MAGNETOTHERMODYNAMIC STRESS AND PERTURBATION OF MAGNETIC FIELD VECTOR IN A HOLLOW CYLINDER

An analytical method is presented to investigate magnetothermoelastic waves and perturbation of the magnetic field vector produced by thermal shock in a hollow conducting cylinder. By means of finite integral transforms the exact expressions for magnetothermodynamic stress and perturbation response of an axial magnetic field vector in a hollow cylinder were obtained. From sample numerical calculations the dynamic effect on both magnetothermostress and perturbation of the axial magnetic field vector is revealed and is discussed.     

The dynamic response and perturbation of magnetic field vector of orthotropic cylinders under various shock loads

In this paper, an analytical method is introduced to solve the problem for the dynamic stress-focusing and centred-effect of perturbation of the magnetic field vector in orthotropic cylinders under thermal and mechanical shock loads. Analytical expressions for the dynamic stresses and the perturbation of the magnetic field vector are obtained by means of finite Hankel transforms and Laplace transforms. The response histories of dynamic stresses and the perturbation of the field vector are also obtained. In practical examples, the dynamic focusing effect on both magnetoelastic stress and perturbation of the axial magnetic field vector in an orthotropic cylinder subjected to various shock loads is presented and discussed.     

MAGNETOTHERMODYNAMIC STRESS AND PERTURBATION OF MAGNETIC FIELD VECTOR IN A SOLID CYLINDER

A theoretical method is presented to analyze magnetothermoelastic waves and perturbation of the magnetic field vector produced by thermal shock in a solid conducting cylinder. By means of finite integral transforms the exact expressions for magnetothermodynamic stress and perturbation response of an axial magnetic field vector in a solid cylinder were obtained. From sample numerical calculations the focusing effect on both magnetothermostress and perturbation of the axial magnetic field vector is revealed and is discussed.     

Magnetothermoelastic interactions in hollow structures of functionally graded material subjected to mechanical loads

This paper considers the magnetothermoelastic problem of functionally graded material (FGM) hollow structures subjected to mechanical loads. Exact solutions for stresses and perturbations of the magnetic field vector in FGM hollow cylinders and FGM hollow spheres are determined using the infinitesimal theory of magnetothermoelasticity. The material stiffness, thermal expansion coefficient and magnetic permeability are assumed to obey the same simple power-law variation through the structures’ wall thickness. The aim of this research is to understand the effect of composition on magneto- thermoelastic stresses and to design optimum FGM hollow cylinders and hollow spheres.     

Eigenfunction expansion method to analyze thermal shock behavior in magneto-thermoelastic orthotropic medium under three theories

This article is concerned with a study of thermal shock response in infinite thermoelastic medium under the purview of Lord–Shulman model, Green–Naghdi theory III, and three-phase-lag model of generalized thermoelasticity. The medium under consideration is assumed to be homogeneous, orthotropic, and thermally conducting. The fundamental equations of the two-dimensional problem of generalized thermoelasticity with three-phase-lag model in an infinite elastic medium under the influence of magnetic field are obtained as a vector–matrix differential equation form using normal mode analysis which is then solved by the Eigenfunction expansion method. Numerical results for the temperature, displacements and thermal stress distribution are presented graphically.     

基于摄动法的表贴式永磁电机转子偏心空载气隙磁场计算

采用摄动法解析计算表贴式永磁电机转子偏心空载气隙磁场,以无量纲的偏心扰动量作为摄动变量,可解决表贴式永磁电机内转子结构和外转子结构的转子偏心磁场解析问题。根据气隙区域及永磁体区域的边界条件求解拉普拉斯方程和泊松方程,通过矢量磁位推导出气隙磁通密度的解析表达式,进而应用麦克斯韦应力张量法计算不平衡磁拉力,并将解析法结果与有限元法结果进行比较,发现二者一致性较好,验证了该方法的正确性和有效性。     

THERMOELASTIC ANALYSIS OF LAMINATED PLATES. I: SYMMETRIC SPECIALLY ORTHOTROPIC LAMINATES

Thermally induced deformations and stress resultants in symmetric laminated plates are analyzed. The method of M. Levy is used to study the transverse bending of a specially orthotropic laminate having two simply supported edges and subject to a temperature distribution that does not vary in a direction parallel to the simple supports. A solution is also obtained for the problem of in-plane stretching of the plate middle surface caused by a general three-dimensional temperature field. As an illustrative example, the thermoelastic response of a unidirectionally fiber-reinforced plate to a temperature variation that is linear in the thickness direction is computed.     

