arbitrary curve coordinate system: معادلات الحركة بلغة الإجهادات والحرارة من نوعي إغناتشاك وبيلترامي– ميشيل في أي نظام احداثي منحني

This paper relates to the mathematical linear model of the elastic, homogeneous and isotropic body, with neglected structure and infinitesimal elastic strains, subjected to temperature field; discussed by Hooke, and shortly called (H). We firstly introduce the variable tensorial forms of the traditional and Lame descriptions of the coupled dynamic state of considerable Hooke body, in an arbitrary curve coordinate system. We study the variable tensorial forms in an arbitrary curve coordinate system, of the generalized Beltrami–Michell stress-temperature equations, and of the stress-temperature Ignaczak equations and its completeness problem for the (H) thermoelastic body.

Some Results in Green–Lindsay Thermoelasticity of Bodies with Dipolar Structure

The main concern of this study is an extension of some results, proposed by Green and Lindsay in the classical theory of elasticity, in order to cover the theory of thermoelasticity for dipolar bodies. For dynamical mixed problem we prove a reciprocal theorem, in the general case of an anisotropic thermoelastic body. Furthermore, in this general context we have proven a result regarding the uniqueness of the solution of the mixed problem in the dynamical case. We must emphasize that these fundamental results are obtained under conditions that are not very restrictive.

The Generalized Thermodynamical Beltrami – Michell Tensorial Equations for the general Thermodynamical State of the Hooke Body: معادلات بيلترامي- ميشيل التنسورية الترموديناميكية المعممة لأجل الحالة الترموديناميكية العامة لجسم هوك

This paper concerns the mathematical linear model of the elastic, homogeneous and isotropic body, with no considerable structure and with infinitesimal elastic strains, subjected to Thermal effects, in the frame of coupled thermoelectrodynamics; discussed firstly by Hooke (in the isothermal case), and shortly called (H). In this paper, firstly we introduce the invariable tensorial traditional and Lame descriptions of the coupled dynamic, thermoelastic, homogeneous and isotropic Hooke body, which initial configuration forms a simply-connected region in the three dimensional euclidean manifold. The news of this paper consists in deriving the invariable tensorial, generalized Beltrami – Michell stress-temperature equations for the (H) thermoelastic body (in the more general case than the thermal stress state), which initial configuration forms a simply-connected region in the three dimensional euclidean manifold. Finally, we end the paper by suggesting the problem for discussing, in addition to another open problem.

On the Partition of Energies for the Backward in Time Problem of Thermoelastic Materials with a Dipolar Structure

We first formulate the mixed backward in time problem in the context of thermoelasticity for dipolar materials. To prove the consistency of this mixed problem, our first main result is regarding the uniqueness of the solution for this problem. This is obtained based on some auxiliary results, namely, four integral identities. The second main result is regarding the temporal behavior of our thermoelastic body with a dipolar structure. This behavior is studied by means of some relations on a partition of various parts of the energy associated to the solution of the problem.