PUBLICATIONS ON THERMAL STRESSES

This paper is concerned with the theoretical treatment of transient thermoelastic problem involving a functionally graded hollow cylinder due to asymmetrical heating from its surfaces. The thermal and thermoelastic constants of the hollow cylinder are expressed as power functions of the radial coordinate variable. The exact solution for the two-dimensional temperature change in a transient state, and thermal stresses of a hollow cylinder under the state of plane strain is obtained herein. Some numerical results are shown in figures. Furthermore, the influence of the nonhomogeneity of the material upon the temperature change and stresses is investigated.     

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.     

Transient Piezothermoelastic Analysis for a Functionally Graded Thermopiezoelectric Hollow Cylinder

This paper is concerned with the theoretical treatment of transient piezothermoelastic problem involving a functionally graded thermopiezoelectric hollow cylinder due to uniform heat supply. The transient one-dimensional temperature is analyzed by the method of Laplace transformation. The thermal, thermoelastic and piezoelectric 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 piezothermoelastic response of a functionally graded thermopiezoelectric hollow cylinder. Some numerical results for the temperature change, the displacement, the stress and electric potential distributions are shown. Furthermore, the influence of the nonhomogeneity of the material upon the temperature change, displacement, stresses and electric potential is investigated.     

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     

Thermoelastic interaction in functionally graded thick hollow cylinder with temperature-dependent properties

The prediction of thermoelastic behavior induced by transient thermal shock is important to evaluate the durability of functionally graded materials. The purpose of this article is to study the axisymmetric thermoelastic interaction in a functionally graded thick hollow cylinder by an asymptotic approach. The governing equations with variable material properties, which are spatially graded and temperature dependent, are proposed based on the generalized theory of thermoelasticity with one relaxation time (L–S theory). The Laplace transform technique is used to derive the general solutions with the cylinder divided into thin cylinders and material properties assumed constant in each thin cylinder. The inverse Laplace transform is then conducted analytically by some approximations in the time domain, and the short-time solution of the problem with its interior boundary subjected to a sudden temperature rise and the outer surface maintained at constant temperature are obtained. Utilizing these asymptotic solutions, the propagation of thermal and thermoelastic waves are studied, which display dependence of each wave’s propagation upon the relaxation time, volume fraction parameter and temperature. The distributions of the radial displacement, temperature and stresses are also plotted and discussed. These results reveal effects of these variable material properties with spatial position and temperature on thermoelastic behavior.     

Thermal fracture of cracked cylinders associated with nonclassical heat conduction: The effect of material property

The thermoelastic problem of a transversely isotropic hollow cylinder containing a circumferential crack is investigated in the present article based on the non-Fourier heat conduction theory. The temperature and stress fields are obtained by solving the coupled partial differential equations in the Laplace domain, and corresponding thermal axial stress with minus sign is then applied to the crack surface to form a mode I crack problem. Three different kinds of crack are considered, and the singular integral equation method is adopted to solve the fracture problem. Finally, with the definition of stress intensity factor, the effect of material properties, coupling parameter, and crack geometry on the hyperbolic thermal fracture responses of a transversely isotropic hollow cylinder excited by a thermal loading is visualized.     

THERMOELASTIC POTENTIAL FUNCTIONS IN TRANSVERSELY ISOTROPIC SOLIDS AND THEIR APPLICATIONS

An explicit solution composed of two thermoelastic potential functions is proposed in cylindrical coordinates and is applied to an analysis for steady-state, axially asymmetric thermal stresses in a long hollow cylinder. The solution is obtained with no assumptions of temperature fields. The temperature and stress fields in the long hollow cylinder made of magnesium are analyzed for the sake of application of the solution.     

Influence of thermal stresses on thermal diffusion of hydrogen

Thermal diffusion of hydrogen atoms in zirconium taking into account thermal stresses is investigated. As mathematical model the steady-state temperature in the hollow cylinder is considered. The first invariant of the tensor of thermal stresses in the hollow cylinder has a logarithmic dependence on the radial coordinate. Such dependence permits an exact analytical solution of diffusion kinetics problem in view of thermal stresses.     

