THERMAL STRESSES IN A LONG ELASTIC CYLINDER CONTAINING A PENNY-SHAPED CRACK AND EMBEDDED IN A THERMALLY CONDUCTIVE ELASTIC INFINITE MEDIUM

This paper is concerned with- the state of stress in a long circular elastic cylinder with a concentric penny-shaped crack whose surfaces are subjected to a prescribed temperature. The plane of the crack is assumed to be perpendicular to the axis of the cylinder. The cylinder is bonded to a thermally conductive elastic infinite medium. The thermal and elastic constants of the cylinder and infinite medium are assumed to be different. By assuming suitable representations for the temperature function, the heat conduction problem is reduced to the solution of a Fredholm integral equation of the second kind. Similarly, the thermoelastic problem is also reduced to the solution of a Fredholm integral equation of the second kind. A closed-form expression is obtained for the stress-intensity factor. The integral equations are solved numerically, and the results are used to obtain numerical values for the stress intensity factor. These values are presented graphically.     

AXIALLY SYMMETRIC THERMAL STRESS OF A PENNY-SHAPED CRACK UNDER GENERAL HEAT FLUX

This paper presents a solution of the steady-state thermal stress and displacement in an infinite isotropic elastic solid containing a penny-shaped crack whose surfaces are exposed to the general mechanical loading and nonsymmetric heat flux. That is, the heat flux applied to both surfaces of the crack is not the same. The problem is solved using Hankel transforms and the Abel operator of the second kind. Using limiting values of the stress, displacement, and temperature fields at the crack plane in terms of the stress, displacement, temperature, and heat flux discontinuities and boundary conditions of the crack, the problem is reduced to that of solving Abel integral equations that admit closed-form solutions. For a special case of heat flux conditions, stresses at a general point of the medium have been computed and presented graphically.     

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.     

EXACT THERMOELECTROELASTICITY SOLUTION FOR A PENNY-SHAPED CRACK IN PIEZOELECTRIC MATERIALS

This paper investigates the electromechanical fracture behavior of a penny-shaped crack in piezoelectric materials subjected to a uniform heat flow far away from the crack region. The crack is treated as isothermal. First, the temperature field is obtained by using the Hankel transform technique. The thermoelectromechanical field is then investigated by solving the themopiezoelectoelasticity governing equations. The explicit solutions for the stress intensity factors near the crack tip are presented. The exact solution for the whole-field stresses and electric displacements are obtained.     

STABILITY AND STABILIZATION OF THERMALLY INDUCED VIBRATIONS OF CYLINDRICAL SHELLS

A review of the analytical research of smart composite structures that have a relevance to buckling, vibrations, parametric vibrations, and dynamic stability of oneand two-dimensional mechanical systems applied in mechanical and civil engineering is presented. Special attention is paid to the dynamic behavior of circular cylindrical shells due to nonuniform time-dependent temperature fields. The shell is heated, and it is assumed that a time- and space-dependent temperature field is known. To stabilize thermally induced transverse vibrations the host structure is integrated with a control system consisting of piezoelectric sensors and actuators. Distributed piezoelectric elements are implemented to suppress the motion caused by thermal disturbances. Two particular problems are analyzed in detail. The first is devoted to the stability analysis of a closed cylindrical shell subjected to a time-dependent temperature field. The stabilization is obtained by applying the velocity feedback and electroded piezoelectric sensors/actuators with a suitable polarization profile. In the second problem the technique of the dynamic stability analysis is extended to the thermally activated shape memory alloy hybrid rotating cylindrical shell.     

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.     

THERMALLY INDUCED FRACTURE OF A FUNCTIONALLY GRADED PIEZOELECTRIC LAYER

The theoretical analysis of a thermoelectroelasticity problem is developed for a piezoelectric layer due to a thermal load under a uniform electric field and a fixed grip condition. The layer is assumed to be a functionally graded material, meaning that its thermoelectromechanical properties are assumed to be continuous functions of the thickness coordinate. The layer contains an embedded or an edge crack perpendicular to its boundaries. The Fourier transform technique is used to formulate the problem in terms of a singular integral equation. The singular integral equation is solved by using the Gauss–Jacobi integration formula. Numerical calculations are carried out, and the mode I energy density factors are presented for embedded as well as edge cracks for various values of dimensionless parameters representing the size and the location of the crack, the material nonhomogeneity, the surface temperatures, and the loading combinations.     

BACKSCATTER OF ELASTIC WAVE FROM A THERMALLY AFFECTED INHOMOGENEOUS LAYER

The application of the discrete linear inhomogeneous layer element, so-called LILE, is shown to estimate the elastic wave reflectance of a gradient inhomogeneous layer. The LILE stacking model is effectively used in analyzing backscatter inspection of the inhomogeneous solid The discussion focuses on the availability of the new element for computer calculation of the backscatter intensity from a thermally deteriorated layer. The numerical results show the possibilities of inhomogeneous structural inspection and developing images of the affected inhomogeneous region by suitable impedance matching with the surrounding medium.     

