THERMAL STRESSES IN BONDED SOLAR CELLS-THE EFFECT OF THE ADHESIVE LAYER

A two-dimensional, rectangular model of a proposed solar cell structure is analyzed as two plate elements bonded with an elastic continuum. The governing equations are formulated using the principle of minimum potential energy, with displacement components that vary linearly through the thickness of the adhesive layer. An approximate solution is constructed for a particular class of material properties and is characterized by a boundary layer near the unloaded edge. Both interface stress components achieve their largest values at the edge, and the maximum shear stress is independent of the Young's Modulus of the substrate.     

AXISYMMETRIC THERMAL STRESSES IN AN ANISOTROPIC FINITE HOLLOW CYLINDER

The problems of linear thermoelasticity in a transversely isotropic hollow cylinder of finite length are solved by a direct power series approximation through the application of the Lanczos-Chebyshev method. Coefficients in the “economized” series are determined by collocation at selected Chebyshev points. Formulations are given to show that the same approach can be applied to all linear types of boundary conditions. A numerical example has been used for comparison with pubished solutions from a potential function approach, and with “long cylinder” solutions. The magnitude of end effects has been shown.     

ANALYSIS ON TRANSIENT THERMAL STRESSES IN AN ANNULAR FIN

Transient thermal stresses are an important consideration in production processes involving large temperature changes. Recently, thermal stresses have also become significant in design problems related to microelectronic devices through their effects on material properties and system parameters. To calculate the thermal stresses, three kinds of methods are available. The first is the analytical method, in which the elastic theory is used to find the exact solution. The second approach consists of some kind of approximate technique, such as a perturbation procedure. The third method is the use of a numerical process, such as a finite-difference or a finite-element method.

This article investigates the transient thermal stresses in an annular fin with its base subjected to a heat flux of a decayed exponential function of time. In order to obtain the solution of the governing equation, which is a partial differential equation, the following procedures of analysis are used.

1. Normalize the governing partial differential equation subject to appropriate initial and boundary conditions.

2. Take the Laplace transform of the resulting equation with respect to time.

3. Utilize the exponential-like solutions introduced by Keller and Keller to solve the transformed system.

4. Achieve the inverse Laplace transform by means of complex contour integration and the residue theorem.

5. Substitute the temperature distribution function into the governing equation of thermal stresses. Then use Simpson's rule to obtain the thermal stress distribution as a function of time and position of the fin.     

THERMAL STRESSES IN AN ORTHOTROPIC SLAB CONTAINING A PLANE FLAW

This paper examines the stationary temperature and stress fields in an orthotropic elastic slab containing a plane interior region which resists heat flow. Over this region of imperfection the heat flux is assumed to be proportional to the local temperature difference, whereas the stress and displacement components are taken to be continuous. Each face of the slab is subject to an arbitrary temperature variation. Numerical results are given for isotropic and orthotropic slabs with flaws of various lengths and heat-flow resistances.     

THERMAL STRESSES AROUND AN INSULATED BARRIER

The main interest in this study is to determine the thermal stresses around an insulated barrier due to constant heat flux in a homogeneous semi-infinite medium. Reducing the diffusion equation to a singular integral equation, the temperature distribution around the insulated barrier is obtained by defining an unknown function, the so-called density function, as a series expansion of orthogonal polynomials. After the temperature distribution is obtained then it can be used in equilibrium equations as an input function to find thermal stresses for different thickness parameters. Using the solution of equilibrium equations one can also obtain displacements around an insulated barrier as a secondary interest of the problem.     

THERMAL STRESSES IN ORTHOTROPIC DISK DUE TO ROTATING HEAT SOURCE

A quasi-state stress-field generated in an orthotropic elastic circular disk by a heat source rotating on a concentric circular path is investigated. An exact solution is developed in terms of doubly infinite series, using a stress-function approach. Numerical results are given for a boron-epoxy fiber-reinforced composite material and the effect of orthotropy on the distribution of thermal stresses is studied by comparing the orthotropic results with those for an isotropic material.     

