The axisymmetric thermoelastic problem of a uniformly heated, functionally graded isotropic hollow cylinder is considered. An analytical form of solution is proposed, For the case when the Young's modulus and ther...The axisymmetric thermoelastic problem of a uniformly heated, functionally graded isotropic hollow cylinder is considered. An analytical form of solution is proposed, For the case when the Young's modulus and thermal expansion coefficient have a power-law dependence on the radial coordinate, explicit exact solution is obtained. For the degenerated ease, i.e. when the cylinder is homogeneous and isotropie, no stresses will occur provided it is subjected to a uniform temperature. Numerical results are finally given and some important inclusions are obtained.展开更多
In this paper, an analytical and numerical study of strain fields, stress fields and displacements in a rotating hollow cylinder, whose walls were completely made in Functionally Graded Materials (FGM), was conducted....In this paper, an analytical and numerical study of strain fields, stress fields and displacements in a rotating hollow cylinder, whose walls were completely made in Functionally Graded Materials (FGM), was conducted. We have considered the rotating hollow cylinder submitted to an asymmetric radial loading. It is assumed that, because of the functional graduation of the material, the mechanical properties such as Young elastic modulus and the density varies in the radial direction, in accordance with a the power law function. The inhomogeneity parameter was selected between -1 and 1. On the basis of the second law of Newton, Hooke’s law and the strain-stress relationship, we established the differential equation which governs the equilibrium for a rotating hollow cylinder. We found the analytical solution and compared to the numerical solution obtained by using the shooting method and the fourth order Runge-Kutta algorithm. The analytical and numerical results lead to the conclusion that the magnitude of the tangential stresses is greater than that of the radial stresses. The changes due to the graduation of FGM does not produce consistent variations in the distribution of radial stresses, but strongly affects the distribution of tangential stresses. The tangential stresses, tangential strains and displacements are much higher at the inner surface of the cylinder wall. The internal radial pressure intensely affects the radial stresses and the radial strain.展开更多
Exact solutions are obtained for transient torsio- nal responses of a finitely long, functionally graded hollow cylinder under three different end conditions, i.e. free-free, free-fixed and fixed-fixed. The cylinder w...Exact solutions are obtained for transient torsio- nal responses of a finitely long, functionally graded hollow cylinder under three different end conditions, i.e. free-free, free-fixed and fixed-fixed. The cylinder with its external surface fixed is subjected to a dynamic shearing stress at the internal surface. The material properties are assumed to vary in the radial direction in a power law form, while keep invariant in the axial direction. With expansion in the axial direction in terms of trigonometric series, the governing equations for the unknown functions about the radial coordinate r and time t are deduced. By applying the variable substitution technique, the superposition method and the separation of variables consecutively, series-form solutions of the equations are obtained. Natural frequencies and the transient torsional responses are finally discussed for a functionally graded finite hollow cylinder.展开更多
The perturbation method is applied to investigate the frictionally excited thermoelastic dynamic instability (TEDI) of a functionally graded material (FGM) coating in half-plane sliding against a homogeneous half-plan...The perturbation method is applied to investigate the frictionally excited thermoelastic dynamic instability (TEDI) of a functionally graded material (FGM) coating in half-plane sliding against a homogeneous half-plane. We assume that the thermoelastic properties of the FGM vary exponentially with thickness. We also examine the effects of the gradient index, sliding speed, and friction coefficient on the TEDI for various material combinations. The transverse normal stress for two different coating structures is calculated. Furthermore, the frictional sliding stability of two different coating structures is analyzed. The obtained results show that use of FGM coatings can improve the TEDI of this sliding system and reduce the possibility of interfacial failure by controlling the interfacial tensile stress.展开更多
An elastodynamic solution for plane-strain response of functionally graded thick hollow cylinders subjected to uniformly-distributed dynamic pressures at boundary surfaces is presented. The material properties, except...An elastodynamic solution for plane-strain response of functionally graded thick hollow cylinders subjected to uniformly-distributed dynamic pressures at boundary surfaces is presented. The material properties, except Poisson＇s ratio, are assumed to vary through the thickness according to a power law function. To achieve an exact solution, the dynamic radial displacement is divided into two quasi-static and dynamic parts, and for each part, an analytical solution is derived. The quasi-static solution is obtained by means of Euler＇s equation, and the dynamic solution is derived using the method of the separation of variables and the orthogonal expansion technique. The radial displacement and stress distributions are plotted for various functionally graded material （FGM） hollow cylinders under different dynamic loads, and the advantages of the presented method are discussed. The proposed analytical solution is suitable for analyzing various arrangements of hollow FGM cylinders with arbitrary thickness and arbitrary initial conditions, which are subjected to arbitrary forms of dynamic pressures distributed uniformly on their boundary surfaces.展开更多
Analytical solutions to rotating functionally graded hollow and solid long cylinders are developed. Young＇s modulus and material density of the cylinder are assumed to vary exponentially in the radial direction, and ...Analytical solutions to rotating functionally graded hollow and solid long cylinders are developed. Young＇s modulus and material density of the cylinder are assumed to vary exponentially in the radial direction, and Poisson＇s ratio is assumed to be constant. A unified governing equation is derived from the equilibrium equations, compatibility equation, deformation theory of elasticity and the stress-strain relationship. The governing second-order differential equation is solved in terms of a hypergeometric function for the elastic deformation of rotating functionally graded cylinders. Dependence of stresses in the cylinder on the inhomogeneous parameters, geometry and boundary conditions is examined and discussed. The proposed solution is validated by comparing the results for rotating functionally graded hollow and solid cylinders with the results for rotating homogeneous isotropic cylinders. In addition, a viscoelastic solution to the rotating viscoelastic cylinder is presented, and dependence of stresses in hollow and solid cylinders on the time parameter is examined.展开更多
文摘The axisymmetric thermoelastic problem of a uniformly heated, functionally graded isotropic hollow cylinder is considered. An analytical form of solution is proposed, For the case when the Young's modulus and thermal expansion coefficient have a power-law dependence on the radial coordinate, explicit exact solution is obtained. For the degenerated ease, i.e. when the cylinder is homogeneous and isotropie, no stresses will occur provided it is subjected to a uniform temperature. Numerical results are finally given and some important inclusions are obtained.
