Nonaxisymmetric Thermomechanical Analysis of Functionally Graded Hollow Cylinders

Analytical solutions for nonaxisymmetric, thermomechanical response of functionally graded hollow cylinders are obtained in this article. The hollow cylinders are assumed to be subjected to nonaxisymmetric mechanical and transient thermal loads. Properties of functionally graded material are considered as temperature-independent and continuously varying in radial direction. Employing complex Fourier series and Laplace transform techniques, analytical solutions of time-dependent temperature and thermomechanical stresses are obtained. Numerical values of temperature and stresses of a FGM hollow cylinder under assumed thermomechanical loads are presented in graphical form.     

Transient Thermo-Mechanical Analysis of Functionally Graded Hollow Circular Cylinders

Thermo-mechanical analysis of functionally graded hollow circular cylinders subjected to axisymmetric mechanical and transient thermal loads is carried out in this study. Thermo-mechanical properties of functionally graded materials (FGM) are assumed to be temperature independent and vary continuously in the radial direction of the cylinder. Employing the Laplace transform, the Galerkin method and series method for ordinary differential equations, solutions for the time-dependent temperature and transient thermo-mechanical stresses are obtained. As an example, a molybdenum/mullite FGM with material properties obeying the exponential law is considered. Effects of heat transfer coefficients and gradient parameters of FGM on the time-dependent temperature and transient thermal stresses are discussed in detail.     

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.     

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.     

Effects of electrode particle morphology on stress generation in silicon during lithium insertion

We study the effects of particle morphology and size on stress generation during Li insertion into Si particles using a fully coupled diffusion-elasticity model implemented in a finite element formulation. The model includes electrochemical reaction kinetics through a Butler-Volmer equation, concentration-dependent material properties, and surface elasticity. Focusing on two idealized geometries (hollow spheres and cylinders), we simulate stresses during Li insertion in Si. These systems describe a wide variety of morphologies that have been fabricated and studied experimentally, including particles, nanowires, nanotubes, and porous solids. We find that stresses generated in solid particles during Li insertion decrease as particle radii decrease from μm-scale, but reach a minimum at about 150 nm. Surface stresses then begin to dominate the stress states as the particle size continues to decrease. The minimum occurs at larger radii for hollow particles. We also find that hollow particles experience lower stresses than solid ones, but our results suggest that there is not a significant difference in maximum stress magnitudes for spherical and cylindrical particles. Studying the influence of concentration-dependent elastic moduli we find that while they can significantly influence stress generation for potentiostatic insertion, their role is minimal when surface reaction kinetics are considered.     

Exact and Approximate Solutions of Thermoelastic Stresses in Functionally Graded Cylinders

Thermoelasticity behavior of functionally graded thick hollow cylinders with power law and exponentially variations of material properties versus radius is studied analytically. Temperature, displacement and thermomechanical stress distributions are obtained and discussed. Approximate homogeneous multilayer semi-analytical method is used successfully with adequate accuracy and finite layers. Different combinations of ceramics and metals are checked out for thermoelastic stresses due to high temperature and internal pressure. We conclude that the approximate method is simple and has appropriate results. The effects of high temperature on the stresses are more important than the high internal pressure.     

Magnetothermoelastic creep analysis of functionally graded cylinders

This paper describes time-dependent creep stress redistribution analysis of a thick-walled FGM cylinder placed in uniform magnetic and temperature fields and subjected to an internal pressure. The material creep, magnetic and mechanical properties through the radial graded direction are assumed to obey the simple power law variation. Total strains are assumed to be the sum of elastic, thermal and creep strains. Creep strains are time, temperature and stress dependent. Using equations of equilibrium, stress–strain and strain–displacement a differential equation, containing creep strains, for displacement is obtained. Ignoring creep strains in this differential equation a closed form solution for the displacement and initial magnetothermoelastic stresses at zero time is presented. Initial magnetothermoelastic stresses are illustrated for different material properties. Using Prandtl–Reuss relation in conjunction with the above differential equation and the Norton’s law for the material uniaxial creep constitutive model, the radial displacement rate is obtained and then the radial and circumferential creep stress rates are calculated. Creep stress rates are plotted against dimensionless radius for different material properties. Using creep stress rates, stress redistributions are calculated iteratively using magnetothermoelastic stresses as initial values for stress redistributions. It has been found that radial stress redistributions are not significant for different material properties, however major redistributions occur for circumferential and effective stresses.     