TRANSIENT THERMAL SINGULAR STRESSES OF MULTIPLE CRACKING IN A W-Cu FUNCTIONALLY GRADED DIVERTOR PLATE

We consider the transient thermal singular stresses of multiple cracking in a functionally graded divertor plate due to a thermal shock. The plate is made of a graded layer bonded between a homogeneous substrate and a homogeneous coating, and it is subjected to a cycle of heating and cooling on the coating surface of the plate. The surface layer contains a parallel array of embedded or edge cracks perpendicular to the boundaries. The thermal and elastic properties of the material are dependent on the temperature and the position. Finite element calculations are carried out, and the transient thermal stress intensity factors are shown graphically.     

THERMAL STRESSES IN AN INFINITE PLATE WITH TWO ROWS OF HOLES

Abstract

A theoretical method is presented for a two-dimensional, steady thermoelastic problem of perforated plates with two rows of holes. The analysis is developed by the complex variable approach. The numerical results for stress concentration factors are given in the form of curves for a wide range of diameter/pitch. The extension of the present method to holes of arbitrary shape, number, and array is quite straightforward.     

AXISYMMETRIC QUASI-STATIC THERMAL STRESSES IN AN ELASTIC SEMI-SPACE SUBJECT TO A ROTATING FRICTIONAL HEATING ON ITS BOUNDARY

The problem in which two half-spaces make contact in a circular region and rotate about the common axis is considered. The contact pressure is assumed to be Hertzian, and a solution is given first for the transient temperature field and then for the corresponding thermal stresses. The effects of variation in space and time and the contact conditions are evaluated.     

THERMAL STRESSES IN COMPOSITE CYLINDERS

Abstract

This paper is concerned with the static problem of the linear theory of thermo-elasticity for a composite cylinder. The cylinder is assumed to be occupied by different inhomogeneous and anisotropic elastic materials. The method described is also used to study the deformation of a circular cylinder made of two different homogeneous and isotropic materials.     

THERMAL STRESSES IN LAMINATED BEAMS

This paper considers laminated beams consisting of layers of different materials fastened together by thin adhesives. The stresses that result from subjecting the beam to temperature stimuli are calculated. The problem is treated by two-dimensional elasticity theory in conjunction with the variational theorem of complementary energy. A pair of governing differential equations is developed, and boundary conditions concerning stress-free surfaces and ends of the beam are satisfied. The calculation of the distributions of interlaminar normal and shear stresses shows that high stress intensity occurs in the end zones of the beam. Thus, the satisfaction of end conditions is of prime importance in the analysis of laminated structural elements. Delamination failure-when it occurs - will probably start at the ends of the beam, This agrees with observed failures of laminated structural elements subjected to stress-free end conditions.     

STEADY THERMAL STRESSES IN AN INFINITE NONHOMOGENEOUS ELASTIC SOLID CONTAINING A CRACK

This article considers the crack problem for an infinite nonhomogeneous elastic solid subjected to steady heat flux over the crack surfaces. The aim is to understand the effect of nonhomogeneities of materials on stress intensity factors. By using the Fourier transforms, the problem is reduced to a Fredholm integral equation of the second kind which is solved numerically. Results are presented illustrating the influence of the nonhomogeneity of the material on the stress intensity factors. For some groups of the material constants, there exist minimum stress intensity factors, which is very interesting for the understanding of compositions of advanced functionally gradient materials.     

THERMAL STRESSES AROUND AN ELASTIC RIBBONLIKE INCLUSION WITH GOOD THERMAL CONDUCTIVITY

Plane-deformation problems of thermal stresses around an elastic ribbonlike conductor in an infinite, homogeneous, isotropic medium under uniform heat flow are analyzed by the method of continuous distribution of singular points. The line heat sources and concentrated forces are distributed continuously along the ribbonlike conductor. The boundary conditions yield a system of singular integral equations for density functions with Cauchy kernels and logarithmic singular kernel. A solution is assumed in the form of the product of a series of Chebyshev polynomials of the first kind and their weight function and is determined by transforming the singular integral equations into linear algebraic equations. One of the advantages of this method is that the strength of the thermal-stress singularity at the tips of the ribbonlike conductor can be easily evaluated. Numerical results for the strength of the thermal-stress singularity are plotted in terms of nondimensional parameters, consisting of the dimensions of the ribbonlike conductor and the material constants of the conductor and matrix.     

