New Analysis for The FGM Thick Cylinders Under Combined Pressure and Temperature Loading

An analytical solution for computing the radial and circumferential stresses in a FGM thick cylindrical vessel under the influence of internal pressure and temperature is presented in this paper. It has been assumed that the modulus of elasticity and thermal coefficient of expansion were varying through thickness of the FGM material according to a power law relationship. Nevertheless the value of the Poisson ratio was taken as constant throughout the material. In the analysis presented here the effect of non-homogeneity in FGM thick cylinder was implemented by choosing a dimensionless parameter, named β, which could be assigned an arbitrary value affecting the stresses in the cylinder. Using Maple 9.5, distribution of stresses in radial and circumferential directions for FGM cylinders under the influence of internal pressure and temperature gradient were obtained. Graphs of variations of stress versus radius of the cylinder were plotted for different values of β. Cases of pressure, temperature and combined loadings were considered separately. It was concluded that by changing the value of β, the properties of FGM could be so modified that the lowest stress levels were reached. The stresses which were produced in FGM and homogeneous material with the same boundary conditions were compared to obtain the optimum value of β.