Transient Thermal Stress Problem Research Articles

Review Paper on Green’s Function- A Mathematical Approach for Investigation of Thermal Stresses in Steam Turbine Rotor

In online systems, a numerical technique based on Green’s function for estimating and analyzing thermal stresses subjected to transient conditions proved to be effective. The need for utility power plants to have great operating flexibility necessitates the use of online systems for controlling and monitoring damage to important components, such as steam turbine rotors. Different data and mathematical models are used in such systems to calculate thermal stresses and manage them continuously. Thermal fatigue is becoming more of a worry in power plant workers as the trend toward “two-shifting” operating methods grows. Thermal power plants are anticipated to be a form of energy mix for the near future when they’re under pressure from society to produce in a more efficient and flexible manner.For transient thermal stress problems, Green’s function approach offers a flexible approach for assessing benchmark elastic answers. Green’s functions (deduced using finite element unit temperature phase answers) are frequently believed to be independent of temperature in order to ease integration. During startup, the turbine shafts of coal power plants are subjected to significant stresses caused by high pressures and temperatures. Thermal gradients approach the design threshold at the very same time that steam temperatures via components quickly transition from minimum to maximum temperature, reducing the rotor’s useful lifetime. Thermal property assessments predicated on relatively stable heating are implicit procedures wherein the temperature-dependent properties and characteristics are determined by comparing the experimental results with heat-transfer concept.

Stochastic transient analysis of thermal stresses in solids by explicit time-domain method

Stochastic heat conduction and thermal stress analysis of structures has received considerable attention in recent years. The propagation of uncertain thermal environments will lead to stochastic variations in temperature fields and thermal stresses. Therefore, it is reasonable to consider the variability of thermal environments while conducting thermal analysis. However, for ambient thermal excitations, only stationary random processes have been investigated thus far. In this study, the highly efficient explicit time-domain method (ETDM) is proposed for the analysis of non-stationary stochastic transient heat conduction and thermal stress problems. The explicit time-domain expressions of thermal responses are first constructed for a thermoelastic body. Then the statistical moments of thermal displacements and stresses can be directly obtained based on the explicit expressions of thermal responses. A numerical example involving non-stationary stochastic internal heat generation rate is investigated. The accuracy and efficiency of the proposed method are validated by comparison with the Monte-Carlo simulation.

Transient thermal stress analysis for a circumferentially cracked hollow cylinder based on memory-dependent heat conduction model

A newly proposed memory-dependent heat conduction model is applied to investigate the transient thermal stress problem of a hollow cylinder containing an embedded internal or surface circumferential crack. The cylindrical system is subjected to thermal shock at the inner surface and with an insulated outer surface. Laplace integral transform is adopted to obtain the analytical solutions for temperature and thermal stress field in an un-cracked hollow cylinder. Then based on the superposition method, the axial stress with minus sign is applied on the crack surface to form a mode I crack problem. Integral transform techniques are employed to reduce the mixed boundary value problem to a singular integral equation. Finally, the effects of time delay, kernel function and crack geometry on the transient temperature, thermal axial stress and thermal stress intensity factors are analyzed for embedded internal and surface cracks. The results show that the thermal stress state at the crack tip is different when the three parameters take different values, which is important to make predictions regarding the stability of crack growth, thermal fatigue life, etc.

Transient thermal stresses of annulus elliptical plate with mixed-type boundary conditions.

In this paper, we deal with transient thermal stress problem of an annulus elliptical plate subjected to internal heat source with mixed-type boundary conditions. The solution of conductivity equation and the corresponding initial and boundary conditions are obtained by employing anew integral transform technique.The governing equation for small deflection is found and utilized to find intensities of thermal bending moments and twisting moments, etc. involving Mathieu and modified functions and their derivatives. The analytical solution for the thermal stress components are obtained in terms of resultant forces and resultant moments, and same are illustrated graphically.

A Comparison of Simple Methods to Incorporate Material Temperature Dependency in the Green's Function Method for Estimating Transient Thermal Stresses in Thick-Walled Power Plant Components.

The threat of thermal fatigue is an increasing concern for thermal power plant operators due to the increasing tendency to adopt “two-shifting” operating procedures. Thermal plants are likely to remain part of the energy portfolio for the foreseeable future and are under societal pressures to generate in a highly flexible and efficient manner. The Green’s function method offers a flexible approach to determine reference elastic solutions for transient thermal stress problems. In order to simplify integration, it is often assumed that Green’s functions (derived from finite element unit temperature step solutions) are temperature independent (this is not the case due to the temperature dependency of material parameters). The present work offers a simple method to approximate a material’s temperature dependency using multiple reference unit solutions and an interpolation procedure. Thermal stress histories are predicted and compared for realistic temperature cycles using distinct techniques. The proposed interpolation method generally performs as well as (if not better) than the optimum single Green’s function or the previously-suggested weighting function technique (particularly for large temperature increments). Coefficients of determination are typically above , and peak stress differences between true and predicted datasets are always less than 10 MPa.