文摘In this paper, an analytical and numerical study of strain fields, stress fields and displacements in a rotating hollow cylinder, whose walls were completely made in Functionally Graded Materials (FGM), was conducted. We have considered the rotating hollow cylinder submitted to an asymmetric radial loading. It is assumed that, because of the functional graduation of the material, the mechanical properties such as Young elastic modulus and the density varies in the radial direction, in accordance with a the power law function. The inhomogeneity parameter was selected between -1 and 1. On the basis of the second law of Newton, Hooke’s law and the strain-stress relationship, we established the differential equation which governs the equilibrium for a rotating hollow cylinder. We found the analytical solution and compared to the numerical solution obtained by using the shooting method and the fourth order Runge-Kutta algorithm. The analytical and numerical results lead to the conclusion that the magnitude of the tangential stresses is greater than that of the radial stresses. The changes due to the graduation of FGM does not produce consistent variations in the distribution of radial stresses, but strongly affects the distribution of tangential stresses. The tangential stresses, tangential strains and displacements are much higher at the inner surface of the cylinder wall. The internal radial pressure intensely affects the radial stresses and the radial strain.
基金supported by the National Natural Science Foundation of China ( 10872179 and 10725210)the Zhejiang Provincial Natural Science Foundation of China (Y7080298) Zijin Plan of Zhejiang University
文摘Exact solutions are obtained for transient torsio- nal responses of a finitely long, functionally graded hollow cylinder under three different end conditions, i.e. free-free, free-fixed and fixed-fixed. The cylinder with its external surface fixed is subjected to a dynamic shearing stress at the internal surface. The material properties are assumed to vary in the radial direction in a power law form, while keep invariant in the axial direction. With expansion in the axial direction in terms of trigonometric series, the governing equations for the unknown functions about the radial coordinate r and time t are deduced. By applying the variable substitution technique, the superposition method and the separation of variables consecutively, series-form solutions of the equations are obtained. Natural frequencies and the transient torsional responses are finally discussed for a functionally graded finite hollow cylinder.
基金National NaturalScience Foundation of China (Grants 11502089 and 11725207).
文摘The perturbation method is applied to investigate the frictionally excited thermoelastic dynamic instability (TEDI) of a functionally graded material (FGM) coating in half-plane sliding against a homogeneous half-plane. We assume that the thermoelastic properties of the FGM vary exponentially with thickness. We also examine the effects of the gradient index, sliding speed, and friction coefficient on the TEDI for various material combinations. The transverse normal stress for two different coating structures is calculated. Furthermore, the frictional sliding stability of two different coating structures is analyzed. The obtained results show that use of FGM coatings can improve the TEDI of this sliding system and reduce the possibility of interfacial failure by controlling the interfacial tensile stress.
文摘An elastodynamic solution for plane-strain response of functionally graded thick hollow cylinders subjected to uniformly-distributed dynamic pressures at boundary surfaces is presented. The material properties, except Poisson＇s ratio, are assumed to vary through the thickness according to a power law function. To achieve an exact solution, the dynamic radial displacement is divided into two quasi-static and dynamic parts, and for each part, an analytical solution is derived. The quasi-static solution is obtained by means of Euler＇s equation, and the dynamic solution is derived using the method of the separation of variables and the orthogonal expansion technique. The radial displacement and stress distributions are plotted for various functionally graded material （FGM） hollow cylinders under different dynamic loads, and the advantages of the presented method are discussed. The proposed analytical solution is suitable for analyzing various arrangements of hollow FGM cylinders with arbitrary thickness and arbitrary initial conditions, which are subjected to arbitrary forms of dynamic pressures distributed uniformly on their boundary surfaces.
文摘Analytical solutions to rotating functionally graded hollow and solid long cylinders are developed. Young＇s modulus and material density of the cylinder are assumed to vary exponentially in the radial direction, and Poisson＇s ratio is assumed to be constant. A unified governing equation is derived from the equilibrium equations, compatibility equation, deformation theory of elasticity and the stress-strain relationship. The governing second-order differential equation is solved in terms of a hypergeometric function for the elastic deformation of rotating functionally graded cylinders. Dependence of stresses in the cylinder on the inhomogeneous parameters, geometry and boundary conditions is examined and discussed. The proposed solution is validated by comparing the results for rotating functionally graded hollow and solid cylinders with the results for rotating homogeneous isotropic cylinders. In addition, a viscoelastic solution to the rotating viscoelastic cylinder is presented, and dependence of stresses in hollow and solid cylinders on the time parameter is examined.
