THERMOELASTIC PROBLEM OF ARC CRACK WITH HEAT SOURCE OR DOUBLET

The problem of a circular arc-shaped crack in an infinite plate under the action of a heat source or doublet is solved by using the complex variable function method. The original problem can be considered a superposition of three particular problems. The first problem relates to a heat source applied at the origin point (z = 0) of an infinite continuous medium. In the second problem, the heat flow passes through the arc crack face. In the third problem, tractions are applied on the arc crack face. All three problems can be solved in a closed form. When heat sources are present, the behavior of the complex potentials is studied in detail. Finally, the solution for the original problem is obtained.     

TRANSVERSELY ISOTROPIC THERMOELASTIC PROBLEM OF UNIFORM HEAT FLOW DISTURBED BY A PENNY-SHAPED CRACK

A solution for an antisymmetrical problem of uniform heat flow disturbed by a penny-shaped crack in a transversely isotropic medium is obtained using the techniques of Hankel transforms and multiple integrations. The thermal stresses and displacements in the crack plane are obtained in closed forms. The stress intensity factor is shown to be dependent upon the material properties.     

GREEN'S FUNCTIONS OF POINT HEAT SOURCE IN VARIOUS THERMOELASTIC BOUNDARY VALUE PROBLEMS

With an emphasis on derivation, this paper reviews Green's functions for a point heat source in various thermoelastic boundary value problems for an infinite plane with an inhomogeneity. The inhomogeneity boundary conditions considered are external force, displacement, and mixed boundaries. The derivation is accomplished with three kinds of function for mapping, temperature, and stress. Stress functions for different boundary value problems are presented, and stress distributions along the inhomogeneity boundary are plotted in figures.     

THERMOELASTIC PROBLEM OF UNIFORM HEAT FLOW DISTURBED BY A FLAT TOROIDAL CRACK IN A TRANSVERSELY ISOTROPIC MEDIUM

The thermoelastic problem of uniform heat flow disturbed by a flat toroidal crack in a transversely isotropic medium is investigated using the method of Hankel transforms. The three-part mixed thermoelastic boundary conditions are satisfied using the tech niques of triple integral equations and multiplying factors. The stress intensity factors at the inner and outer crack tips are obtained in exact expressions as the products of a dimensional quantity and nondimensional functions. The fracture transition of a flat toroidal crack to a penny-shaped crack and to a two-dimensional line crack is studied at different values of the ratio of the inner crack radius to the outer crack radius.     

A NONIDEAL CONTACT PROBLEM OF THERMOELASTICITY FOR TWO SOLIDS WITH A HEAT SOURCE

A generalized Hertz problem of thermoelastic solids in pressure, contacting over convex surfaces, has been discussed. At a certain moment of time a concentrated source of heat starts acting. Therefore the heat flux flowing through the region of contact is nonstationary. The problem considered is axially symmetric. The purpose is twofold: first the problem of thermoelasticity with time variation of temperature is taken into account; second the “paradox of a cooled sphere” has been investigated under time-dependent conditions. There is a possibility that the character of the boundary conditions can change in time. To obtain the solution we have applied the Laplace and Hankel integral transforms. The main point is to discuss the cases when the boundary conditions are such that the problem can be considered in terms of classical thermoelasticity and when the Barber-type boundary conditions have to be used. The solution has been obtained by means of a devised numerical algorithm such that the procedure is simplified. The results have been presented in diagram form suitable for discussion.     

THERMOELASTIC PROBLEM OF STEADY-STATE HEAT FLOW DISTURBED BY A CRACK PERPENDICULAR TO THE GRADED INTERFACIAL ZONE IN BONDED MATERIALS

The plane thermoelasticity equations are used to investigate the steady-state nonisothermal crack problem for bonded materials with a graded interfacial zone. The interfacial zone is modeled as a nonhomogeneous interlayer having continuously varying thermoelastic moduli in the exponential form between the dissimilar, homogeneous half-planes. A crack is assumed to exist in one of the half-planes oriented perpendicular to the nominal interface, disturbing a uniform heat flow. Based on the method of Fourier integral transform, formulation of the crack problem is reduced to solving two sets of Cauchy-type singular integral equations for temperature and thermal stress fields. The heat-flux intensity factors and the thermally induced mode II stress intensity factors are defined in order to characterize the singular behavior of temperature gradients and thermal stresses, respectively, in the vicinity of the crack tips. In the numerical results, the values of heat-flux and thermal-stress intensity factors are presented for various combinations of material and geometric parameters of the dissimilar media bonded through a thermoelastically graded interfacial zone. The influence of crack-surface partial conductance on the near-tip temperature and thermal stress fields is also addressed.     