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.     

A Thermo-Mechanical Analysis of Isotropic and Composite Beams via Collocation with Radial Basis Functions

In this article, the mechanical behavior of beams subjected to thermal loads is investigated. The temperature field is obtained by exactly solving Fourier's heat conduction equation and it is considered as an external load within the mechanical analysis. Several higher-order beam models as well as Timoshenko's classical theory are derived thanks to a compact notation for the a priori approximation of the displacement field upon the cross-section. The governing differential equations and boundary conditions are obtained in a compact nucleal form that does not depend upon the displacements’ expansion order. The latter can be regarded as a free parameter of the formulation. A meshless strong-form solution based upon collocation with Wendland's radial basis functions is adopted. Isotropic and laminated orthotropic beams are investigated. Results are validated toward an analytical Navier-type solution and three-dimensional FEM results. It is shown that good accuracy can be obtained.     

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     

Transient Thermal Stresses in an Orthotropic Cylinder under the Hyperbolic Heat Conduction Model

An important consideration in design involving high temperature variation is the determination of the thermal stresses developed. The numerical solution for thermoelastic transient response of orthotropic cylinder subjected to a constant temperature at the surface is presented. The thermoelastic equations with one relaxation time developed by Lord and Shulman with uncoupled thermoelasticity assumption are used in the present work. The hyperbolic heat conduction model is used for the prediction of the temperature history. Thermally induced displacement and stresses are determined. A numerical method based on implicit finite difference scheme is used to calculate the temperature, displacement, and stress distributions within the cylinder. Numerical examples for orthotropic, transverse isotropic, and isotropic cylinders were carried out for the stresses. Furthermore, the results of the numerical solution and the exact solution at the steady state condition are compared.     

THERMOELASTIC BUCKLING OF LAMINATED COMPOSITE CONICAL SHELLS

Within the framework of three-dimensional (3D) elasticity, an asymptotic theory is presented for the thermoelastic buckling analysis of laminated composite conical shells subjected to a uniform temperature change. A dimensionless parameter of thermal load related to the temperature change is defined. The method of perturbation is applied in the present formulation where the critical thermal loads and the primary field variables are expanded as a series of even powers of a small perturbation parameter. Through a straightforward derivation, the asymptotic formulation leads to recursive sets of governing equations for various orders. The classical shell theory is derived as a first-order approximation to the 3D theory. The method of differential quadrature is used to solve for the asymptotic solutions at each order level. The solvability conditions and normalization conditions for higher-order problems are derived. By considering these conditions, we can obtain the higher-order modifications. The critical thermal loads of simply supported, cross-ply conical shells are studied to demonstrate the performance of the present asymptotic theory.     

TRANSIENT THERMOELASTIC SOLUTION OF A MULTILAYERED ORTHOTROPIC HOLLOW CYLINDER FOR AXISYMMETRIC PROBLEMS

The thermoelastic dynamic solution of a multilayered orthotropic hollow cylinder in the state of axisymmetric plane strain is obtained. By the method of superposition, the displacement is divided into two parts: one is quasi static and the other is dynamic. The quasi-static solution is derived by the state-space method, and the dynamic solution is obtained by the separation-of-variables method coupled with the initial parameter method as well as the orthogonal expansion technique. The present method is suitable for a multilayered orthotropic hollow cylinder consisting of arbitrary layers and subjected to arbitrary axisymmetric thermal loads. Numerical results are finally presented and discussed.     

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.     