TEMPERATURE AND THERMAL STRESSES IN A BRAKE DRUM SUBJECTED TO CYCLIC HEATING

For the optimized design of a brake drum, it appears to be very important to examine the transient temperature and thermal stress distributions in the brake drum. In the direct measurement, of them, however, a number of difficulties are involved In this study, in order to examine the initiation mechanism of the thermal crack in the brake drum, the temperature and thermal stress distributions in the brake drum in the course of their heating and cooling were investigated by using a two-dimensional axisymmetric Finite Element Method. The effect of a circumferential fin near the open end of the brake drum was also examined.     

APPLICATION OF TAYLOR TRANSFORMATION TO THE THERMAL STRESSES IN ISOTROPIC ANNULAR FINS

This article presents the stresses distribution in a perfectly elastic isotropic annular fin. The Taylor transformation method is used to solve the nonlinear temperature field equation. The stresses distribution are integrated obtain the results. The thickness of the fins is assumed to be sufficiently small so as to have a state of plane stress and one-dimensional heat conduction.     

THERMAL STRESSES IN FUNCTIONALLY GRADED MATERIALS

The thermal stress problems of functionally graded materials (FGMs), as one of the advanced high-temperature materials capable of withstanding the extreme temperature environments, are discussed. The FGMs consist of the continuously changing composi tion of two different materials. For example, one is an engineering ceramic to resist the severe thermal loading from the high-temperature environment, and the other is a light metal to maintain the structural rigidity. When the FGMs are subjected to extremely severe thermal loading, large thermal stresses are produced in the FGMs. Therefore, one of the most important problems of FGMs is how to decrease thermal stresses and how to increase heat resistance. The optimal composition profile problems of the FGMs in decreasing thermal stresses are discussed in detail. When FGMs are subjected to extremely severe thermal loading, the FGMs are damaged. The crack initiates on the ceramic surface and propagates in the FGMs. It is important to discuss the thermal stresses in the FGMs with various types of cracks. The thermal stress intensity factors in the FGMs with various types of crack are treated analytically and numerically. The optimal composition profile problems of the FGMs in decreasing thermal stress intensity factor are studied. Finally, the crack propagation paths due to thermal shock are discussed.     

THERMAL STRESSES IN JOINED SEMI-INFINITE SOLIDS

The elastic stress field caused by an ellipsoidal inclusion with uniform dilatational eigenstrains in one of two perfectly bonded semi-infinite solids is investigated. The thermal stress in domain z induced by the temperature variation j T could be simulated effectively by pure dilatational eigenstrain. The solutions are obtained using the method of dilatation centers. The potential functions for the problem solved are the harmonic potential functions of attracting matter filling the element of volume and expressed in terms of derivatives of elliptic integrals. Numerical examples are given to show the normal and tangential stresses along the boundary of the ellipsoidal inclusion and the maximum principle stresses along the major and minor axes in the inclusion that are important to the fracture problems. The effects of the inclusion depth from the interface, the ratio of elastic moduli of joined semi-infinite solids, the shapes of the inclusion and the rotation angle of the ellipsoidal inclusion are also studied. They are of great significance in physical applications pertaining to thermal stress problems.     

THERMAL STRESSES IN MICROSTRETCH ELASTIC CYLINDERS

The present paper is concerned with the problem of thermal stresses in isotropic microstretch elastic cylinders. The temperature distribution is assumed to be a general polynomial in the axial coordinate. As in classical theory, the problem is reduced to solving the plane strain problem.     

STRESS INTENSITY FACTOR FOR TRANSIENT THERMAL STRESSES IN AN INFINITE ELASTIC BODY WITH AN EXTERNAL CRACK

Abstract

This paper deals with a transient thermal stress problem in an infinite body with an external crack. The elastic medium is cooled by time- and position-dependent temperature on the external crack. It is very difficult to obtain the analytical expression for the temperature, so the finite-difference method is used with respect to a time variable. Thus, the analytical expression for the temperature with respect to the spatial variables may be obtained. The temperature solution reduces to a dual-integral equation for spatial variables by use of the finite-difference method for a time variable. The numerical results for stress intensity factor are obtained.     

BUCKLING OF PLATES DUE TO SELF-EQUILIBRATED THERMAL STRESSES

Thermal buckling of load-free supported plates is considered. Especially the influence of the distribution of the applied temperature field on buckling modes and proper values is investigated, ft turns out that fields of temperature‐shock type are most critical and lead to the lowest proper values of buckling.