Mechanical and thermal stresses of a functionally graded circular hollow cylinder with finite length

By using a multi-layered approach based on the theory of laminated composites, the solutions of temperature, displacements, and thermal/mechanical stresses in a functionally graded circular hollow cylinder are presented in this paper. The cylinder has finite length and is subjected to axisymmetric thermal and mechanical loads. The material properties are assumed to be temperature-independent and radially dependent, but are assumed to be homogeneous in each layer. As an illustration, the numerical results for a mullite/molybdenum functionally graded circular hollow cylinder are also presented.     

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 σ_θθ.     

A criterion-selection diagram for the thermal shock resistance of a hollow circular cylinder

Abstract

The characteristics of thermally induced failure are investigated for a hollow circular cylinder exposed to a convective cooling at the inner surface. The transient fields of both temperature and thermal stresses are given in closed forms over the full range of Biot number. The thermal shock resistance (TSR) is analyzed based on two distinct failure criteria. Namely, the strength-based failure criterion is adopted for a nearly flaw-free cylinder while the fracture toughness-based one is used for the counterpart with an inner crack-like flaw. From each criterion, the admissible maximum temperature drop is obtained assuring that a hollow cylinder can tolerate without failure. The influence of flaw size on the TSR is quantified and a criterion-selection diagram is proposed for the TSR characterization. These results are deemed to be of importance from the perspective of estimating the TSR of a hollow circular cylinder.     

Axisymmetric thermoelastic analysis in a finite hollow cylinder due to nonuniform thermal shock

An exact solution is obtained for two-dimensional elastodynamic analysis of finite hollow cylinder excited by nonuniform thermal shock. The cylinder is simply-supported at the two ends and is traction-free at the internal and external cylindrical surfaces. Based on the uncoupled linear thermoelastic theory, the solution is developed by employing the expansion of trigonometric series method and the separation of variables technique. The obtained solution contains two infinite series. One is trigonometric function and the other is Bessel function. The coefficients in the series solution are determined by the orthogonal properties of the functions. Numerical experiments are presented for describing the thermal dynamic behaviors of finite hollow cylinder.     

Thermoviscoelastic Dynamic Behavior of a Double-Layered Hollow Cylinder Under Thermal Shocking

In this article, thermoviscoelastic dynamic behavior of a double-layered cylinder with a thermal barrier coating under radially symmetric mechanic and thermal loadings is investigated. The double-layered hollow cylinder is constructed of a viscoelastic layer and a homogenous layer, and the cylinder is subjected to thermal shocking. The material parameters of the cylinder are assumed to be temperature-dependent. The governing equation of the motion of the double-layered hollow cylinder under both dynamic mechanical and thermal loads is obtained based on the plane-stain theory, meanwhile, the transient heat transfer problems are solved by the finite difference method (FDM), Newmark method (NM), and iterative method. Numerical results show that mechanical load, boundary conditions, temperature field and whether considering the viscoelasticity of the inner layer each have a great influence on the dynamic behavior of the double-layered hollow cylinder.     

Thermoelastic analysis of a cylindrical vessel of functionally graded materials

This paper presents a novel method for analyzing steady thermal stresses in a functionally graded hollow cylinder. The thermal and thermoelastic parameters are assumed to arbitrarily vary along the radial direction of the hollow cylinder. The boundary value problem associated with a thermoelastic problem is converted to a Fredholm integral equation. By numerically solving the resulting equation, the distribution of the thermal stresses and radial displacement is obtained. The numerical results obtained are presented graphically and the influence of the gradient variation of the material properties on thermal stresses is investigated. It is found that appropriate gradient can make the distribution of thermal stresses more gentle in the whole structure.     

PUBLICATIONS ON THERMAL STRESSES

This paper is concerned with the theoretical treatment of transient thermoelastic problem involving a functionally graded hollow cylinder due to asymmetrical heating from its surfaces. The thermal and thermoelastic constants of the hollow cylinder are expressed as power functions of the radial coordinate variable. The exact solution for the two-dimensional temperature change in a transient state, and thermal stresses of a hollow cylinder under the state of plane strain is obtained herein. Some numerical results are shown in figures. Furthermore, the influence of the nonhomogeneity of the material upon the temperature change and stresses is investigated.     

STEADY THERMAL STRESSES IN A HOLLOW CIRCULAR CYLINDER AND A HOLLOW SPHERE OF A FUNCTIONALLY GRADIENT MATERIAL

This paper considers the steady thermal stresses in a hollow circular cylinder and a hollow sphere made of a functionally gradient material (FGM). The aim of this research is to understand the effect of the composition on stresses and to design the optimum FGM hollow circular cylinder and hollow sphere. We discuss the influence of inside radius size on stresses and the available temperature regions. We also compare these results with those of a FGM plate.     