GREEN'S FUNCTION FOR THERMAL STRESS MIXED BOUNDARY VALUE PROBLEM OF AN INFINITE PLANE WITH AN ARBITRARY HOLE UNDER A POINT HEAT SOURCE

Green's function of a point heat source is derived for a mechanical mixed boundary value problem of an infinite plane with an arbitrary hole, for which zero-displacement and traction-free boundary conditions are prescribed to its boundary. As the thermal boundary condition on the hole, either an adiabatic or isothermal condition is considered. By employing the mapping technique and complex variable method, an explicit solution including a hypergeometrical function is obtained. Stress distributions are shown in illustrative examples for a square hole.     

POINT SOURCE OF HEAT IN AN ELASTOPLASTIC MEDIUM

Abstract

An infinite elastoplastic medium (Tresca's criterion) is loaded with a spherically symmetrical time-dependent temperature distribution. The thermal expansion induced by changes in temperature can lead to the generation of plastic zones. It is shown that relatively simple formulas can be used to calculate the boundaries of the plastic zones for any temperature distribution. The cases of increasing and decreasing plastic zones are considered. These formulas are applied to the case of a constant point source of heat acting during a finite or infinite interval of time.     

THERMOELASTIC PROBLEM FOR A GRIFFITH CRACK IN A PLATE WITH TEMPERATURE-DEPENDENT PROPERTIES UNDER A LINEAR TEMPERATURE DISTRIBUTION

This paper is concerned with a method for calculating the thermal-stress distribution in a plate exhibiting temperature-dependent properties. Using the perturbation method, general equations for the displacements are found. The equations can be solved by using four displacement functions. Following this method, a solution is derived for calculating the stress intensity factor for a Griffith crack in a temperature-sensitive plate under a linear temperature distribution, where we assume that the temperature field is not disturbed by the crack. (Under these conditions, if a plate is temperature-insensitive, the stress intensity factor for the crack is zero.) In this case, whether the stress intensity factor is zero or not depends only on the temperature variation of the coefficient of thermal expansion. A numerical example is given for a plate made of steel.     

THERMOELASTIC ANALYSIS FOR A SEMI-INFINITE PLANE SUBJECTED TO A MOVING GAUSSIAN HEAT SOURCE

Three- and two-dimensional analytical solutions are developed for the temperature due to a moving heat source with a Gaussian type distribution. The thermal stresses in a semi-infinite plane are expressed in terms of Bessel functions and exponential integrals. For nonzero values of r₀v/ (2D), a dip is found for the σ_xx component on the traction-free surface and is due to the changing sign of the temperature gradient. Parametric studies are made for different r₀V/ (2D) values.     

INERTIAL EFFECTS OF A TRANSIENT THERMOELASTIC PROBLEM IN A THICK PLATE WITH AN AXISYMMETRIC TEMPERATURE

This paper concerns an axisymmetric dynamic treatment of a three-dimensional thermoelastic problem in a thick plate that is exposed to the temperature of surrounding medium depending on the position and time. In the present investigation, the Laplace transform and the convolution theorem are used, and an exact solution that is valid for the whole time interval without approximation is obtained. The thermal stresses are compared with the corresponding quasi-static stresses and the corresponding one-dimensional stresses.     

THE IMPACT OF A THERMOELASTIC ROD AGAINST A HEATED BARRIER WITH ACCOUNT OF FINITE SPEED OF HEAT PROPAGATION

This paper examines the impact of a thin thermoelastic bar of finite length with a heat-insulated lateral surface against a heated massive barrier. The hyperbolic equation of heat conduction is used. During impact, thermoelastic waves propagate along the bar, and behind the wave fronts a solution is constructed in terms of ray series. The stresses, temperature, displacement velocity, and heat flux profiles are obtained. Also, the time-dependent contact stress and temperature and the contact time as a function of the temperature of wall heating, heat flow relaxation time, impact velocity, and coefficient of convective heat exchange from the wall to the rod are investigated.     

NUMERICAL RESOLUTION OF A PHASE CHANGE PROBLEM WITH ZERO LATENT HEAT

Two numerical methods to simulate Ike behavior of a class offree-boundary thermal systems are presented and compared. The state of the system is governed by the conduction equation, where an isotherm defines the moving boundary for which a Neumann condition is considered. Unlike the classical Stefan problem, the moving boundary velocity does not appear explicitly in the heal balance

One method is based on the Friedman transformation and leads to a variational inequality defined on a fixed domain. Computation of the front velocity is not required

The other method uses the Landau transformation, leading to a new state equation of the convection-conduction type on a fixed domain. The convective part in the equation is due to the moving boundary. Estimation of the front velocity is obtained from the field temperature in the neighborhood of the boundary

The comparison between the two methods is performed on two examples—a freezing and a melting case—the exact solutions of which are known.     

