Elastic And Thermoelastic Analysis Of Anisotropic Functionally Graded Cylinders

As a new type of composite material,functionally gradient materials(FGM)have attracted more and more attention due to their excellent mechanical properties and wide application prospects.According to the characteristics of the preparation process,functionally graded materials exhibit anisotropic properties.In this paper,the elastic and thermoelastic problems of anisotropic functionally graded cylinders are studied.Unlike the previous analysis,this paper does not need to assume the specific form of material performance in advance.The major contents are as follows:First,the pure elastic analysis of an anisotropic functionally graded cylinder subjected to pressure is carried out.It is assumed that the material parameters of the cylinder exhibit gradient changes in any form of function along the radius.The radial stress is used to express the circumferential stress and radial displacement,then substitute into the equilibrium equation.The analyzed problem is converted into a Fredholm integral equation about the radial stress combined with the boundary conditions.Then,all the stress distribution and the displacement distribution in the structure can be obtained by solving the integral equation.The validity and accuracy of the provided method are verified by comparing the exact solutions with the gradient parameter as a power function.The effects of the gradient parameters and anisotropy on the elastic field are given in the numerical examples.The results show that the radial stress of the cylinder is less affected by the gradient parameters and the anisotropy degree,but the hoop stress will be significantly affected by the gradient parameters and the anisotropy of the Vogit law.Secondly,the thermoelastic analysis of the anisotropic functionally gradient cylinder under axisymmetric condition is carried out with the same assumption that the material parameters of the cylinder are in a gradient in the direction of the radius.The research method is similar to the first part.First,the temperature field is determined by the heat conduction equation and the boundary condition of the steady state temperature field.Then the thermoelastic problem is converted to the integral equation about the radial stress,and the stress field and displacement field of the whole structure are obtained by solving the integral equation.The influences of different gradient parameters and anisotropy on the temperature field and thermoelastic field of functionally graded cylinder are analyzed numerically.The results show that the gradient parameters and various anisotropy degrees have little influence on the temperature distribution of the anisotropic functionally gradient cylinder in the steady temperature field,but it has an obvious influence on the thermal stress field and displacement field of the cylinder,and the influence of the circumferential stress is particularly complex.Finally,the transient thermo-elasticity of anisotropic functionally graded cylinders is analyzed.The transient heat conduction equation of cylinder is transformed into a Fredholm integral equation on temperature field by using Laplace transform and integral method,and the temperature field distribution is determined by numerical solution of integral equation and Laplace inverse transformation.The transient thermoelastic problem of the functionally graded cylinder is converted to the problem of transient thermo-elasticity by the same method as the first chapter.A Fredholm integral equation for radial stress is obtained,and the integral equation is solved to determine the thermal stress distribution of the cylinder in transient temperature field.The influences of gradient parameter and anisotropy degree on transient thermal response behavior in transient temperature field are analyzed numerically.The results show that,the gradient parameter and the anisotropy degree have significant influence on the thermal behavior of the cylinder,and the effect of the gradient parameter and the anisotropy degree on the thermal response of the cylinder is different at different time and different component parts with the same transient temperature field.The result of this paper can help the researchers and design staff to select the appropriate gradient parameters in the synthetic materials and the structure,so as to optimize the design,improve the safety and service life of the structure.