Transient Thermal Stress Problem of a Functionally Graded Magneto-Electro-Thermoelastic Hollow Cylinder Due to a Uniform Surface Heating

This article is concerned with the theoretical analysis of the functionally graded magneto-electro-thermoelastic hollow cylinder due to uniform surface heating. We analyze the transient thermal stress problem for a functionally graded hollow cylinder constructed of the anisotropic and linear magneto-electro-thermoelastic materials using a laminated composite model as one of theoretical approximation under a plane strain state. As an illustration, we carry out numerical calculations for a functionally graded hollow cylinder constructed of piezoelectric and magnetostrictive materials and examined the behaviors in the transient state. We investigate the effects of the nonhomogeneity of material on the stresses, electric potential, and magnetic potential, and the effect of the applied electric potential on the thermal stress σθθ.

OS1703 集光太陽放射を受ける組合せ平板の非定常熱伝導・熱応力問題

OS1703 集光太陽放射を受ける組合せ平板の非定常熱伝導・熱応力問題

Transient Thermal Stress Problem of a Functionally Graded Magneto-Electro-Thermoelastic Hollow Sphere.

This article is concerned with the theoretical analysis of the functionally graded magneto-electro-thermoelastic hollow sphere due to uniform surface heating. We analyze the transient thermoelastic problem for a functionally graded hollow sphere constructed of the spherical isotropic and linear magneto-electro-thermoelastic materials using a laminated composite mode as one of theoretical approximation in the spherically symmetric state. As an illustration, we carry out numerical calculations for a functionally graded hollow sphere constructed of piezoelectric and magnetostrictive materials and examine the behaviors in the transient state. The effects of the nonhomogeneity of material on the stresses, electric potential, and magnetic potential are investigated.

Exact solution of transient thermal stress problem of a multilayered magneto-electro-thermoelastic hollow sphere

This paper presents the theoretical analysis of a multilayered magneto-electro-thermoelastic hollow sphere under unsteady and uniform surface heating. We obtain the exact solution of the transient thermal stress problem of the multilayered magneto-electro-thermoelastic hollow sphere in the spherically symmetric state. As an illustration, we perform numerical calculations of a two-layered composite hollow sphere made of piezoelectric and magnetostrictive materials and investigate the numerical results for temperature change, displacement, stress, and electric and magnetic potential distributions in the transient state are shown in figures.

Transient thermal stress analysis of a functionally graded magneto-electro-thermoelastic strip due to nonuniform surface heating

This article is concerned with the theoretical analysis of the functionally graded magneto-electro-thermoelastic strip due to unsteady and nonuniform surface heating in the width direction. We analyze the transient thermal stress problem for a functionally graded strip constructed of the anisotropic and linear magneto-electro-thermoelastic materials using a laminated composite mode as one of theoretical approximation. The transient two-dimensional temperature is analyzed by the methods of Laplace and finite sine transformations. We obtain the solution for the simply supported and functionally graded magneto-electro-thermoelastic strip under a plane strain state. As an illustration, we carried out numerical calculations for a functionally graded strip composed of piezoelectric BaTiO 3 and magnetostrictive CoFe 2O 4, and examined the behaviors in the transient state for temperature change, stress, electric potential and magnetic potential distributions. Furthermore, the effects of the nonhomogeneity of material on the stresses, electric potential, and magnetic potential are investigated.

Transient Thermoelastic Problem for a Laminated Composite Hollow Sphere with an Interlayer of Functionally Graded Material

This paper is concerned with theoretical treatment of transient thermal stress problem involving a laminated composite hollow sphere with an interlayer of functionally graded material. The thermal and thermoelastic constants of the interlayer are expressed as power function of the radial coordinate variable. We obtain the exact solution for the one-dimensional temperature change, and thermal stresses of a hollow sphere. The numerical calculations are carried out for functionally graded materials composed of alumina and aluminum alloy. Some numerical results for the temperature change, the displacement and the stress distributions are shown. Furthermore, the influence of the thickness of the interlayer is investigated.

Transient Thermoelastic Analysis for a Laminated Composite Strip with an Interlayer of Functionally Graded Material

This paper is concerned with the theoretical treatment of transient thermal stress problem involving a laminated composite thick strip with an interlayer of functionally graded material due to nonuniform heat supply in the width direction. The thermal and thermoelastic constants of the interlayer of functionally graded material are assumed to vary exponentially in the thickness direction. We obtain the exact solution for the two-dimensional temperature change in a transient state, and thermal stresses of a simple supported strip under the state of plane strain. Some numerical results for the temperature change, the displacement and the stress distributions are shown in figures. Furthermore, the influence of the thickness and position of the interlayer is investigated.

