Inverse problem of thermoelasticity for the isotropic medium containing a cavity in the case of triaxial tension with constant temperature on the surface

We consider the inverse problem of thermoelasticity for an isotropic medium containing a cavity of unknown shape and subjected to the action of mechanical and thermal loads. Nonlinear equations are deduced for the geometric parameters of an ellipsoidal equistressed cavity. Similar relations for mechanical loads obtained by the other authors follow from the constructed equations as special cases. The numerical analysis is performed and the relationship between the values of the loads and the parameters of the cavity is investigated. The stresses on the equistressed surface of the cavity are found and the influence of temperature on the relationship between the parameters of loads and the geometric characteristics of the equistressed cavity is analyzed. __________ Translated from Problemy Prochnosti, No. 1, pp. 121–131, January–February, 2007.     

Finite element method of thermal shock problem in a non-homogeneous isotropic hollow cylinder with two relaxation times

A solution of thermal shock problem of generalized thermoelasticity of a non-homogeneous isotropic hollow cylinder using finite element method is developed. Lord–Shulman and Green–Lindsay for the generalized thermoelasticity model are selected for that purpose which reduces to the classical model by appropriate choice of the parameters. The problem has been solved numerically using a finite element method (FEM). Numerical results for the temperature distribution, displacement, radial stress and hoop stress are represented graphically. The results indicate that the effects of nonhomogeneity are very pronounced. The effects of nonhomogeneity is presented with the three theories.     

A unified generalized thermoelasticity solution for the transient thermal shock problem

A unified generalized thermoelasticity solution for the transient thermal shock problem in the context of three different generalized theories of the coupled thermoelasticity, namely: the extended thermoelasticity, the temperature-rate-dependent thermoelasticity and the thermoelasticity without energy dissipation is proposed in this paper. First, a unified form of the governing equations is presented by introducing the unifier parameters. Second, the unified equations are derived for the thermoelastic problem of the isotropic and homogeneous materials subjected to a transient thermal shock. The Laplace transform and inverse transform are used to solve these equations, and the unified analytical solutions in the transform domain and the short-time approximated solutions in the time domain of displacement, temperature and stresses are obtained. Finally, the numerical results for copper material are displayed in graphical forms to compare the characteristic features of the above three generalized theories for dealing with the transient thermal shock problem.     

Application of group theory to the analysis of the equations of stationary heat conduction and static thermoelasticity

Similarity transformations are constructed and used to obtain an exact solution of the axially symmetric boundary-value problem of static thermoelasticity for a half space whose free surface is heated by a continuous point heat source. It is shown that this solution agrees with the solution obtained earlier by the method of thermoelastic potentials. Franko L'viv State University, L'viv. Translated from Fizyko-Khimichna Mekhanika Materialiv, Vol. 35, No. 3, pp. 69–73, May–June, 1999.     

Flash Method for the Remote Sensing of the Thermal Diffusivity and the Absorption Coefficient at the Excitation Wavelength of Thin Film Materials

A novel front-face flash-monitoring algorithm for remote sensing of the thermal diffusivity and the absorption coefficient at the excitation wavelength of thin film materials is presented. The method relies on the surface transient temperature vs. time curve initiated by a short-duration heating pulse that is followed by time intervals during which the temperature response depends sensitively on the absorption coefficient and thermal diffusivity. An analytical solution of the problem has been derived to solve the inverse heat-transfer problem and, by comparison with a numerical experiment, to check the accuracy of the proposed algorithm for obtaining the absorption coefficient at the excitation wavelength and thermal diffusivity. The uncertainty of the proposed method is better than 0.1%. Paper presented at the 17th European Conference on Thermophysical Properties, September 5–8, 2005, Bratislava, Slovak Republic.     

Inverse Problem of Evaluation of the Coefficient of Friction of Layers According to the Data of Measurements of the Surface Displacements

We consider a one-dimensional model of friction contact of two layers of different nature. The lower surface of the first layer is elastically fixed and the second layer is pressed to the upper surface of the first layer and moves along this surface with variable velocity. As a result of friction, heat is produced on the contact surface according to the Amonton's law. For known boundary and initial conditions, we pose the problem of evaluation of the friction coefficient and the intensity of friction heat flux according to given values of the vertical displacements of the upper surface of the second layer. The posed problem is reduced to the inverse contact problem of thermoelasticity described by the Volterra integral equation of the first kind. The solution of the problem obtained by the method of averaging of functional corrections enables us to study the time behavior of the indicated quantities for the entire period of interaction of the bodies and establish the dependence of the friction coefficient on the basic parameters of the process (sliding velocity, contact pressure, and temperature of the contact surface). The solution of the direct contact problem of thermoelasticity is used to perform the numerical verification of the proposed method for the solution of the inverse problem.     