TIME-DEPENDENT MODEL OF A BUOYANT DOWNWARD FLAME SPREAD OVER A THERMALLY THIN SOLID FUEL

A time-dependent model was developed and solved numerically to study a purely buoyant downward flame spread over a thermally thin solid fuel in various gravity environments. According to the specified burn-out solid density and no retained ash, the flame propagation behavior over a thin solid fuel surface could be simulated. At ignition, the flame is premixed. After several transition burnouts the flame transitions into a self-sustained steady spread diffusion flame. When the gravity level was varied, the Damkohler number effects were verified. An unstable flame spread was noted near the extinction limit at which the flame spread rate decelerated. Blow-off extinction was predicted after the flame spread a short distance. The ignition delay time increased with increasing gravity level. Compared with the experimental measurements, the predicted blow-off extinction limit was closer than that predicted by the steady combustion model.     

THERMALLY INDUCED DEFORMATIONS OF COMPOSITE TUBES SUBJECTED TO A NONUNIFORM HEAT SOURCE

Analytical solutions are obtained for thermally induced axisymmetric elastic and elastic-plastic deformations in nonuniform heat-generating composite tubes with fixed ends. Thermoelastic solutions are obtained using four different boundary conditions: (i)free, (ii) radially constrained and free, (iii) free and pressurized, (iv) free and radially constrained. Elastic-plastic solutions are obtained for a composite tube having free inner and radially constrained outer boundaries using Tresca's yield condition and its associated flow rule. The first two stages of elastic-plastic deformations are studied considering nonlinearly hardening, linearly hardening, and perfectly plastic material behavior. The theory developed is illustrated in several numerical examples.     

TRANSIENT THERMO-VISCOELASTIC RESPONSE OF A CRACK IN A LAYERED STRUCTURE

This article examines the application of a numerical method of transient stress analysis for the study of a crack located in a viscoelatic layer bonded to an elastic substrate. The layered structure containing the defect is subjected to heat conduction and associated thermo-viscoelastic effects. The finite-element technique is used to examine the time-dependent variation in the stress intensity factor at the crack tip due to a sudden reduction in the temperature at the surface of the layered structure. Numerical results presented in the article illustrates the influence of the thermo-viscoelastic coupling on the crack behavior.     

THERMAL SHOCK PROBLEMS OF ELASTIC BODIES WITH A CRACK

This paper deals with thermal shock, problems of elastic bodies with a crack. The case considered is that of an infinitely long circular cylinder with an edge crack, and a homogeneous flat plate with an edge crack initially at uniform temperature and suddenly immersed into a medium of lower temperature. The thermal disturbance near the crack tip is assumed to be neglible in the analysis of the temperature field because thermal shocks occur very quickly. We analyze the transient thermal stress problems of elastic solids with a crack and determine the stress intensity factor at the crack tip. The nondimensional maximum transient stress intensity factor is expressed as a function of the Biot number and the nondimensional crack length. Then we propose simplified formulations of the nondimensional maximum transient stress intensity factor as a function of the Biot number and the nondimensional crack length.     

可利用低品位热源的热声驱动脉管制冷机

针对原有热声驱动脉管制冷机实验装置,改进了板叠冷端夹套式水冷却器内部的丝网填料,进一步优化了小孔阀和双向进气阀的开度,获得了116．4K的最低制冷温度。通过操作脉管制冷机双向进气阀,使系统的起振温度从560℃降低为370℃,为低品位能源的利用创造了条件。     

ROUGH SIZE ESTIMATION OF A THERMALLY FRACTURED ZONE IN AN INFINITE HOT ROCK MASS

Abstract

Concerning the extraction of geothermal energy from a deep thermal reservoir by the downhole coaxial heat exchanger with a thermally insulated inner pipe proposed by Morita et al, we obtained rough estimates of a size of the fractured zone induced by thermal stresses due to injecting cold water into the hot rock mass through the pipe. We assumed complete spherical symmetry of the temperature and stress fields. At the rough estimation, we considered three typical or extreme cases. (1) The fracturing affects neither the loading capacity of a fractured rock mass nor the temperature distribution within the formation. (2) The fractured zone completely loses its loading capacity and is fully invaded by the borehole water. No disturbance of the fracturing makes any difference in the temperature. (3) The rock formation is assumed to have an appropriately increased fictitious conduction substituted for the heat transfer enhanced by the expected convection within the fractured zone in order to discuss the effects of an occurrence of heat convection within the fractured zone on the temperature and stress distributions and the fractured zone size. As a result, the size of the zone has been estimated to be about ten or more times the borehole radius.     

