THE DISTURBANCE OF A UNIFORM HEAT FLOW BY TWO LINE CRACKS IN AN INFINITE ANISOTROPIC THERMOELASTIC SOLID

Integral transform techniques are used to determine the stress intensity factors of a pair of colinear line cracks that disturb a uniform heat flow in an anisotropic thermoelastic solid that is under uniaxial tension. A solution is given for the case in which the tension is large enough to ensure that the cracks open fully.     

TWO CRACK GROWTHS IN A FUNCTIONALLY GRADED PLATE UNDER THERMAL SHOCK

This article examines the problem of two thermal cracks under a transient temperature field in a ceramic/metal functionally graded plate. When the functionally graded plate is subjected to thermal shock, multiple cracks often occur on the ceramic surface. It is shown that the crack paths are influenced by interaction between multiple cracks and a compositional profile of the functionally graded plate. Transient thermal stresses are treated as a linear quasi-static thermoelastic problem for a plane strain state. The crack paths of two cracks are obtained using the finite element method with mode I and mode II stress intensity factors.     

THREE-DIMENSIONAL TRANSIENT THERMAL STRESS ANALYSIS OF A NONHOMOGENEOUS HOLLOW CIRCULAR CYLINDER DUE TO A MOVING HEAT SOURCE IN THE AXIAL DIRECTION

In this paper, a theoretical analysis of a three-dimensional transient thermal stress problem is developed for a nonhomogeneous hollow circular cylinder due to a moving heat source in the axial direction from the inner and /or outer surfaces. Assuming that the hollow circular cylinder has nonhomogeneous thermal and mechanical material properties in the radial direction, the heat conduction problem and the associated thermoelastic behaviors for such nonhomogeneous medium are developed by introducing the theory of laminated composites as one of theoretical approximation. The transient heat conduction problem is treated with the help of the methods of Fourier cosine transformation and Laplace transformation, and the associated thermoelastic field is analyzed making use of the thermoelastic displacement potential, Michell's function, and the Boussinesq's function. Some numerical results for the temperature change and the stress distributions are shown in figures, and the effect of relaxing the thermal stress in the nonhomogeneous hollow circular cylinder and the influence of the velocity of a moving heat source are briefly discussed     

THERMOMECHANICAL ANALYSIS OF FUNCTIONALLY GRADED CYLINDERS AND PLATES

The dynamic thermoelastic response of functionally graded cylinders and plates is studied. Thermomechanical coupling is included in the formulation, and a finite element model of the formulation is developed. The heat conduction and the thermoelastic equations are solved for a functionally graded axisymmetric cylinder subjected to thermal loading. In addition, a thermoelastic boundary value problem using the first-order shear deformation plate theory (FSDT) that accounts for the transverse shear strains and the rotations, coupled with a three-dimensional heat conduction equation, is formulated for a functionally graded plate. Both problems are studied by varying the volume fraction of a ceramic and a metal using a power law distribution.     

Thermal Stresses Induced by a Variable Heat Source in a Rectangle and Variable Pressure at Its Boundary by Finite Fourier Transform

This paper deals with the two-dimensional, non-homogeneous boundary value problem for static, isotropic and thermoelastic material occupying an infinitely long cylinder with a rectangular cross-section. The cylinder is surrounded by a given temperature and subjected to variable pressures at its boundaries. We deal with static, uncoupled, linear thermoelasticity. The equations of heat conduction and mechanical problem are considered separately. The technique of the finite Fourier transform is used for the solution. The thermoelastic behavior, due to an internal heat generation within the domain, is discussed. The results for displacement and stresses have been computed from the Airy stress function and are illustrated graphically.     

A Plane Magnetothermoelastic Waves Reflection and Refraction Between Two Solid Media with External Heat Sources and Initial Stress

In this article, an estimation to illustrate the reflection and transmission of thermoelastic waves at the interface of two different thermoelastic solid half-spaces under initial stress, magnetic field, and external heat sources is made. The governing equations are considered for an isotropic and homogeneous generalized thermoelastic model under initial stress, heat sources, magnetic field, and perfect boundary condition. The reflected and transmitted waves amplitudes are obtained for the incidence of SV-waves. Approximate expressions are obtained as a special case from the present problem. The results obtained are computed numerically for the amplitude ratios under initial stresses and are displayed graphically. It appears that the effects of initial stress, magnetic field, and external heat sources are very pronounced on the propagation phenomena. If the magnetic field and heat sources are neglected, the results obtained then lead to the same results obtained by relevant authors.     

