Transient Thermoelastic Problem Research Articles

Stress Singularity in Transient Thermoelastic Field of a Fiber-Reinforced Composite Tube

The present paper discusses a transient thermoelastic contact problem in a fiber-reinforced composite tube. The tube is inserted into a supporting body such as a ring, and subjected to heating and hydrostatic pressure in it. The fiber-reinforced composite possesses strong thermal and mechanical anisotropies, so the thermoelastic analysis of anisotropic material is very important. The stress produced in the tube has singularity at the end of contacted surface of the tube. The stress singularity may lead to a crack on the surface so that the tube may fracture. If we consider the safety of the tube in service, it is very important to evaluate the stress singularity. For that, the transient thermoelastic contact problem of the tube is analyzed, and the stress distribution and the strength of the stress singularity become clear.

BEM analysis of the transient axisymmetric thermoelastic problem.

In this paper, we deal with the boundary element formulation of the transient axisymmetric thermoelastic problem. For the formulation of the problem, we introduce the thermoelastic displacement potential function. Using this function, we indirectly obtain Green's functions of the thermal displacement and thermal stress components and their boundary integral representations. Performing the time integration analytically, the resultant function is separated into two parts: the steady and the transient parts. We observe singularity at the boundary integration only in the steady part.

An analytical solution for a plane thermoelastic problem in nonhomogeneous multiply connected regions. 2nd Report. Transient thermal stresses in nonhomogeneous hollow circular plates of variable thickness subjected to asymmetric heating.

A transient plane-stress thermoelastic problem in a nonhomogeneous hollow circular plate of variable thickness is formulated in terms of a stress function by deriving new Michell integral conditions necessary for the assurance of single-valuedness of rotation and displacement. An analytical solution is presented for thermal stresses in a nonhomogeneous hollow circular plate subjected to unaxisymmetic heating on the boundary surfaces, which has the plate thickness, Young's modulus and thermal conductivity in forms of different power laws of the radial coordinate; the coefficient of linear thermal expansion is given as an arbitrary function of the radial coordinate. Numerical calculations are carried out over a wide range of the nonhomogeneous thermal conductivity, Young's modulus, coefficient of linear thermal expansion and plate thickness. The effects of nonhomogeneous thermal and mechanical properties on the relaxation of thermal stress and its application to the design of functionally gradient materials (FGM) are discussed.

Coupled thermoplastic problem of an infinite solid containing a penny-shaped crack

This paper deals with the transient thermoelastic problem of an infinite solid containing a penny-shaped crack under consideration of the coupling effect between the temperature and strain fields. The elastic solid is cooled by the medium at the time- and position-dependent temperature on the crack surface. A finite difference formulation based on the time variable alone is used to solve the coupled thermoelastic problem of an infinite solid containing a penny-shaped crack. The analytical solution for the spatial variables, however, can be obtained by use of the thermoelastic potential and harmonic functions. The numerical results of the transient stress intensity factor are shown for the coupling effect between the temperature and strain fields.

Boundary integral analysis of transient thermoelasticity

AbstractA simple and efficient method for the solution of uncoupled transient thermoelastic problems using boundary integral techniques is presented. The method employs a Laplace transformation to remove temporarily the time dependence of the governing equations. Numerical analysis is then carried out in the transform space, and results in the time‐position space are found by numerical inversion of the Laplace transform. The method has the advantage that it avoids time‐stepping and the costly evaluation of domain integrals. Boundary element and analytic solutions are compared, and the effect of cooling on the stresses around a deep underground opening is examined.

Hybrid finite element analysis of transient thermoelastic fracture problems subjected to general heat transfer conditions

This paper presents the singular characteristics of heat flux in the vicinity of the crack-tip for two dimensional transient thermoelastic fracture problems subjected to general heat transfer conditions at crack surfaces. Based on a restricted variational principle, a rigorous hybrid finite element procedure is then developed to perfectly describe the singularities of heat flux and thermal stress induced at the crack-tip. For verification purposes, the examples of transient thermoelastic problems with insulated crack surfaces are first analyzed. Excellent agreements between the computed results and referenced solutions can be drawn. To evaluate the influence of heat convection and radiation on the computation of temperature distributions and thermal stress intensity factors, several numerical examples are also presented.