Thermal Stresses in a Hollow Cylinder with Convective Boundary Conditions on the Inside and Outside Surfaces

Analytical solutions for thermal stresses (radial, tangential, and axial) in a hollow cylinder with uniform internal heat generation for the thermal boundary condition of convective heating on the inside surface and convective cooling on the outside surface are derived. The analysis assumes the ends of the cylinder to be clamped, the axial strain to be negligible, and the radial stresses on the inside and the outside surfaces to be zero. Results are presented to illustrate the effects of internal heat generation parameter Q, convective environment temperatures ratio θ*, Biot number for convection on the inside surface Bi ₁, Biot number for convection on the outside surface Bi ₂, and the radii ratio ρ on thermal stresses distribution in the cylinder. The analytical solutions should serve as benchmarks for validating the numerical codes for dealing with more complicated cases.     

Development of new analytical solutions for elastic thermal stress components in a hollow cylinder under sinusoidal transient thermal loading

For the analysis of high-cycle thermal fatigue due to striping (such as has been observed due to turbulence at mixing tees of class 1–2–3 piping of nuclear power reactors) it can be necessary to consider the time-dependent temperature gradient within the pipe wall thickness rather than just at the surface. To address this, a set of analytical solutions with several new features has been developed for the temperature field and the associated elastic thermal stress distributions for a hollow circular cylinder subjected to sinusoidal transient thermal loading at the inner surface. The approach uses a finite Hankel transform and some properties of Bessel functions. The analytical predictions have been successfully benchmarked by comparison with results from finite element analysis, and also with some results of independent studies.     

Classical and minimum entropy generation analyses for steady state conduction with temperature dependent thermal conductivity and asymmetric thermal boundary conditions: Regular and functionally graded materials

Minimum entropy generation (MEG) temperature profiles are derived for steady conduction in a plane wall, a hollow cylinder and a hollow sphere and compared with the classical results. Cases of constant thermal conductivity, temperature dependent and location dependent thermal conductivities for each geometry are analyzed. Results are presented for the classical and the minimum entropy temperature profiles illustrating the effect of thermal asymmetry and variable thermal conductivity in each geometry. These results show that the difference between the classical and the MEG temperature profiles is largest when there is a strong thermal asymmetry. For all three geometries, the effect of temperature dependent thermal conductivity on the classical temperatures is moderate but its effect on the MEG temperatures is only small. Both the classical and minimum entropy generation rates, for each geometry, are found to be strong functions of thermal asymmetry and thermal conductivity variation parameter. Comparison of results for a hollow cylinder and a hollow sphere reveals that rate of entropy generation in a hollow sphere is much higher than in a hollow cylinder for the same thermal asymmetry and radius ratio.     

Axisymmetric mechanical and thermal stresses in thick short length FGM cylinders

The exact solution of steady-state two-dimensional axisymmetric mechanical and thermal stresses for a short hollow cylinder made of functionally graded material is developed. Temperature, as functions of radial and longitudinal directions, is solved analytically, using the generalized Bessel function. A standard method is used to solve a non-homogeneous system of partial differential Navier equations with non-constant coefficients, using Fourier series, rather than potential functions method.     

Magnetothermostress Wave Propagation and Perturbation of Magnetic Field Vector in an Orthotropic Laminated Hollow Cylinder

An analytical method is developed to determine the transient response of magneto-thermostress and perturbation of the magnetic field vector produced in orthotropic laminated hollow cylinders subjected to thermal shock, and permeated by a primarily uniform magnetic field. A magnetothermostress equation for each separate hollow cylinder is found by making use of a series of simply mathematical transform. Then, by using the interface continuity conditions between layers and the boundary conditions at the internal and external surfaces of the orthotropic laminated hollow cylinders, the unknown constants involved are determined. Thus, an exact expression for the magnetothermostress wave propagation and the perturbation response of magnetic field vector in the orthotropic laminated hollow cylinders are obtained. From sample numerical calculations, some characters of magnetothermodynamic stresses and perturbation of magnetic field vector in orthotropic laminated hollow cylinders are revealed and discussed.     

