THERMAL STRESSES IN A FLAT PLATE SUBJECTED TO CONVECTIVE HEATING INDUCED BY PIECEWISE LINEAR VARIATION OF AMBIENT TEMPERATURE

The problem of determining the stress state in a plate subjected to a thermal transient is often encountered in engineering practice. Available solutions are limited to special cases and are not easy to use. The aim of this work is to provide a simple tool for stress and strain calculations due to piecewise linear variation of ambient temperature. A variational approach is applied to obtain approximate temperature and stress distributions within the plate in a simple analytic form. Stress diagrams derived from the exact temperature distribution are used to assess the accuracy of the method. The method is finally used to determine the magnitude of thermal stresses induced by thermal cycling. The results are shown to be in agreement with those of previous studies     

ROLE OF ABSORPTION COEFFICIENT IN THE FREQUENCY DEPENDENCE OF THE THERMAL STRESSES IN A PARTIALLY ABSORBING PLATE SUBJECTED TO CYCLIC THERMAL RADIATION: A BRIEF NOTE

The frequency dependence of the thermal stresses in a partially absorbing plate subjected to cyclic thermal radiation is shown to be a function of optical thick ness.     

ANALYSIS OF THERMAL STRESSES IN A FLAT PLATE SUBJECTED TO CONDUCTIVE HEAT TRANSFER WITH THERMAL BOUNDARY CONDUCTANCE

An analysis is presented of the effect of a finite boundary conductance on the magnitude of the thermal stresses in a flat plate subjected to symmetric and asymmetric conductive heat transfer from an infinite, mechanically noninteracting medium.     

TRANSIENT THERMAL STRESSES IN A THIN ELASTIC PLATE DUE TO A RAPID DUAL-PHASE-LAG HEATING

Thermal stresses generated within a thin plate as a result of a fast heating rate are investigated numerically using the dual-phase-lag heat conduction model. The quantitative and qualitative predictions of the dual-phase-lag model for the thermal stresses are compared with the predictions of the diffusion (parabolic) and wave (hyperbolic) heat conduction models. It is found that the predictions of the three models differ in the early stages of the heating process and then give almost the same predictions as they approach the steady-state limit.     

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.     

THERMAL STRESSES IN A LONG CIRCULAR CYLINDER SUBJECTED TO SUDDEN COOLING DURING TRANSIENT CONVECTION HEATING

An analysis is presented of the thermal stresses encountered during cooling of a solid circular cylinder initially heated from uniform temperature by Newtonian convection, followed by sudden cooling prior to reaching thermal equilibrium during the heating phase of the cycle. The numerical results indicate that the magnitude of the stresses attained during the cooling phase increases with increasing duration of heating, but are less than the corresponding values encountered for convective cooling from a condition of initial uniform temperature. The relevance of these results to the prediction or interpretation of thermal fatigue behavior is noted.     

THERMAL STRESSES IN PARTIALLY ABSORBING FLAT PLATE DUE TO SUDDEN INTERRUPTION OF STEADY-STATE ASYMMETRIC RADIATION,II: CONVECTIVE COOLING AT FRONT SURFACE

In Part II of this study the thermal stresses are analyzed in a partially absorbing flat plate, due to a sudden interruption of steady-state asymmetric radiation on the convectively cooled front face. As in the case of Part I, the maximum tensile stresses occur in the rear face. For the optical thickness μa ≥ 0.5, the maximum tensile stress initially rises to a peak and then decreases with time. On the other hand, for μa ≤ 0.5, the stresses decrease monotonically with time.

A comparison of the results for the front (Part II) and rear (Part I) cooling indicates that values of the maximum stress are numerically indentical for small values of heat transfer coefficient h, and plate thickness a. Increasing difference in the magnitude of the stresses for the two cases is found with increasing h and a.     

THERMAL STRESSES IN A PARTIALLY ABSORBING FLAT PLATE SYMMETRICALLY HEATED BY THERMAL RADIATION AND COOLED BY CONVECTION

The stresses due to “thermal trapping” of internally absorbed radiation in solid materials are analyzed for a flat plate symmetrically heated by radiation and cooled by convection for finite values of the heat transfer coefficient. The thermal-stress state consists of an initial transient followed by a steady-state stress at t -> ∞ and involves a reversal in the sign of the stresses. The maximum value of the transient stress increases with optical thickness, whereas the maximum value of the steady-state stress occurs at an optical thickness μa = 1·3 with zero stresses at μa. = 0 and ∞.     