Thermoelastic study of a functionally graded annular fin with variable thermal parameters using semiexact solution

Abstract

In this paper, the thermoelastic behavior of a functionally graded material (FGM) annular fin is investigated. The material properties of the annular fin are assumed to vary radially. The heat transfer coefficient and internal heat generation are considered to be functions of temperature. A closed form solution of nonlinear heat transfer equation for the FGM fin is obtained using the homotopy perturbation method (HPM) which leads to nonuniform temperature distributions within the fin. The temperature field is then coupled with the classical theory of elasticity and the associated thermal stresses are derived analytically. For the correctness of the present closed form solution for the stress field, the results are compared with the ANSYS-based finite element method (FEM) solution. The present HPM-based closed form solution of the stress field exhibits a good agreement with the FEM results. The effect of various thermal parameters such as the thermogeometric parameter, conduction-radiation parameter, internal heat generation parameter, coefficient of variation of thermal conductivity, and the coefficient of thermal expansion on the thermal stresses are discussed. The results are presented in both nondimensional and dimensional form. The dimensional stress analysis discloses the suitability of FGM as the fin material in practical applications.     

Transient stress analysis of sandwich plate and shell panels with functionally graded material core under thermal shock

A finite element formulation for stress analysis of functionally graded material (FGM) sandwich plates and shell panels under thermal shock is presented in this work. A higher-order layerwise theory in conjunction with Sanders’ approximation for shells is used to develop the finite element formulation for transient stress analysis of FGM sandwich panels. The top and the bottom surfaces of FGM sandwich panels are made of pure ceramic and metal, respectively, and core of the sandwich is assumed to be made of FGM. The temperature profile in the thickness direction of the panels is considered to be varying as per the Fourier’s law of heat conduction equation for unsteady state. The heat conduction equations are solved using the central difference method in conjunction with the Crank–Nicolson approach. Transient thermal displacements of the sandwich panels are obtained using Newmark average acceleration method and the transient thermal stresses are obtained using stress–strain relations, subsequently. Results obtained from the present layerwise finite element formulations are first validated with available solutions in literature. Parametric studies are taken up to study the effects of volume fraction index, temperature dependency of material properties, core thickness, panel configuration, geometric and thermal boundary conditions on transient thermal stresses of FGM sandwich plates and shells.     

Influence of aluminum precursors on structure and acidic properties of hollow silica–alumina composite spheres,and their activity for hydrolytic dehydrogenation of ammonia borane

In this study, we investigated the influence of aluminum precursors on structure and acidic properties of hollow silica–alumina composite spheres, as well as their activity for hydrolytic dehydrogenation of ammonia borane. Hollow silica–alumina composite spheres were prepared via the sol–gel method using polystyrene particles as templates. Activities of the hollow spheres prepared using various aluminum precursors for hydrolytic dehydrogenation of ammonia borane were compared. The molar ratios of evolved hydrogen to ammonia borane introduced were 1.0, 2.8, 1.5, and 3.0 in the presence of the hollow spheres prepared using aluminum ethoxide, aluminum isopropoxide, aluminum tributoxide, and aluminum-tri-sec-butoxide, respectively. Hollow spheres prepared using aluminum precursors with branched alkyl groups exhibit more hydrogen evolution than those prepared using aluminum precursors with normal alkyl groups. From the result of solid-state ²⁷Al nuclear magnetic resonance spectra and temperature-programmed desorption of ammonia, 4-coordinated aluminum species are related to Brønsted acid sites, and highly dispersed aluminum species increase the number of Brønsted acid sites.     

Fabrication of hollow metal oxide–nickel composite spheres and their catalytic activity for hydrolytic dehydrogenation of ammonia borane

In this paper, we report an effective approach to the fabrication of hollow titania–nickel composite spheres, hollow zirconia–nickel composite spheres, and hollow silica–nickel composite spheres. In this approach, metal oxide–nickel composite shells were coated on polystyrene particles by the sol–gel method and the polystyrene templates were dissolved subsequently, or even synchronously, in the same medium to form hollow spheres. Neither additional dissolution nor a calcination process was needed to remove the polystyrene templates. The as-prepared hollow metal oxide–nickel composite spheres were characterized by transmission electron microscopy. The catalytic activities of hollow titania–nickel composite spheres, hollow zirconia–nickel composite spheres, and hollow silica–nickel composite spheres for hydrolytic dehydrogenation of aqueous NaBH₄/NH₃BH₃ solution were compared. The evolutions of 64, 58, and 18 mL hydrogen were finished in about 49, 69, and 162 min in the presence of the hollow titania–nickel composite spheres, hollow zirconia–nickel composite spheres, and hollow silica–nickel composite spheres from aqueous NaBH₄/NH₃BH₃ solution, respectively. The molar ratios of the hydrolytically generated hydrogen to the initial NH₃BH₃ both in the presence of hollow titania–nickel composite spheres, hollow zirconia–nickel composite spheres, and hollow silica–nickel composite spheres are 2.8, 2.4, and 0.1 (the theoretical value of 3.0), respectively, indicating that the hollow titania–nickel composite spheres and hollow zirconia–nickel composite spheres show much higher hydrogen evolution rates and the amount of hydrogen evolution via hydrolytic dehydrogenation of ammonia borane than the hollow silica–nickel composite spheres. From the results of ATR-IR spectra, a certain amount of residual PS templates exists in hollow silica–nickel composite spheres, and the amount of the residual PS templates were able to be reduced by increasing the amount of aqueous ammonia solution used for the preparation. The catalytic activity of hollow silica–nickel composite spheres increases when the amount of residual PS templates decreases.     

