Exact Elasticity Solutions for Thick-Walled FG Spherical Pressure Vessels with Linearly and Exponentially Varying Properties

Abstract

In this paper, exact closed-form solutions for displacement and stress components of thick-walled functionally graded (FG) spherical pressure vessels are presented. To this aim, linear variation of properties, as an important case of the known power-law function model is used to describe the FG material distribution in thickness direction. Unlike the pervious studies, the vessels can have arbitrary inner to outer stiffness ratio without changing the function variation of FGM. After that, a closed-form solution is presented for displacement and stress components based on exponential model for variation of properties in radial direction. The accuracy of the present analyses is verified with known results. Finally, the effects of non-homogeneity and different values of inner to outer stiffness ratios on the displacement and stress distribution are discussed in detail. It can be seen that for FG vessels subjected to internal pressure, the variation of radial stress in radial direction becomes linear as the inner stiffness becomes five times higher than outer one. When the inner stiffness is half of the outer one, the distribution of the circumferential stress becomes uniform. For the case in which the external pressure is applied, as the inner to outer shear modulus becomes lower than 1/5, the value of the maximum radial stress is higher than external pressure.