TRANSIENT THERMOELASTIC ANALYSIS OF DISK BRAKES IN FRICTIONAL CONTACT

The transient analysis of the thermoelastic contact problem of automotive disk brakes with frictional heat generation is performed using the finite element method. To analyze the thermoelastic phenomenon occurring in disk brakes, the coupled heat conduction and elastic equations are solved with contact problems. In the present work, the fully implicit transient scheme for the thermoelastic analysis is used to improve the accuracy of computations at every time step. The numerical simulation for the thermoelastic behavior of disk brakes is obtained in drag brake condition. The computational results are presented for the distributions of pressure and temperature on each friction surface between the contacting bodies. Also, the thermoelastic instability (TEI) phenomenon (the unstable growth of contact pressure and temperature) is investigated in the present study. The effects of the rotating speed of the disk on thermoelastic behaviors, such as the temperature distribution and contact ratio of the friction surfaces, are investigated.     

Transient Thermal Stresses of a Cross-Ply Laminated Cylindrical Shell Using a Higher-Order Shear Deformation Theory

This paper is concerned with the theoretical treatment of transient thermoelastic problem of a cross-ply laminated cylindrical shell due to axisymmetrical heat supply. We analyze the transient thermoelastic problem of a cross-ply laminated cylindrical shell under a simply supported condition using a higher-order shear deformation theory. Some numerical results for the temperature change, the displacements and the stresses are shown in figures. Furthermore, numerical results from this formulation are compared with those obtained using classical and first-order shear deformation theories.     

Transient Thermoelastic Analysis for a Functionally Graded Hollow Cylinder

This paper is concerned with the theoretical treatment of transient thermoelastic problem involving a functionally graded hollow cylinder due to uniform heat supply. The transient one-dimensional temperature is analyzed by the method of Laplace transformation. The thermal and thermoelastic constants of the hollow cylinder are expressed as power functions of the radial coordinate. We obtain the one-dimensional solution for the temperature change in a transient state, and thermoelastic response of a functionally graded hollow cylinder. Some numerical results for the temperature change, the displacement and the stress distributions are shown. Furthermore, the influence of the nonhomogeneity of the material upon the temperature change, displacement and stresses is investigated.     

An investigation on thermoelastic interactions under an exact heat conduction model with a delay term

The present work is concerned with a very recently proposed heat conduction model: an exact heat conduction model with a single delay term. A generalized thermoelasticity theory was proposed by Roy Choudhuri based on the heat conduction law with three-phase-lag effects for the purpose of considering the delayed response in time due to the microstructural interactions in the heat transport mechanism. However, the model defines an ill-posed problem in Hadamard sense. Quintanilla has recently proposed to reformulate this heat conduction model as an alternative heat conduction theory with a single delay term and subsequently, Leseduarte and Quintanilla investigated the spatial behavior of the solutions for this theory and they extended the results to a thermoelasticity theory by considering the Taylor series approximation of the equation of heat conduction with one delay term. In the present work, we consider the thermoelasticity theory based on this newly proposed heat conduction model and investigate a problem of thermoelastic interactions. State-space approach is used to formulate the problem and the formulation is then applied to a problem of an isotropic elastic half-space with its plane boundary subjected to sudden increase in temperature and zero stress. The integral transform method is applied to obtain the solution of the problem. A detailed analysis of analytical results is provided by finding the short-time approximated solutions of different field variables analytically and comparing the results of the present model with the corresponding results reported for other existing theories. An attempt has also been made to illustrate the problem and numerical values of field variables are obtained for a particular material. Results are analyzed with different graphs. To the best of the author\textquoteright s knowledge, this thermoelastic model is not yet investigated by any researcher in this direction.     

A NOTE ON THE THEORY OF THERMOELASTIC DAMPING

This paper consists of three parts. In the first part, the problem of the conversion of mechanical energy into heat is treated, while in the second a general theory of thermoelastic friction in three-dimensional finite bodies is developed. In the third part, explicit results are obtained for thermoelastic damping in vibrating elastic beams. All investigations are based on the linear theory of thermoelasticity.     

On thermoelastic problem of a thermosensitive functionally graded rectangular plate with instantaneous point heat source

The present article attempts to investigate transient thermoelastic problem of a functionally graded thin rectangular plate with thermosensitive and spatial variable dependent material properties. All the material properties are assumed to be isotropic. Kirchhoff’s variable transformation is used to deal with the nonlinearity of the three dimensional heat conduction equation and that equation is solved by the integral transform method considering an instantaneous point heat source. The thermoelastic behavior of the rectangular plate is studied together with the thermal deflection and thermally induced resultant moments. Numerical computations are carried out for ceramic-metal-based functionally graded material, in which alumina is selected as ceramic and nickel as metal. The results are illustrated graphically.     

THERMAL-STRESS PROBLEMS IN INDUSTRY. 1: ON THERMOELASTIC DISTORTION IN MACHINING METALS

Abstract

This paper is a theoretical analysis of the thermoelastic effect upon accuracy in the machining of metals. The problem is reduced to the unsteady thermoelastic analysis of a solid cylinder heated on the surface axisym-metrically by a moving heat source under an axial restraint. The thermal and elastic distortions of the workpiece are computed, and the error in the shape is plotted.