THERMOELASTIC PROBLEM OF CURVILINEAR CRACK WITH A POINT HEAT SOURCE

Boundary value problems for a circular-arc crack embedded in an infinite medium due to a point heat source are formulated and solved in closed form. Based on the Hilbert problem formulation and a special technique of contour integration, exact solutions of a semicircular crack are obtained in an explicit form. It is found that the thermal stresses or temperature giadient near the tips of a curved crack always possess the characteristic inverse square-root singularity in terms of the radial distance away from the crack tip under the application of a heat source. The simultaneous existence of mode-I and mode-II stress intensity factors are shown in this article to be dependent on the strength of a heat source, heat conductivity, as well as thermal and elastic isotropy. The nonnegative mode-I stress intensity factor is found to be present in this article for the application of the heat sink, which validates the fully open crack assumption.     

全饱和型太阳池的热稳定性条件

对太阳池的一般特征及共工作原理、双扩散系统所遵循的流体力学普遍方程组、具有非恒定的温度和盐浓度梯度的双扩散系统进行介绍，并对全饱和型太阳池的热稳定性条件进行讨论。     

STABILITY OF A PROPAGATING INTERPHASE BOUNDARY IN A THERMOPLASTIC MATERIAL

We study the morphological stability of a propagating planar interphase boundary in a thermoplastic material deformed in antiplane shear. The plane interphase boundary is found to be stable if σ₀/(₄ρcrpar;V₀ ²where c is the specific heat per unit uolume; p is the mass density; V₀is a proagation speed; and σ₀is a function of the material moduli and the state of deformation of the body.     

A NEW MODEL OF FUNCTIONALLY GRADED COATINGS WITH A CRACK UNDER THERMAL LOADING

A new model for fracture analysis oaf functionally graded materials (FGMs) with arbitrarily varying material properties under thermal loading is developed. The FGM is modeled as a multilayered medium and in each layer both shear modulus and thermal conductivity are assumed to be a linear function of the depth and are continuous on the subinterfaces. To make the crack problem tractable, thermal expansion and conductivity of the FGMs are supposed to have the same form. With this new model, the crack problem of a functionally graded coating bonded to a homogeneous substrate under steady-state thermal loading is investigated. Employment of the Fourier integral transform technique reduces the problem to a system of Cauchy singular integral equations that are solved numerically. Thermal stress intensity factors (TSIFs) are obtained for various forms of thermal conductivity or expansion. The results reveal that the present model is very efficient and in the frame of the present model both the form of thermal conductivity/expansion and that of its derivative can influence the TSIFs significantly.     

ON THE EXISTENCE OF GENERALIZED SOLUTIONS FOR THERMALLY INDUCED VIBRATIONS IN A NONHOMOGENEOUS AND NONLINEAR PLATE

The existence of generalized solutions of a nonlinear problem concerning thermally induced vibrations in a nonhomogeneous plate is considered. The boundary conditions are for convenience, assumed to be homogeneous. This corresponds to the physical situation of a clamped plate. The initial conditions are imposed on one function only. The method of dealing with the problem is analogous to that for a homogeneous plate without the influence of temperature. Some lemmas and a theorem are formulated; the theorem asserts that under certain conditions on the temperature there exists at least one generalized solution to the problem.     

A VARIATIONAL FINITE LAYER TECHNIQUE FOR THE INVESTIGATION OF THERMALLY INDUCED STRESS CONCENTRATIONS IN COMPOSITE STRUCTURES

The technical relevance of stress fields near free laminate edges under mechanical and/or hygrothermal loads (“free-edge effect”) has long been recognized. However, the state of stress near free laminate corners (i.e., at corners that are generated by two merging straight free laminate edges) has gone nearly unnoticed in the open literature. To gain further insight into the mechanics of free-corner stress fields (“free-corner effect”), the present contribution is devoted to the closed-form analysis of displacements, strains and stresses in the vicinity of free rectangular corners of symmetric crossply laminates under uniform thermal load by means of a layerwise C⁰-continuous displacement approach. The laminate is discretized into an arbitrary number of mathematical layers through the thickness. However, concerning the two in-plane directions, no discretization is employed, but on the contrary, unknown in-plane functions are assumed that are then determined by application of the principle of minimum potential energy of the laminate. Due to some simplifying prerequisite assumptions concerning the utilized displacement approach and performing a separation of the in-plane variables, the resultant governing Euler–Lagrange equations are ordinary second-order differential equations that can be solved in a closed–form way. Hence, all state variables of the given thermoelastic free-corner problem can be written in a closed-form manner, which makes the present method easily applicable and allows a good insight into the underlying mechanics. Given boundary conditions of traction-free laminate edges are satisfied in an average sense. The present method is easily applicable, requires little computational effort, and is in excellent conformity with accompanying finite element computations. Because the presented approach enables a closed-form analytic formulation with respect to the in-plane coordinates, it is appropriate to designate the methodology as a finite layer technique.