TRANSIENT THERMOELASTIC PROBLEM FOR AN INFINITE PLATE CONTAINING A PENNY-SHAPED CRACK AT AN ARBITRARY POSITION

This article deals with the transient thermoelastic problem for an infinite plate containing a penny-shaped crack that is parallel to the surfaces of the plate but at an arbitrary position of the plate. The transient thermal stresses are set up by the heat generation on the surfaces and the sudden heat exchange on the surfaces. By using the finite difference method for the time variable, the analytical solution for spatial variables can be obtained. The numerical results for the temperature and stress intensity factor are obtained, and results are shown in graphs.     

THERMOELASTIC WAVES IN A HELIX WITH PARABOLIC OR HYPERBOLIC HEAT CONDUCTION

Of concern is the steady-state thermoelastodynamics of a helix, whose material is governed by a coupled thermoelastic model. Heat transfer follows either a parabolic (Fourier) or a hyperbolic (Maxwell–Cattaneo) rule. As a result, in the one-dimensional setting, there are three coupled differential equations that lead to a fast (primarily axial) and a slow (primarily torsional) wave. Particularly for harmonic motions, we find that the thermal diffusivity and the relaxation time (of the Maxwell–Cattaneo model) have minor effects, whereas the thermoelastic coupling constant is dominant—it speeds up these waves—and overall there is damping. Additionally, we review and note differences from solutions of equations governing plane harmonic waves in a non-centrosymmetric, thermoelastic micropolar continuum in three dimensions.     

变温热源地热热泵系统的可用能分析

地热能作为一种新能源已成为许多国家的研究重点，如何提高地热能的利用率是其重要的研究方向，而热泵又是其中一项关键技术。本文针对地热热泵系统的变温热源，从减小可用能损失的角度进行了详尽的理论分析。首先，对该地热热泵系统中的各个主要部件进行了可用能分析，发现和能损失情况均与循环工质的性能有关；其次，在实际工况下比较了纯工质和非共沸混合工质的可用能损失情况；最终提出了几种有可能应用于实际地热热泵工况下的循环工质。     

THERMAL STRESS PROBLEM FOR MIXED HEAT CONDUCTION BOUNDARY AROUND AN ARBITRARILY SHAPED HOLE WITH CRACK UNDER UNIFORM HEAT FLUX

This article deals with a thermal stress problem for thermal conduction around an arbitrarily shaped hole with a crack under uniform heat flux. Two cases for the hole edge and the crack faces are assumed: adiabatic and isothermal conditions or vice versa (isothermal and adiabatic). A closed-form solution is obtained using conformal mapping, dislocation functions, and the complex variable method. Results of temperature, heat flux, stress, and stress intensity factor are illustrated.     

THE COUPLED THERMOELASTICITY PROBLEM OF THE TRANSIENT MOTION OF A LINE HEAT/MECHANICAL SOURCE OVER A HALF-SPACE

Abstract

A procedure is developed for obtaining fundamental thermoelastic two-dimensional solutions for thermal and/or mechanical loadings moving unsteadily over the surface of a half-space. These solutions are within the bounds of the transient coupled thermoelastodynamic theory of M. A. Biot. The concentrated line loadings (sources) are suddenly applied on the surface of the half-space and then move in a fixed direction with nonuniform speed. The problem is of basic interest in contact mechanics and tribology, and it is especially related to the well-known heat checking problem (thermo-mechanical cracking in an unflawed half-space material from high-speed asperity excitations). Here, an exact and general formulation is considered and explicit results are given for some special cases. These results are obtained by generating asymptotic expressions from one- and two-sided Laplace transforms and then performing the inversions in an exact manner.     

TRANSIENT THERMOELASTIC ANALYSIS OF AN ANNULAR FIN WITH COUPLING EFFECT AND VARIABLE HEAT TRANSFER COEFFICIENT

A hybrid numerical method of the Laplace transformation and the finite difference method is applied to solve the transient thermoelastic problem of an annular fin, in which the thermomechanical coupling effect is taken into account in the governing equation of heat conduction and the heat transfer coefficient is a function of the radius of the fin. The general solutions of the governing equations are first solved in the transform domain. Then the inversion to the real domain is completed via the method of matrix similarity transformation and Fourier series technique. The transient distributions of temperature increment and thermal stresses of the fin in the real domain are calculated numerically. The presented method is more efficient in computing time and is applicable to other types of boundary conditions.     

一种利用地下水预处理新风的复合式地源热泵空调系统

提出一种新型的可直接利用地热能预处理新风的地下水地源热泵空调系统,分析该新系统工作原理及新回风空气处理方法,建立热力学数学模型,对新型复合式地源热泵空调系统与传统地下水地源热泵空调系统的循环特性与能耗进行计算比较分析.结果表明,复合式地下水地源热泵空调系统节能效果显著高于传统地下水地源热泵空调系统.