Magnetohydrodynamic Natural Convection in a Square Enclosure with Four Circular Cylinders Positioned at Different Rectangular Locations

We deploy a finite volume numerical computation to investigate the two-dimensional hydromagnetic natural convection in a cooled square enclosure in the presence of four inner heated circular cylinders with identical shape. The inner circular cylinders are placed in a rectangular array with equal distance away from each other within the enclosure and moving along the diagonals of the enclosure. All the walls of the enclosure are kept isothermal with temperatures less than that of the cylinders. A uniform magnetic field is applied along the horizontal direction normal to the vertical wall. All solid walls are assumed electrically insulated. Simulations are performed for a range of the controlling parameters such as the Rayleigh number 10³ to 10⁶, Hartmann number 0 to 50, and the dimensionless horizontal and vertical distance from the center of a cylinder to center of another cylinder 0.3 to 0.7. The study specifically aims to understand the effects of the location of the cylinders in the enclosure on the magnetoconvective transport, when they moved along the diagonals of the enclosure. It is observed that the unsteady behavior of the flow and thermal fields at relatively larger Rayleigh numbers and for some cylinder position are suppressed by imposition of the magnetic field. The heat transfer strongly depends on the position of the cylinders and the strength of the magnetic field. Hence, by controlling the position of the objects and the magnetic field strength, a significant control on the hydrodynamic and thermal transport can be achieved.     

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 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.     

Role of suction/injection and slip flow on hydromagnetic free convective flow in a vertical coaxial cylinder under the influence of radial magnetic field

This investigation attempts to address heat and mass transfer behavior exhibited by a steady fully developed natural convective flow of a viscous, incompressible, and electrically conducting fluid in a vertical porous annulus in the presence of radially applied magnetic field and velocity slip. The motion of the fluid in the annular gap is triggered by the buoyancy forces due to temperature gradient of the inner and outer cylinders. The governing momentum and energy equations responsible for the flow are transformed into dimensionless forms using the appropriate dimensionless parameters. Accordingly, analytical solutions of the energy and momentum fields are derived with the appropriate boundary conditions. The effects of the controlling parameters involved in the flow on the temperature field, velocity field, and drag on the walls of the cylinders are illustrated graphically and with the aid of tables. Findings affirm that fluid temperature can be decreased/increased by increasing suction/injection on the porous wall. Furthermore, the fluid flow in the annular gap can be enhanced by increasing Grashof number, fluid injection, and velocity slip.     

THREE-DIMENSIONAL TRANSIENT THERMAL STRESS ANALYSIS OF A NONHOMOGENEOUS HOLLOW CIRCULAR CYLINDER DUE TO A MOVING HEAT SOURCE IN THE AXIAL DIRECTION

In this paper, a theoretical analysis of a three-dimensional transient thermal stress problem is developed for a nonhomogeneous hollow circular cylinder due to a moving heat source in the axial direction from the inner and /or outer surfaces. Assuming that the hollow circular cylinder has nonhomogeneous thermal and mechanical material properties in the radial direction, the heat conduction problem and the associated thermoelastic behaviors for such nonhomogeneous medium are developed by introducing the theory of laminated composites as one of theoretical approximation. The transient heat conduction problem is treated with the help of the methods of Fourier cosine transformation and Laplace transformation, and the associated thermoelastic field is analyzed making use of the thermoelastic displacement potential, Michell's function, and the Boussinesq's function. Some numerical results for the temperature change and the stress distributions are shown in figures, and the effect of relaxing the thermal stress in the nonhomogeneous hollow circular cylinder and the influence of the velocity of a moving heat source are briefly discussed     

Laminar and turbulent natural convection from a stack of thin hollow horizontal cylinders: A numerical study

Three dimensional natural convection from a stack of thin hollow horizontal cylinders has been investigated numerically in both laminar and turbulent regimes of Rayleigh number (Ra) spanning in the range 10⁴ to 10⁸ and 10¹⁰ to 10¹³, respectively. In the present study, the length to diameter ratio (L/D) of the cylinders is considered in the range 0.5–20. Thin horizontal hollow cylinders of three, six, and ten in numbers are arranged in a triangular manner to form three different types of stacks of same length scale. The full Navier-Stokes equation along with the energy equation are solved to predict the flow pattern and heat loss from the cylinders. The present computational study is able to capture very interesting buoyancy plume structures around the stack of short and long hollow cylinders. The average Nusselt number (Nu) shows a positive dependence on Ra for all L/D. In addition, Nu for a stack of three cylinders is found to be marginally higher than the stack of six cylinders followed by ten cylinders. Empirical correlations are developed for Nu as a function of Ra and L/D, which would be beneficial to academic researchers as well as practicing engineers.