Effect of anisotropy on axisymmetric dynamic response of thick-walled cylinders

Effect of anisotropy on the free and forced vibration behavior of hollow cylinders under dynamic internal pressure is investigated. The material is assumed to be cylindrically orthotropic. Laplace transform method is used and the inversion into the time domain is performed exactly using calculus of residues. Complex Laplace parameter in the free vibration equation has directly given natural frequencies and the results are listed in tabular form. On the inner surface various axisymmetric dynamic pressures are applied and hoop stresses are presented in the form of graphs for different values of an anisotropy parameter and wall thickness. The anisotropy parameter which essentially indicates the degree of anisotropy is the square root of a modulus ratio defined as the ratio of circumferential modulus to radial modulus. Increasing the anisotropy parameter provides a stress-amplification effect for thick-walled cylinders. Closed-form solutions obtained in the present paper are tractable and they allow for further parametric studies. The anisotropy constant is a useful parameter from a design point of view in that it can be tailored for specific applications to control the stress distribution. The numerical values used are chosen arbitrarily and do not necessarily represent a certain material     

THERMO-ELASTO-PLASTIC STRESSES OF FUNCTIONALLY GRADED MATERIAL PLATE WITH A SUBSTRATE AND A COATING

Functionally graded material (FGM) has an excellent ability to reduce thermal stresses, especially in high-temperature applications such as the international thermo-nuclear experimental reactor (ITER). In the present study, the thermo-elasto-plastic behaviors of a particle-reinforced FGM plate (FGP) with substrate and coating layers are presented in the fabrication process. The thermo-elasto-plastic constitutive equation of a particle-reinforced composite taking temperature change and damage process into consideration is used to calculate the thermo-elasto-plastic stresses. The macroscopic stress components as well as the microscopic stress components are obtained using the temperature-dependent properties of the constituent materials. The FGP consists of the coating layer, the FGM layer, and the substrate layer. The FGM layer is divided into three regions. First, the region near the metal substrate is metal rich; and the metal is considered a matrix, while the ceramic is considered particles. Second, the region near the ceramic coating is ceramic rich, so the materials of the matrix and the particle are opposite those of the first region. Third, the middle region between the previous two regions is metal and ceramic that are perfectly mixed. In the third region the macroscopic analysis is made because the difference between the volume fractions of the ceramic and the metal is so small that it is difficult to consider one of them as a matrix or particles. The substrate and coating effects on the thermo-elasto-plastic stresses and optimal profile of the volume fraction of the ceramic are presented using the finite element method.     

Dynamic Thermoelastic Behavior of a Double-layered Hollow Cylinder with an FGM Layer

In this article, dynamic thermoelastic behavior of a double-layered cylinder with an FGM layer under mechanical and thermal loadings are investigated. The double-layered hollow cylinder is constructed by an FGM layer and a homogenous layer. Utilizing the Finite difference method and Newmark method, the governing equation of the double-layered hollow cylinder under both dynamic mechanical and thermal loads is solved. The accuracy of the approach is validated by comparing the results with the existing analytical ones. Numerical results show that volume exponent of the FGM layer, the thickness ratio of two layers and temperature change have significant effect on the dynamic behaviors of the double-layered hollow cylinder.     

Magneto-Thermo-Elastic Stresses Induced by a Transient Magnetic Field in a Conducting Hollow Circular Cylinder

We investigate the dynamic and quasi-static behavior of magneto-thermo-elastic stresses induced by a transient magnetic field in a conducting hollow circular cylinder. A transient magnetic field defined by an arbitrary function of time acts on the outer surface of the hollow cylinder and parallel to it. The fundamental equations of plane axisymmetrical electromagnetic, temperature and elastic fields are formulated, and solutions for the magnetic field, eddy current, temperature change and dynamic and quasi-static solutions for stresses and deformations are analytically derived in terms of the arbitrary function. The stress solutions are determined to be sums of a thermal stress component caused by eddy current loss and a magnetic stress component caused by the Lorentz force. The case of a magnetic field defined by a smoothed ramp function with a sine-function profile is examined in particular, and the dynamic and quasi-static behavior of the stresses and deformations are numerically calculated.     