汽轮机转子温度场和热应力的动态分析

将空心的汽轮机转子简化成长圆筒壁模型,在一定的假设条件下得到了描述其导热特性的微分方程。利用复频域分析方法求解了长圆筒壁的一维动态导热特性,并根据热弹性理论得到了转子温度场和热应力的传递函数。进而对内表面绝热、外表面为阶跃温度输入和内、外表面都为阶跃温度输入的两种情况下转子温度场和热应力的变化进行了计算和分析。计算结果表明,采用对转子内、外表面同时加热或冷却的方法,能够在不增加热应力的条件下,加速转子达到温度平衡状态,有利于缩短汽轮机组的开停机时间,并提高跟踪机组负荷变化的灵活性。     

Asymmetric mechanical and thermal stresses in 2D-FGPPMs hollow cylinder

The general solution of steady-state asymmetric mechanical and thermal stresses of a hollow thick cylinder made of fluid-saturated functionally graded porous piezoelectric materials based on two-dimensional equations of thermoelasticity is considered. The general form of thermal and mechanical boundary conditions is considered on the inside and outside surfaces. A direct method is used to solve the heat conduction equation and the nonhomogeneous system of partial differential Navier equations, using the complex Fourier series and the power law functions method. The material properties are assumed to depend on the radial and circumferential variables and are expressed as power law functions along the radial and circumferential direction.     

Simulation of thermal stresses in anode-supported solid oxide fuel cell stacks. Part II: Loss of gas-tightness, electrical contact and thermal buckling

Structural stability issues in planar solid oxide fuel cells arise from the mismatch between the coefficients of thermal expansion of the components. The stress state at operating temperature is the superposition of several contributions, which differ depending on the component. First, the cells accumulate residual stresses due to the sintering phase during the manufacturing process. Further, the load applied during assembly of the stack to ensure electric contact and flatten the cells prevents a completely stress-free expansion of each component during the heat-up. Finally, thermal gradients cause additional stresses in operation.The temperature profile generated by a thermo-electrochemical model implemented in an equation-oriented process modelling tool (gPROMS) was imported into finite-element software (ABAQUS) to calculate the distribution of stress and contact pressure on all components of a standard solid oxide fuel cell repeat unit.The different layers of the cell in exception of the cathode, i.e. anode, electrolyte and compensating layer were considered in the analysis to account for the cell curvature. Both steady-state and dynamic simulations were performed, with an emphasis on the cycling of the electrical load. The study includes two different types of cell, operation under both thermal partial oxidation and internal steam-methane reforming and two different initial thicknesses of the air and fuel compressive sealing gaskets.The results generated by the models are presented in two papers: Part I focuses on cell cracking. In the present paper, Part II, the occurrences of loss of gas-tightness in the compressive gaskets and/or electrical contact in the gas diffusion layer were identified. In addition, the dependence on temperature of both coefficients of thermal expansion and Young's modulus of the metallic interconnect (MIC) were implemented in the finite-element model to compute the plastic deformation, while the possibilities of thermal buckling were analysed in a dedicated and separate model.The value of the minimum stable thickness of the MIC is large, even though significantly affected by the operating conditions. This phenomenon prevents any unconsidered decrease of the thickness to reduce the thermal inertia of the stack. Thermal gradients and the shape of the temperature profile during operation induce significant decreases of the contact pressure on the gaskets near the fuel manifold, at the inlet or outlet, depending on the flow configuration. On the contrary, the electrical contact was ensured independently of the operating point and history, even though plastic strain developed in the gas diffusion layer.     

Transient thermal stress analysis of a functionally graded thick hollow cylinder with temperature-dependent material properties

This article deals with the study of temperature distribution and thermal stresses of a functionally graded thick hollow cylinder with temperature dependent material properties. All the material properties except Poisson’s ratio are assumed to be dependent on temperature and spatial coordinate z. The two-dimensional transient heat conduction equation is solved under convective heat transfer condition with varying point heat source. The influence of inhomogeneity parameters on the thermal and mechanical behavior is examined. Numerical computations are performed for ceramic-metal-based functionally graded material, in which alumina is selected as ceramic and nickel as metal.     

THERMOELASTIC POTENTIAL FUNCTIONS IN TRANSVERSELY ISOTROPIC SOLIDS AND THEIR APPLICATIONS

An explicit solution composed of two thermoelastic potential functions is proposed in cylindrical coordinates and is applied to an analysis for steady-state, axially asymmetric thermal stresses in a long hollow cylinder. The solution is obtained with no assumptions of temperature fields. The temperature and stress fields in the long hollow cylinder made of magnesium are analyzed for the sake of application of the solution.     

Mechanical and thermal stresses in a functionally graded hollow cylinder due to radially symmetric loads

In this paper, a general analysis of one-dimensional steady-state thermal stresses in a hollow thick cylinder made of functionally graded material is developed. The temperature distribution is assumed to be a function of radius, with general thermal and mechanical boundary conditions along the inside and outside surfaces. The material properties, except Poisson's ratio, are assumed to depend on variable the r and they are expressed as power functions of r. The direct method is used to solve the heat conduction and Navier equations.