Online determination of transient thermal stresses in critical steam turbine components using a two-step algorithm

The article presents a novel algorithm for robust calculation of thermal stresses in steam turbine components during transient operating conditions. Stress calculations are performed in 2 steps: in the first step an unsteady radial temperature distribution in the component model is computed, and based on this thermal stresses at critical locations are determined in the second step. The radial temperature distribution is obtained by solving the Fourier-Kirchhoff equation for a cylinder or sphere by means of a finite difference method. The thermal stresses are computed using the Duhamel integral and Green functions evaluated with a constant heat transfer coe?cient and used with an equivalent steam temperature obtained from the surface heat flux.     

ANALYTICAL SOLUTION OF A PYROELECTRIC HOLLOW CYLINDER FOR PIEZOTHERMOELASTIC AXISYMMETRIC DYNAMIC PROBLEMS

By virtue of the separation of variables technique, the piezothermoelastic axisymmetric dynamic problem of a pyroelectric hollow cylinder is transformed to a second kind of Volterra integral equation about a function with respect to time, which can be solved successfully by means of the interpolation method. Then the solution of displacements, stresses, electric displacements, and electric potential are obtained. The present method is suitable for a pyroelectric hollow cylinder with an arbitrary thickness subjected to arbitrary thermal loads. Numerical results are presented.     

UNSTEADY THERMAL STRESS ANALYSIS IN AXISYMMETRIC PROBLEMS BY MEANS OF BOUNDARY ELEMENT METHOD

The boundary integral formulation for unsteady thermal stresses in axisymmetric quasi-static problems is proposed. It is shown that axisymmetric unsteady thermal stress problems can be easily solved without the volume integral by means of the thermoelastic displacement potential and boundary element method. It is also shown that the time integral can be easily carried out analytically. In order to investigate the accuracy of rhis method, unsteady thermal stress distributions for a hollow circular cylinder and a torus are obtained.     

Transient Thermo-Mechanical Analysis of Functionally Graded Hollow Circular Cylinders

Thermo-mechanical analysis of functionally graded hollow circular cylinders subjected to axisymmetric mechanical and transient thermal loads is carried out in this study. Thermo-mechanical properties of functionally graded materials (FGM) are assumed to be temperature independent and vary continuously in the radial direction of the cylinder. Employing the Laplace transform, the Galerkin method and series method for ordinary differential equations, solutions for the time-dependent temperature and transient thermo-mechanical stresses are obtained. As an example, a molybdenum/mullite FGM with material properties obeying the exponential law is considered. Effects of heat transfer coefficients and gradient parameters of FGM on the time-dependent temperature and transient thermal stresses are discussed in detail.     

Nonaxisymmetric Thermomechanical Analysis of Functionally Graded Hollow Cylinders

Analytical solutions for nonaxisymmetric, thermomechanical response of functionally graded hollow cylinders are obtained in this article. The hollow cylinders are assumed to be subjected to nonaxisymmetric mechanical and transient thermal loads. Properties of functionally graded material are considered as temperature-independent and continuously varying in radial direction. Employing complex Fourier series and Laplace transform techniques, analytical solutions of time-dependent temperature and thermomechanical stresses are obtained. Numerical values of temperature and stresses of a FGM hollow cylinder under assumed thermomechanical loads are presented in graphical form.     

THERMOELASTIC TRANSIENT RESPONSE OF MULTILAYERED HOLLOW CYLINDER WITH INITIAL INTERFACE PRESSURE

This article deals with the transient response of one-dimensional axisymmetric quasi-static coupled thermoelastic problems with initial interface pressure. The initial interface pressure in a multilayered cylinder caused by the heat-assembling method is considered as an initial condition for the thermoelastic equilibrium problem. The Laplace transform and finite difference methods are used to analyze problems. Using the Laplace transform with respect to time, the general solutions of the governing equations are obtained in the transform domain. The solution is obtained using the matrix similarity transformation and inverse Laplace transform. We obtained solutions for the temperature and thermal stress distributions in a transient state. Moreover, the computational procedures established in this article can solve the generalized thermoelasticity problem for a multilayered hollow cylinder.     

