Department of Mechanical Engineering, Yasouj University, Yasouj, Iran.
Using the Frobenius series method (FSM), an analytical solution is developed to obtain mechanical stresses of thick spherical pressure vessels made of functionally graded materials (FGMs). The cylinder pressure vessel is subjected to uniform internal pressure. The modulus of elasticity is graded along the radial direction according to power functions of the radial direction. It is assumed that Poisson’s ratio is constant across the cylinder thickness. Primarily, displacements and stresses is obtained as closed-form solutions. Next, the profiles are plotted for different values of inhomogeneity constant along the radial direction. Finally, the problem was solved, using the finite element method (FEM). The obtained results of finite element method were compared with those of the analytical method. The analytical solutions and the solutions carried out through the FEM show good agreement. The values used in this study are arbitrary chosen to demonstrate the effect of inhomogeneity on displacements, and stresses distributions.