THERMAL STRESSES IN PARTIALLY ABSORBING FLAT PLATE DUE TO SUDDEN INTERRUPTION OF STEADY-STATE ASYMMETRIC RADIATION,I: CONVECTIVE COOLING AT REAR SURFACE

An analysis is presented of the thermal stresses in a partially absorbing flat plate due to sudden interruption of steady-state asymmetric thermal radiation on the front face with convection cooling at the rear face. Maximum transient tensile stresses occur in the rear surface and are almost independent of the heat transfer coefficient, h. For optical thicknesses of ≥ 0.5 μa, the maximum tensile stress initially rises to reach a peak and then decreases with time. In contrast, for thicknesses ≤ 0.5 μa, the stresses decrease monotonically. It is shown that a plot of nondimensional stress as a function of nondimensional time for a given value of pa and h does not result in a universal plot from which thermal stresses can be obtained for any value of plate thickness.     

THERMAL STRESSES IN A PARTIALLY ABSORBING FLAT PLATE ASYMMETRICALLY HEATED BY CYCLIC THERMAL RADIATION AND COOLED BY CONVECTION

Abstract

An analysis is presented for the temperatures and thermal stresses in a partially absorbing flat plate subjected to normally incident cyclic thermal radiation on the front face, and cooled by convection on the rear face.

The resulting temperature and stress responses are cyclic in nature, with the temperatures and stresses in the center and the back face lagging behind those in the front face. The amplitude of the temperature fluctuation is found to be a maximum in the front face. During the initial thermal cycles the maximum stress in the plate is compressive. In contrast, when the plate approaches thermal equilibrium after many cycles, the maximum stress is tensile. The values of the maximum tensile and compressive stresses were found to depend on the frequency of the incident cyclic radiation.     

THERMAL STRESSES IN A PARTIALLY ABSORBING FLAT PLATE ASYMMETRICALLY HEATED BY CYCLIC THERMAL RADIATION AND COOLED BY CONVECTION: ADDENDUM

This article is devoted to model and analyze the transverse deflection and thermal moment of transverse vibrations in a transversely isotropic, thermo-elastic beam resonator under the action of time harmonic concentrated load. The governing equations of flexural vibrations and thermal moment in a transversely isotropic, thermo-elastic Euler–Bernoulli beam have been derived in a closed form. A time harmonic point load is assumed to act on the beam at a given distance from the origin. The beam is assumed to be at either clamped-clamped (CC), simply supported-simply supported (SS), clamped-simply supported (CS), or clamped-free (CF) conditions at its ends. The Laplace transform technique has been used to find the transverse deflection and thermal moment in the transform domain due to the action of concentrated load in a beam under above conditions in case of both free and forced vibrations. The analytic expressions obtained in the physical domain after inversion of Laplace transforms have been computed numerically with the help of MATLAB software for silicon material beam. The results for coupled thermo-elastic, elastic, and isotropic beams have been deduced as special cases. The computer-simulated results have been presented graphically. The study may find applications in development and design of resonators (sensors), precision thermometers, and energy harvesters.     

EDGE-CRACKED PLATE WITH ONE FREE AND ONE CONSTRAINED BOUNDARY SUBJECTED TO SUDDEN CONVECTIVE COOLING

The transient thermal stress edge crack problem for an elastic strip with free and fully constrained boundaries is considered. The plate is suddenly subjected to convective cooling on the face containing the edge crack while the other face is insulated. The solution of the problem is obtained by using the superposition technique results in a singular integral equation that is solved numerically. The results of the transient temperature and thermal stress distributions in the uncracked strip are presented. Also, numerical results are obtained for the stress-intensity factor in terms of the Fourier number, crack length, and different values of the Biot number.     

