Analytical solution of elastic–plastic stress for double-layer FGM spherical shell subjected to pressure and temperature load

Elastic–plastic analysis of thick homogenous sphere which was coated internally with functionally graded materials (FGMs) subjected to the temperature gradient and pressure under the assumption of axisymmetric deformation is presented in this paper. As a novel idea, the elastic material properties of the composite at the inner and external radius of the FGM sphere are calculated based on the Mori–Tanaka method and the yield stress is varied according to the rule of mixture. Hence, the effective material properties of FGM coating as the power function of the radius are calculated based on the Mori–Tanaka method. Analytical equations for radial and circumferential stresses, radial displacement, and temperature are obtained. According to the analytical solution, the results of the numerical solution were examined which shows good agreement between the simulation and analysis results. Effects of internal pressure and temperature gradient on radial stress, circumferential stress, and radial displacement are investigated. Results show that as internal pressure increases, the maximum circumferential stress moves from the inner towards the external radius. It is also turned out that for low-temperature quantities, the sign of both radial and circumferential stresses is changed somewhere in the wall thickness of the sphere.