Analysis of Thermoelastic Waves in Functionally Graded Hollow Spheres Based on the Green-Lindsay Theory

In this article, the Green–Lindsay theory of thermoelasticity is employed to study the thermoelastic response of functionally graded hollow spheres. This generalized coupled thermoelasticity theory admits the second sound phenomena and depicts a finite speed for temperature wave propagation. The materials of the hollow sphere are assumed to be graded through its thickness in the radial direction while a symmetric thermal shock load is applied to its boundary. The Galerkin finite element method via the Laplace transformation is used to solve the coupled form of governing equations. A numerical inversion of the Laplace transform is employed to obtain the results in time domain. Using the obtained solution, the temperature, displacement, radial stress, and hoop stress waves propagation are studied. Also the material distribution effects on temperature, displacement and stresses are investigated. Finally, the obtained results for the Green–Lindsay theory are compared with the results of classical thermoelasticity theory.     

Dynamic Thermoelastic Behavior of a Double-layered Hollow Cylinder with an FGM Layer

In this article, dynamic thermoelastic behavior of a double-layered cylinder with an FGM layer under mechanical and thermal loadings are investigated. The double-layered hollow cylinder is constructed by an FGM layer and a homogenous layer. Utilizing the Finite difference method and Newmark method, the governing equation of the double-layered hollow cylinder under both dynamic mechanical and thermal loads is solved. The accuracy of the approach is validated by comparing the results with the existing analytical ones. Numerical results show that volume exponent of the FGM layer, the thickness ratio of two layers and temperature change have significant effect on the dynamic behaviors of the double-layered hollow cylinder.     

Steady-state Green's functions for thermal stresses within rectangular region under point heat source

This article presents new steady-state Green's functions for displacements and thermal stresses for plane problem within a rectangular region. These results were derived on the basis of structural formulas for thermoelastic Green's functions which are expressed in terms of Green's functions for Poisson's equation. Structural formulas are formulated in a special theorem, which is proved using the author's developed harmonic integral representation method. Green's functions for thermal stresses within rectangle are obtained in the form of a sum of elementary functions and ordinary series. In the particular cases for a half-strip and strip, ordinary series vanish and Green's functions are presented by elementary functions. These concrete results for Green's functions and respective integration formulas for thermoelastic rectangle, half-strip and strip are presented in another theorem, which is proved on the basis of derived structural formulas. New analytical expressions for thermal stresses to a particular plane problem for a thermoelastic rectangle under a boundary constant temperature gradient also are derived. Analytical solutions were presented in the form of graphics. The fast convergence of the infinite series is demonstrated on a particular thermoelastic boundary value problem (BVP). The proposed technique of constructing thermal stresses Green's functions for a rectangle could be extended to many 3D BVPs for unbounded, semibounded, and bounded parallelepipeds.     

Estimation of Heat Flux and Thermal Stresses in Functionally Graded Hollow Circular Cylinders

In this study, an inverse algorithm based on the conjugate gradient method and the discrepancy principle is applied to estimate the unknown time-dependent heat flux at the inner surface of a functionally graded hollow circular cylinder from the knowledge of temperature measurements taken within the cylinder. Subsequently, the distributions of temperature and thermal stresses in the cylinder can be determined as well. It is assumed that no prior information is available on the functional form of the unknown heat flux; hence the procedure is classified as the function estimation in inverse calculation. The temperature data obtained from the direct problem are used to simulate the temperature measurements, and the effect of the errors in these measurements upon the precision of the estimated results is also considered. Results show that an excellent estimation on the time-dependent heat flux, temperature distributions, and thermal stresses can be obtained for the test case considered in this study.     

Asymmetric mechanical and thermal stresses in 2D-FGPPMs hollow cylinder

The general solution of steady-state asymmetric mechanical and thermal stresses of a hollow thick cylinder made of fluid-saturated functionally graded porous piezoelectric materials based on two-dimensional equations of thermoelasticity is considered. The general form of thermal and mechanical boundary conditions is considered on the inside and outside surfaces. A direct method is used to solve the heat conduction equation and the nonhomogeneous system of partial differential Navier equations, using the complex Fourier series and the power law functions method. The material properties are assumed to depend on the radial and circumferential variables and are expressed as power law functions along the radial and circumferential direction.