Generalized Coupled Transient Thermoelastic Plane Problems by Laplace Transform/Finite Element Method

A general finite-element model is proposed to deal with dynamic theromelastic problems especially with longer transient period. The method consists of formulating and solving the problem in the Laplace transform domain by the Finite Element Method (FEM) and then numerically inverting the transformed solution to obtain the time-domain response. Therefore, the transient solutions at any time could be evaluated directly. A number of examples are presented which demonstrate the accuracy, efficiency, and versatility of the proposed method, and show the effects of relaxation times, inertia, and thermoelastic coupling terms.

Solution for the thermoelastic problem in vertically inhomogeneous media

The fundamental transient-thermoelastic problem with body forces and a heat source in vertically inhomogeneous media is investigated by a method presented in this paper. The basic equations in Fourier transforms and Laplace transform are obtained in the form of two sets of first order linear ordinary differential equations inz, Eq. (7). Furthermore, forN-layered media, the general solution in the transformed spaces of thej-th layer is given for fully connected interface between layers, Eq. (11). Finally, under general condition, a closed-form solution for the quasi-static transient displacements, stresses, temperature in the body can be obtained by the convolution theorems for the two integral transforms. In the final solution, the Green's functions can be expressed in terms of Hankel transforms of order zero and unity as well as inverse Laplace transform, and come out rather neatly.

Transient thermoelastic contact problem of a transversely isotropic cylinder

This paper concerns a transient thermoelastic contact problem in a transversely isotropic infinite cylinder inserted into a heated rigid ring. It is assumed that the heat transfer coefficient at the bonded surface is different from the coefficient at the traction-free boundary surface. A finite difference formulation with respect only to time is used to solve the three-dimensional transient heat conduction equation for the temperature field. The thermal stress field is analyzed by means of the transversely isotropic potential function method. The radial, hoop and axial stresses have singularities at the end of the contact surface. The concentration factors that may be used to evaluate the strength of the stress singularities are introduced.

Transient Thermoelastic Fields in a Transversely Isotropic Infinite Solid With a Penny-Shaped Crack

The present paper deals with a transient thermoelastic problem for an axisymmetric transversely isotropic infinite solid with a penny-shaped crack. A finite difference formulation based on the time variable alone is proposed to solve a three-dimensional transient heat conduction equation in an orthotropic medium. Using this formulation, the heat conduction equation reduces to a differential equation with respect to the spatial variables. This formulation is applied to attack the transient thermoelastic problem for an axisymmetric transversely isotropic infinite solid containing a penny-shaped crack subjected to heat absorption and heat exchange through the crack surface. Thus, the thermal stress field is analyzed by means of the transversely isotropic potential function method.

Stress intensity factor for transient thermal stresses in a transversely isotropic infinite body with an external circular crack

The present work deals with the transient thermal stress in a transversely isotropic infinite body with an external circular crack. The surface cooling of the crack depends on position and time. Since it it usually very difficult to obtain an analytical solution for the temperature field, a finite difference formulation with respect to a tive variable is introduced. In the first step, applying this method to the general heat conduction equation in an orthotropic body, a very compact difference equation with respect to the spatial variables is obtained. In the second step, this method is applied to the transient thermoelastic problem in a transversely isotropic infinite body with an external circular crack subjected to heat exchange on the crack surface. Thermal stresses are analyzed by means of the transversely isotropic potential functions method.

Transient thermoelastic problem in a long circular cylinder with temperature dependent properties.

The thermal and mechanical properties of materials vary with temperature, so the temperature dependence of materials must be taken into consideration in the thermal stress analysis of modern structural elements. This paper is concerned with a transient thermoelastic problem in a long circular cylinder exhibiting temperature-dependent thermal and mechanical properties. This problem is solved by the perturbation method. The fundamantal problem for the perturbation method may be treated by the thermoelastic potential function and Love's function, and the n-th problem can be solved by displacement functions.

Transient thermoelastic crack problems in transverse isotropy.