Brittle-fracture criterion and durability of materials under thermomechanical action

Consideration has been give to the thermoelasticity problem for a plane containing a rectilinear crack under the conditions of constant tensile stress and a nonuniform stationary temperature field. The system’s thermodynamic potential from whose stationary condition the criterion of brittle fracture of a material has been established has been computed by solution of the problem indicated. The average durability of the material under thermomechanical action has been evaluated. __________ Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 81, No. 2, pp. 394–400, March–April, 2008.     

Mechanical/Thermal Sources in a Micropolar Thermoelastic Medium Possessing Cubic Symmetry without Energy Dissipation

The present problem is concerned with the study of the deformation of a thermoelastic micropolar solid possessing cubic symmetry under the influence of various sources acting on the plane surface. The analytic expressions of displacement components, microrotation, force stress, couple stress, and temperature distribution are obtained in the physical domain for the Green and Nagdhi (G–N) theory of thermoelasticity by applying the integral transforms. A numerical inversion technique has been applied to obtain the solution in the physical domain. The numerical results are presented graphically for a particular material.     

Fundamental solutions of thermoelasticity equations for a semimoment isotropic medium

The Kupradze matrix of fundamental solution of the system of thermoelasticity equations for a semimoment isotropic medium with account for the relaxation time of thermal perturbations in it has been obtained. __________ Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 80, No. 2, pp. 193–196, March–April, 2007.     

Thermoelastic State of a Half Space Containing a Thermally Active Circular Crack Perpendicular to Its Edge

The problem of stationary thermal conductivity and thermoelasticity is solved by the method of boundary integral equations for a semiinfinite body containing a circular crack perpendicular to its edge provided that temperature (or a heat flow is specified) on the crack surfaces. The boundary of the body is unloaded and either is thermally insulated or its temperature is equal to zero. We study the influence of the depth of location of the circular crack on the stress intensity factor for a constant temperature (or heat flow) specified on the crack surfaces. Under thermal loading (unlike the case of constant force loading), the stress intensity factors attain their maximum values on the side of the half space opposite to its boundary. __________ Translated from Fizyko-Khimichna Mekhanika Materialiv, Vol. 41, No. 2, pp. 16–22, March–April, 2005.     

Convective cooling in contact problems of thermoelasticity with frictional heat generation

Contact problems with frictional heat generation are, as a rule, studied under idealized conditions of perfect thermal insulation of the surfaces of bodies outside the region of contact. We solve an axially symmetric contact problem of stationary thermoelasticity for semibounded bodies of revolution by taking into account the effect of convective cooling of the free surfaces. The problem is reduced to a system of Fredholm integral equations. An approximate solution of these equations is obtained in terms of simple analytic relations. We determine the conditions under which the influence of convective heat exchange on the level and distribution of contact stresses can be neglected. Franko L'viv State University. Translated from Fizyko-Khimichna Mekhanika Materialiv, Vol. 33, No. 6, pp. 75–80, November–December, 1997.     

A Generalized Thermoelasticity Problem for a Half-Space with Heat Sources and Body Forces

In this work, a two-dimensional problem of distribution of thermal stresses and temperature in a linear theory of a generalized thermoelastic half-space under the action of a body force and subjected to a thermal shock on the bounding plane is considered. Heat sources permeate the medium. The problem is in the context of the theory of generalized thermoelasticity with one relaxation time. Laplace and exponential Fourier transform techniques are used. The solution in the transformed domain is obtained by a direct approach. The inverse double transform is evaluated numerically. Numerical results are obtained and represented graphically.     

Thermal field on the surface of a material heated by a laser pulse in a narrow ring of illumination

Based on a solution of the problem of the temperature effect of instantaneous heat sources uniformly distributed in a thin plane ring on the boundary of a semünfinite body and different approximations of that solution, we constructed a dynamic model of a thermal field on the surface of a material heated by a laser pulse in a narrow ring of illumination. Scientific Center for Opticophysical Investigations Moscow. Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 69, No. 1, pp. 55–64, January–February, 1996.     

