We discuss a version of the mathematical theory of the quantitative description of the mechanical behavior of deformable bodies of different electrical conductivity and susceptibility to magnetization and polarization under the action of an external quasisteady electromagnetic field in both the radio and infrared frequency ranges.In various engineering processes in many areas of_ industry the thermal processing of devices m~de of bothtraditi, ,nal and newmaterials asing electromagnetiefields is receiving ever-wider application. For that reason, to establish reasonable regimes for such processing it is an important current problem to model the interconnection of fields of different physical nature in continuous systems subject to external electromagnetic fields. Certain results in this direction have been obtained for electrically conducting nonferromagnetic nonpolarized bodies in constant fields in the radio frequency range [17,19].In the present paper we study a version of the theory of quantitative description of the interconnection of electromagnetic, temperature, and mechanical fields in electrically conducting bodies that are susceptible to polarization and magnetization under external quasisteady fields of both radio and infrared frequency ranges. In constructing the models we used the properties of the physics of interaction of the field and the substance for such bodies and the methods of the thermomechanics ofpiecewise-homogeneous bodies [1,11, 12,15,18,20].We assume that the displacements and the strains and their velocities are so small that for the bodies being studied in the parameter ranges considered for electromagnetic action (H 0 < 107 A/m, where H o is the characteristic value of the external magnetic field intensity) the linear theory of elasticity is applicable, and that the effect of the motion of the medium on the characteristics of the electromagnetic field can be neglected We choose materials for which the mechanicoelectric and thermoelectric effects are insignificant. Thus we are assuming that the electromagnetic field is an external action on the body, whose effect on the processes of thermal conduction and strain is realized through heat emission and force factors (ponderomotor forces and moments). We state the initial relations for a quantitative description of the parameters of the electromagnetic, thermal, and mechanical processes in two stages [7, 12]. At the first stage we write the equations for the characteristics of the electromagnetic field in quasisteady approximation, and also expressions for the heat emission and force factors in terms of these characteristics. At the second stage we state the problem of thermomechanics for determining the parameters that characterize the thermostressed state.Consider an electrically conducting body subject to the action of an electromagnetic field. The field is created by a system of currents that traverse the exterior region (an inductor having time-modulated power) and are given by the expression j!~ (r, t) = ja(r, t) cos(cot +V 0), div f...

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In this paper, the state-of-the-art investigations of optimization problems with respect to the stress state of technological heating regimes for piecewise-homogeneous glass shell elements have been analysed, which are important for development of different types of production processes during production of elements of modern devices for specific target application, in particular, vacuum and power equipment. The directions of development of this class of problems of optimization and corresponding approaches to their formulation and solving are identified.

We state the initial equations and the boundary conditions for determining the parameters that describe a quasistatic electromagnetic field perturbed by the action of external electric currents in a thin nonferromagnetic shell.Consider a thin electrically conducting shell of constant thickness 2h in a region D in which there is no charge or current. The shell is situated in a dielectric medium Do (which we assume to be approximately a vacuum) and subject to the action of a quasistatic electromagnetic field. The field is generated by a system of quasistatic currents flowing in Do (an inductor of time-varying intensity), given by the expressionwhere r is the radius-vector of the point, w is the cyclic frequency, t is time, r is the initial phase, and jA(r, t) j(t)j~r) is the amplitude, which varies only slightly over the period of an electromagnetic wave, f. = 2pi/w, so that the following condition holds:We pose the problem of determining the parameters that describe the electromagnetic field under such an action in the shell-external medium system. We recall that finding these parameters is the first step in computing the thermoelastic state of electrically conducting shells perturbed by an electromagnetic field [1].We shall start from Maxwell's equations for the external medium (a vacuum) and a solid isotropic nonferromagnetic nonpolarized motionless body with constant (averaged over a temperature interval) material characteristics and neglecting the displacement currents [5]. We write the following system of independent equations with complex current density j. = j(t)Re{j(r)ei~t}, electric field intensities E. = j(t)Re {E(r)ei~t}, E (~ = j(t)Re {E(~ and magnetic field intensities H. = j(~)Re {H(r)e~t}, H(. ~ = j(t)Re//(~ in the region D of the body and Do of the surrounding medium, taking account of relations (1) and (2) Here jg~ = f(r)e ~o is the complex amplitude of the given current density in the surrounding medium; E, H, E (~ and H (~ are the complex amplitudes of the intensities of the electric and magnetic fields in the regions D and D O respectively; ~ = eo~., and # = #0#.~o, and #o are the dielectric permittivity and magnetic permeability of the body and the magnetic permeability of the vacuum; a is the electrical conductivity of the body.Equations (3) must be supplemented by the independent coupling conditions of the characteristics of the electromagnetic field at the interface between the body and the surrounding medium:

We propose a mathematical model for quantitative description of the diffusion process of a gaseous admixture in a solid body (a solid solution) due to electromagnetic radiation in the infrared range. We write out the original relations that describe the diffusion of the admixture in a layer subject to electromagnetic radiation in the heated body.Mass transfer in a multi-component solid body (or a solid solution) may be caused not only by a nonuniform distribution of the concentration of the individual components over the volume, but also by processes of a different physical character, especially electromagnetic, thermal, and mechanical actions. In the continuous models of solid solutions known in the literature the coupling of electromagnetic and diffusion processes is taken into account by adding constituent connections that describe either the coupling between the parameters that characterize the process [17,18] or the thermodynamic fluxes caused by ponderomotor forces (or mass forces equivalent to them) acting on the individual components [1, 13]--the so-called "forced" diffusion. With the first approach it is necessary to determine experimentally the new "electromagnetic/diffusion" characteristics, and with the second it is necessary to determine the forces that act on the individual components of the body, which may differ in their electric or magnetic properties. In the literature the second approach has been applied only to study diffusion in a binary ion solution caused by a stationary electric field [13].The purpose of the present paper is to study diffusion in a semitransparent solid body due to electromagnetic radiation in the infrared range.Our point of departure is the continuous model of a solid solution, in which the balance equation of mechanics and the first and second laws of thermodynamics are written in the context of the single continuum approach for the single continuum of the center of mass of its components. In constructing the constituent connections we apply the assumption of local equilibrium and the methods of nonequilibrium thermodynamics [7,8]. Then by the Euler (field) approach to describing the physical proc~esses being studied in the body the mass-balance law for the k-th component of an n-component solution when there are no chemical reactions in the body has the form [7,8] From nonequilibrium thermodynamics, using the condition of linearity of the constituent connections between the thermodynamic flows and the forces (Onsager's principle) taking account of the connection of the diffusion and thermal processes and the presence of solid forces acting on the body, we obtain the following expression for the total flux of mass of the k-th component [1]: j, = j~r) + j~, + j~/).Here j~r), j~), j/) are the mass fluxes connected with heat transfer (thermodiffusion), the nonuniform distribution of concentrations of the k-th component in the solution, and the action of solid forces on it (the "forced" diffusion), which have the form