新型平板式太阳能冷热联供装置

在积累了太阳固体吸附式制冷循环研究的基础上，与现有的平板式太阳热水器制造技术紧密结合，提出了平板式太阳冷热联供循环方式，并在实验室内成功地制作了实物样机。该装置能有效地回收太阳固体吸附式制冷不中吸附床的显热及吸附热，且操作简便。实验结果有效地支持了所提出的设想，为太阳固体吸附式制冷的实用化应用打下了良好基础。     

A THERMOELASTOPLASTIC SOLUTION FOR A CIRCULAR SOLID CYLINDER SUBJECTED TO HEATING AND COOLING

Abstract

This paper presents a theoretical study of the stresses in an infinite circular solid cylinder subjected to rapid surface heating and cooling. A quasistatic, uncoupled, thermoelastoplastic analysis based on the incremental theory of plasticity is formulated, and a numerical procedure is developed for a method of successive elastic solutions. The material of the cylinder is assumed to have temperature-dependent properties and to be characterized by the Romberg-Osgood stress-strain relation. The transient and residual stress distributions are discussed in detail, along with variations of the equivalent stress and plastic strain with time.     

ANALYSIS OF THERMAL STRESSES IN A SOLID CIRCULAR CYLINDER SUBJECTED TO CONDUCTIVE HEAT TRANSFER WITH THERMAL BOUNDARY CONDUCTANCE

An analysis is presented of the effect of a finite boundary conductance on the magnitude of the thermal stresses in a solid circular cylinder, subjected to conductive heat transfer from an infinite mechanically noninteracting surrounding medium.     

BEHAVIOR OF THERMAL STRESSES IN A RAPIDLY HEATED THIN PLATE

Using the hyperbolic heat conduction model, thermal stresses generated within a rapidly heated thin metal plate are investigated numerically. The effects of different parameters such as the form, duration, amplitude, and penetration depth of the heating source on the temperature, thermal moment, deflection, and thermal stresses are studied. It is found that under ultra-fast heating of very thin plates, the hyperbolic heat conduction model must be adopted to model the thermal behavior.     

THERMOELASTIC VIBRATIONS OF A LAMINATED RECTANGULAR PLATE SUBJECTED TO A THERMAL SHOCK

In this work the response of a rectangular, simply supported, symmetrically laminated, cross-ply composite plate subjected to a thermal shock is developed. The analysis includes the interaction between the strain and temperature fields and investigates the effect of accounting for the orthotropic material properties in the governing elastic and thermal equations. The resulting solution for the vibration of the plate is compared to a previous analysis of a homogeneous, isotropic, rectangular plate. Comparison indicates that while the solutions have similar forms, there are two key quantitative differences between them.     

TRANSIENT VARIATIONS OF THERMAL STRESSES AND THE RESULTING RESIDUAL STRESSES WITHIN A THIN PLATE DURING WELDING PROCESSES

Variations of thermal and residual stresses are investigated inside a thin mild steel plate during welding processes. The temperature distribution is determined analytically using Green's functions. Transient thermal stresses developed within the plate are computed numerically. The resulting residual stresses, which remain after cooling of the plate, are found based on a method presented originally by Tall (L. Tall, Welding Journal, vol. 43, pp. 10–23, 1964). It is found that welding speed and heat source intensity are the main factors that affect the residual stress formation in the plate.     

TRANSIENT THERMAL STRESSES IN A RECTANGULAR PLATE DUE TO NONUNIFORM HEAT TRANSFER COEFFICIENTS

Abstract

The linear problems of transient temperature and thermal stresses in a thin, finite, rectangular plate subjected to heat losses due to nonuniform heat transfer coefficients on the upper and lower plate surfaces are solved by a direct power series approach through the application of the Lanczos-Chebyshev and the discrete least-squares methods. A numerical example demonstrates the accuracies that can be achieved by using only a small number of terms.     

TWO-CRACK PROPAGATION PATHS IN A FUNCTIONALLY GRADED MATERIAL PLATE SUBJECTED TO THERMAL LOADINGS

Two-crack propagation paths in a ceramic/metal functionally graded material plate (FGP) under one-cycle temperature change of heating and cooling are considered. When the FGP is subjected to thermal shock, a single crack or multiple cracks often initiate on the ceramic surface during the cooling process and propagate in the FGP. Crack paths are influenced by the heating temperature conditions, a compositional profile of the FGP, the fracture toughness, interaction among multiple cracks, and so on. Transient thermal stresses are treated as a linear quasi-static thermoelastic problem for a plane-strain state. The crack paths are treated under fracture mechanics using the finite-element method. The effects of heating temperature conditions, a compositional profile of the FGP, the fracture toughness, and a crack space on the crack propagation pattern are discussed and are shown in figures.