Analysis of Thermoelastic Waves in Functionally Graded Hollow Spheres Based on the Green-Lindsay Theory

In this article, the Green–Lindsay theory of thermoelasticity is employed to study the thermoelastic response of functionally graded hollow spheres. This generalized coupled thermoelasticity theory admits the second sound phenomena and depicts a finite speed for temperature wave propagation. The materials of the hollow sphere are assumed to be graded through its thickness in the radial direction while a symmetric thermal shock load is applied to its boundary. The Galerkin finite element method via the Laplace transformation is used to solve the coupled form of governing equations. A numerical inversion of the Laplace transform is employed to obtain the results in time domain. Using the obtained solution, the temperature, displacement, radial stress, and hoop stress waves propagation are studied. Also the material distribution effects on temperature, displacement and stresses are investigated. Finally, the obtained results for the Green–Lindsay theory are compared with the results of classical thermoelasticity theory.     

Investigating the magnetic field effects on thermomechanical stress behavior of thick-walled cylinder with inner FGM layer

In this article, an analytical solution is presented to evaluate the stress field in axisymmetric double-walled cylinder made of functionally graded materials (FGMs) and homogeneous layers subjected to pressure, temperature gradient, and magnetic field loadings. Closed form expressions for radial and circumferential stresses as well as the normalized effective stresses are extracted through solving the governing differential equations. It is concluded that both magnetic field and grading indices of FGM have significant effects on the stress distribution in the cylinder, while the proper parameters setting will result into considerable reduction in the stress quantities.     

THERMALLY INDUCED STRESS WAVES IN FUNCTIONALLY GRADED MATERIALS WITH TEMPERATURE-DEPENDENT MATERIAL PROPERTIES

This article is concerned with the dynamic treatment of thermally induced stress waves in an infinite elastic plate subjected to impulsive electromagnetic radiation. The plate is assumed to be a functionally graded material (FGM), meaning that the material is composed of multiconstituents in ceramics and metals, the volume fractions of which distribute continuously inside the material. The mathematical problem is one of wave propagation in a typical nonhomogeneous material The radiation absorption is assumed to occur at a constant rate for the duration of the pulse and to diminish exponentially with distance from the surface of the plate, assuming negligible heat conduction. In treating problems, the nature of the stress-wave buildup in the plate is studied for the case of a temperature-dependent solid, that is, when material properties vary with temperature. The numerical procedure employs the characteristic method based on the integration of the governing equations along the characteristics. Numerical calculations are carried out for ceramic-metal FGM plates showing the influences of the temperature-dependent material properties and the volume fractions of the phases composing the FGM on the magnitude of the dynamic thermal stresses.     

ON AXISYMMETRIC THERMAL STRESSES IM AN ANISOTROPIC HOLLOW CYLINDER

Abstract

This paper deals with the problem of thermal stresses in a hollow anisotropic cylinder of finite extent arising from axisymmetric temperature variations at the plane ends, the inner and outer curved surfaces being in contact with rigid and smooth insulators. An exact solution is developed using potential functions of displacement. Numerical results are given for cylinders made of magnesium (anisotropic) and copper (isotropic).     

Electrocatalytic performance of Ba-doped TiO2 hollow spheres in water electrolysis

Barium doped titania hollow sphere catalysts of various compositions were prepared and their electrocatalytic performance was evaluated in acidic media. Titania hollow sphere particles were prepared using poly (styrene–methacrylic acid) latex as template material, and BaCl₂ was used precursor material during barium doping over spheres. The morphology and structure of Ba/TiO₂ hollow spheres were characterized by BET, XRD, TGA and TEM analysis. XRD results had confirmed the presence of rutile TiO₂ and BaTiO₃ phases in the catalysts. The catalysts have shown almost similar surface area values (around 97 m²/g) irrespective of their compositions. On the other hand, surface area values were diminished remarkably with rise in the calcination temperatures. In TEM images, hollow sphere formation with uniform layer of barium over the spheres could clearly be observed. Diameter of Ba-doped TiO₂ hollow sphere was found 0.4–0.5 μm irrespective of the variation in calcination temperatures. In cyclic voltammograms, both the hydrogen and oxygen evolution peaks were present for all the hollow sphere samples; although the peak positions had changed to some extent for few samples. Anodic polarization curves have shown 60 mA cm⁻² current density for 20 wt% Ba/TiO₂ hollow sphere sample. Tafel slope is revealed as 122 mV for the same electrocatalyst. Barium doped titania hollow spheres have also shown long time electrocatalytic stability in acid solution.