     

THERMAL SINGULAR STRESSES NEAR A CIRCUMFERENTIAL EDGE CRACK IN A SPHERICAL CAVITY UNDER UNIFORM AXIAL HEAT FLOW

The linear thermoelastic problem of a spherical cavity with a circumferential edge crack is solved. The thermal stresses are caused by a uniform heat flow disturbed by the presence of the crack and the cavity. The surfaces of the crack and the cavity are assumed to be insulated. Integral transform techniques are used to reduce the problem concerning the temperature and thermoelastic fields to that of solving two singular integral equations of the first kind. The integral equations are solved numerically and the variation of the thermal stress intensity factor with the crack depth and the crack opening displacement are shown graphically.     

Solution in Elementary Functions to a BVP of Thermoelasticity: Green's Functions and Green's-Type Integral Formula for Thermal Stresses within a Half-Strip

This article presents new elementary Green's functions for displacements and stresses created by a unit heat source applied in an arbitrary interior point of a half-strip. We also obtain the corresponding new integration formulas of Green's and Poisson's types which directly determine the thermal stresses in the form of integrals of the products of internal distributed heat source, temperature, or heat flux prescribed on boundary and derived thermoelastic influence functions (kernels). All these results are presented in terms of elementary functions in the form of a theorem. Based on this theorem and on derived early by author general Green's type integral formula, we obtain a new solution to one particular boundary value problem of thermoelasticity for half-strip. The graphical presentation of thermal stresses created by a unit point heat source and of thermal stresses for one particular boundary value problem of thermoelasticity for half-strip is also included. The proposed method of constructing thermoelastic Green's functions and integration formulas are applicable not only for a half-strip but also for many other two- and three-dimensional canonical domains of Cartesian system of coordinates.     

THERMOELASTIC PROBLEM OF BONDED ORTHOTROPIC SEMI-INFINITE AND INFINITE STRIPS

The stationary thermoelastic problem for an orthotropic semi-infinite strip bonded to an orthotropic infinite strip is investigated. By using Fourier transforms, the heat conduction problem is reduced to a singular integral equation for the temperature gradient. The associated elasticity problem leads to a system of singular integral equations for strain and stress. Numerical solution of these equations yields temperature, temperature gradient, and stress distributions along the interface, caused by prescribed boundary temperatures.     

AN INFINITE PLATE WITH A FLAW AND SUBJECTED TO UNIFORM HEAT FLOW

The thermoelastic problem of an infinite plate which has a crack or a ribbonlike inclusion and is subjected to remotely uniform heat flow is analyzed under the assumption of linear heat transfer across the flaw. Numerical calculations show that the insulated crack causes an overestimation of the stress singularity, and the insulated inclusion produces an underestimation.     

On the Energy Decay for a Thermoelastic Contact Problem Involving Heat Transfer

A dynamic unilateral contact problem between two thermoelastic beams is considered. Under thermal boundary conditions involving heat transfer, the evolution problem is shown to possess an energy decaying exponentially to zero, as time goes to infinity.     

General decay of solution for a transmission problem in infinite memory-type thermoelasticity with second sound

In this article, we study the initial boundary value problem in one space variable for an elastic–thermoelastic bar with the elastic part being surrounded by two thermoelastic parts in the presence of an infinite memory term, for which the heat conduction in thermoelasticity is described by Cattaneo’s law, removing the physical paradox of infinite propagation speed of signals. The main di?culties in handing this problem are that the system does not have any frictional damping term, and that the dissipative effects of heat conduction induced by Cattaneo’s law are usually weaker than those induced by Fourier’s law. To overcome these di?culties, we shall introduce the second-order energy and two extra functionals. Under appropriate hypothesis on the relaxation function, we establish a general decay result.     

An asymptotic approach to one-dimensional model of nonlinear thermoelasticity at low temperatures and small strains*

A one-dimensional nonlinear homogeneous isotropic thermoelastic model with an elastic heat flow at low temperatures and small strains is analyzed using the method of weakly nonlinear asymptotics. For such a model, both the free energy and the heat flux vector depend not only on the absolute temperature and strain tensor but also on an elastic heat flow that satisfies an evolution equation. The governing equations are reduced to a matrix partial differential equations, and the associated Cauchy problem with a weakly perturbed initial condition is solved. The solution is given in the form of a power series with respect to a small parameter, the coe?cients of which are functions of a slow variable that satisfy a system of nonlinear second-order ordinary differential transport equations. A family of closed-form solutions to the transport equations is obtained. For a particular Cauchy problem in which the initial data are generated by a closed-form solution to the transport equations, the asymptotic solution in the form of a sum of four traveling thermoelastic waves admitting blow-up amplitudes is presented.