Transient thermal stress intensity factors for an internal longitudinal semi-elliptical crack in a thick-walled cylinder

In this paper, the stress intensity factors are derived for an internal semi-elliptical crack in a thick-walled cylinder subjected to transient thermal stresses. First, the problem of transient thermal stresses in a thick-walled cylinder is solved analytically. Thermal and mechanical boundary conditions are assumed to act on the inner and outer surfaces of the cylinder. The quasi-static solution of the thermoelasticity problem is derived analytically using the finite Hankel transform and then, the stress intensity factors are extracted for the deepest point and the surface points of the semi-elliptical crack using the weight function method. The results show to be in accordance with those cited in the literature in the special case of steady-state problem. Using the closed-form relations extracted for the transient thermal stress intensity factors, some conclusive results are drawn.

Multiple axial cracks in a coated hollow cylinder due to thermal shock

The transient thermal stress problem of an inner-surface-coated hollow cylinder with multiple pre-existing surface cracks contained in the coating is considered. The transient temperature, induced thermal stress, and the crack tip stress intensity factor (SIF) are calculated for the cylinder via finite element method (FEM), which is exposed to convective cooling from the inner surface. As an example, the material pair of a chromium coating and an underlying steel substrate 30CrNi2MoVA is particularly evaluated. Numerical results are obtained for the stress intensity factors as a function of normalized quantities such as time, crack length, convection severity, material constants and crack spacing.

3650 一様表面加熱を受けるアングルプライ積層中空円筒の非定常熱弾性解析(S24-3 非定常応答(2),S24 数理・数値解析による先端材料評価)

This paper is concerned with the theoretical treatment of transient thermal stress problem involving an angle-ply laminated hollow cylinder due to uniformly distributed heating. The one-dimensional solution for the temperature change in a transient state, and thermoelastic response of an angle-ply laminated hollow cylinder is obtained herein. As an example, numerical calculations are carried out for a 2-layered angle-ply laminated hollow cylinder made of. Some numerical results for the temperature change, the displacement and the stress distributions in a transient state are shown.

Thermal shock analyses for a strip containing an infinite row of periodically distributed cracks normal to its edge

The transient thermal stress problem of a semi-infinite plate containing an infinite row of periodically distributed cracks normal to its edge is investigated in this paper. The elastic medium is assumed to be cooled suddenly on the crack-containing edge. By the superposition principle, the formulation leads to a mixed boundary value problem, with the negating tractions arisen from the thermal stresses for a crack-free semi-infinite plate. The resulting singular integral equation is solved numerically. The effects on the stress intensity factors due to the presence of periodically distributed cracks in a semi-infinite plate are illustrated. For both the edge crack and the embedded crack arrays, the stress intensity factors increase, due to the reduction of the shielding effect, as the stacking cracks are more separated. For the case of embedded crack array, one has the further conclusion that the stress intensity factors decline as the crack array shifts from the plate edge.

Optimization of Heat-Transfer Coefficient Distribution for Relaxation of Thermal Stress in a Rotating Disk by Genetic Algorithm

Heat-transfer coefficient distributions on both surfaces of a rotating disk are optimized to minimize Mises equivalent thermal stress by the combined use of genetic algorithm and analytical solutions to transient heat conduction and thermal stress problems in the rotating disk subjected to local heat generation near the outer radius. The transient temperature field in the rotating disk with arbitrary, radial change in the heat-transfer coefficient distribution is analyzed by the application of Vodicka's method. The optimized heat-transfer coefficient distributions show three patterns of distribution depending on the heat-transfer coefficient on the outer radius, the disk thickness and the area of the heat generation. Furthermore, it is discussed whether it is possible to realize the optimized heat-transfer coefficient distributions or not.

517 加熱・冷却過程における傾斜機能円筒パネルの非定常熱応力解析(内側加熱の場合)(OS-4 熱弾性・等温弾性(1))

This study is concerned with the theoretical treatment of transient thermal stress problem involving functionally graded cylindrical panel under heated and cooled processes. We obtain the approximate solution for two-dimensional temperature change in a transient state, and thermal stress of simple supported cylindrical panel under the state of plane strain. As an example, numerical calculations are carried out for a functionally graded material of aluminum alloy/alumina, and the behaviors are examined from the initial state of heating to the steady state of the cooled process under inner heating.

918 円周方向に非一様加熱を受ける傾斜機能円筒パネルの非定常熱応力解析

This study is concerned with the theoretical treatment of transient thermal stress problem involving functionally graded cylindrical panel under nonuniform heat supply in the circumferential direction. We obtain the approximate solution for two-dimensional temperature change in a transient state, and thermal stress of simple supported cylindrical panel under the state of plane strain. As an example, numerical calculations are carried out for functionally graded materials, and the numerical results obtained by approximate solution and exact solution are compared.

514 熱放射と物性値の温度依存性を考慮した傾斜機能平板の非定常熱弾性解析

This paper is concerned with the theoretical analysis of transient thermal stress problem of the functionally graded plate with temperature-dependent material properties taking into account the thermal radiation. We analyze the thermoelastic problem by means of the theory of laminated composites as one of the theoretical approximation. With the aide of a finite difference method for time variable and an iteration method, a semi-analytical solution can be obtained. Some numerical results for temperature change and stress distributions in a transient state are shown in figures. The influence of temperature-dependent material properties and thermal radiation is investigated.