Generalized Magneto-thermoelasticity in a Fiber-Reinforced Anisotropic Half-Space

The propagation of plane waves in a fiber-reinforced, anisotropic thermoelastic half-space proposed by Lord–Shulman under the effect of a magnetic field is discussed. The problem has been solved numerically using a finite element method. Numerical results for the temperature distribution, the displacement components, and the thermal stress are given and illustrated graphically. Comparisons are made with the results predicted by the theory of generalized thermoelasticity with one relaxation time for different values of time. It is found that the reinforcement has a great effect on the distribution of field quantities.     

Temperature field in the process of braking of a massive body with composite coating

We obtain the analytic solution of a nonstationary problem of heat conduction for a piecewise homogeneous body formed by a half space and a composite layer applied to its surface. The surface of the layer is heated by a heat flow whose intensity is equal to the specific power of friction in the process of braking. The dependences of the distributions of temperature on the geometric parameters and thermal properties of the composite material and the substrate are investigated. __________ Translated from Fizyko-Khimichna Mekhanika Materialiv, Vol. 43, No. 1, pp. 61–67, January–February, 2007.     

Two-Temperature Generalized Thermoelastic Interactions in an Infinite Body with a Spherical Cavity

This paper is concerned with the determination of the thermoelastic displacement, stress, conductive temperature, and thermodynamic temperature in an infinite isotropic elastic body with a spherical cavity in the context of the two-temperature generalized thermoelasticity theory (2TT). The two-temperature Lord-Shulman (2TLS) model and two-temperature Green–Naghdi (2TGN) models of thermoelasticity are combined into a unified formulation introducing the unified parameters. The medium is assumed initially quiescent. The basic equations have been written in the form of a vector-matrix differential equation in the Laplace transform domain which is then solved by (a) the state-space approach and (b) the eigenvalue approach for any set of boundary conditions. The general solution obtained is applied to a specific problem when the boundary of the cavity is subjected to thermomechanical loading. The numerical inversion of the transform is carried out using Fourier-series expansion techniques. The computed results for thermoelastic stresses, conductive temperature, and thermodynamic temperature are shown graphically for the Lord Shulman model and for two models of Green–Naghdi and the effects of two temperatures are discussed. A comparative study of the two methods has also been carried out.     

Friction-induced formation of heat with account for heat transfer through the contact surface between homogeneous and piecewise-homogeneous semispaces

An analytical solution of the boundary-value heat conduction problem is obtained for a tribosystem consisting of a homogeneous semispace sliding with a constant velocity along the surface of a plane-parallel strip applied to a semi-infinite foundation. The tribosystem is heated as a result of the frictional heat formation on the sliding surface. It is assumed that the thermal contact of the semispace with the strip is not full. With the aid of the Duhamel theorem, a solution for the considered tribosystem, with sliding at a constant deceleration, is also constructed that models heat formation from friction in disk brakes. For the materials of the friction pair "pig iron semispace (disk)–metal-ceramic strip (lining)–steel foundation (frame)," the influence of the coefficient of thermal conductivity of the contact (Biot number) on the temperature distribution was investigated.     

Magneto-thermoelastic Response in a Functionally Graded Isotropic Unbounded Medium Under a Periodically Varying Heat Source

This paper deals with the problem of magneto-thermoelastic interactions in a functionally graded isotropic unbounded medium due to the presence of periodically varying heat sources in the context of linear theory of generalized thermoelasticity with energy dissipation (TEWED) and without energy dissipation (TEWOED) having a finite conductivity. The governing equations of generalized thermoelasticity (GN model) for a functionally graded material (FGM) under the influence of a magnetic field are established. The Laplace–Fourier double transform technique has been used to get the solution. The inversion of the Fourier transform has been done by using residual calculus, where poles of the integrand are obtained numerically in a complex domain by using Leguerre’s method and the inversion of the Laplace transformation is done numerically using a method based on a Fourier series expansion technique. Numerical estimates of the displacement, temperature, stress, and strain are obtained for a hypothetical material. The solution to the analogous problem for homogeneous isotropic materials is obtained by taking a suitable non-homogeneous parameter. Finally, the results obtained are presented graphically to show the effect of a non-homogeneous, magnetic field and damping coefficient on displacement, temperature, stress, and strain.     

Account for heat transfer between elements of a plane parallel strip–foundation friction unit

An analytical solution of the boundary-value heat conduction problem for a tribosystem consisting of a semiinfinite foundation and a plane-parallel strip sliding at a constant velocity along the foundation surface is obtained. The thermal contact between the strip and the foundation is partial. The asymptotics of the solution for low and high values of time have been found. For the materials of the friction pair “metal ceramics strip–pig iron foundation” the influence of the coefficient of thermal conductivity of the contact on temperature distribution was studied.