The present paper if concerned with two transient thermal stress problems in a transversely isotropic infinite solid containing a crack with heat exchange on the crack surface. One is the problem of a penny-shaped crack, and the other is the problem of an external circular crack. It is very difficult to obtain the analytical solution for the temperature field, so only the finite difference method with respect to the time variable is introduced. Thermal stresses are analyzed by means of the transversely isotropic potential functions method. Numerical calculations were carried out for a graphite which belongs under transverse isotropy. The effects of transverse isotropy on the stress intensity factor are shown in the figures.

TRANSIENT THERMOELASTIC PROBLEM OF A BONDED TRANSVERSELY ISOTROPIC INFINITE CYLINDER AND A RIGID RING

Abstract The present paper concerns the transient thermoelastic problem of a bonded transversely isotropic infinite circular cylinder and a heated rigid circular ring. This is a mixed boundary-value problem and may be reduced to that of solving dual-integral equations. The radial, hoop, axial, and shear stresses have singularities at the end of the rigid circular ring on the surface of the circular cylinder. Factors are defined to evaluate the stress singularities

Transient Thermoelastic Problem in an Infinite Body Containing a Penny‐Shaped Crack Due to Time and Position Dependent Temperature Condition

AbstractEs wird das Problem der Übergangswärmespannung für einen unendlichen Körper mit einen pfennigförmigen Riß behandelt. Das elastische Medium wird durch ein zeit‐ und ortsabhängiges Temperaturfeld auf der Rißoberfläche abgekühlt. Mit einem Differenzenverfahren für die Zeitvariable kann man die analytische Lösung bezüglich der Ortsvariablen erhalten. Die Bestimmung der Temperatur wird auf die Lösung einer dualen Integralgleichung für Eulersche Variable reduziert. Das Wärmespannungsproblem führt auf eine singuläre Integralgleichung bekannten Typs. Die numerischen Ergebnisse werden als Funktionen der Fourier‐Zahl dargestellt.

Transient thermal stress in an infinite elastic solid with an external circular crack.

The present work tackles the transient thermoelastic problem for an infinite solid with an external circular crack. It is assumed that the transient thermal stress is set up by the application of heat exchange by convection on the crack surfaces. By use of the finite difference method for the time variable only, the analytical solution for spatial variables can be obtained. The numerical results are shown for the temperature and stress intensity factor.

Transient thermoelastic contact problem of two sliding half-planes

A transient contact problem with frictional heating for two sliding halfplanes is considered. One of the half-planes is slightly rounded to give a hertzian initial pressure distribution; the other is a rigid non-conductor. It is shown that if the ratio of initial width of contact to the width in the steady state is less than some critical value, the contact area shrinks smoothly until the steady state is reached. Otherwise the pressure distribution develops a wavy perturbation and eventually bifurcates. Results are compared with previous approximate solutions.

Transient thermoelastic problem in a plate with a Griffith crack.

This paper treats a transient thermoelastic problem in a thin plate with a Griffith crack perpendicular to the surfaces of the plate. It is assumed that the transient thermal stress is set up by the application of the heat exchange by convection of the surfaces of the crack and plate. By use of finite difference method for time variable, an analytic solution for spatial variables can be obtained. The numerical results are shown in figures.

TRANSIENT THERMOELASTIC CONTACT STRESS IN A SHORT-LENGTH CIRCULAR CYLINDER

Abstract This paper is a treatment of a transient thermoelastic contact problem in a short-length circular cylinder, to which a heated rigid band is bonded. The problem may be reduced to that of solving dual-series equations. The solution meets the boundary conditions on both the lateral surface and the plane ends of the cylinder. The radial, hoop, and axial stresses have singularities at the end of a rigid band on the cylindrical surface.

TRANSIENT THERMOELASTIC CONTACT PROBLEM IN A LONG, CIRCULAR CYLINDER

Abstract This paper treats a transient thermoelastic contact problem in a long, circular cylinder to which a heated rigid band is bonded. The problem may be reduced to that of solving dual-integral equations. The radial, hoop, and axial stresses have singularities at the end of rigid band on the cylindrical surface. The coefficients which may determine the strength of singularities of stresses are introduced.