Stress Analysis of Thick Spherical Pressure Vessel Composed of Transversely Isotropic Functionally Graded Incompressible Hyperelastic Materials

Abstract

In this paper closed form analytical solution for stress components of thick spherical shell made of transversely isotropic functionally graded hyperelastic material subjected to internal and external pressure is presented. Reinforced neo-Hookean strain energy function with variable material parameters is used to model pressure vessel material. The material constants of strain energy function are graded along the radial direction based on a power law function and have been calculated from experimental data by using Levenberg-Marquardt nonlinear regression method. Stress components and stretches of pressure vessel have been obtained for centrally symmetric condition. Following this, profiles of extension ratio, deformed radius of sphere, normalized radial stress and normalized circumferential stress are plotted as a function of radius of sphere in the undeformed configuration for different material inhomogeneity parameter (m). The obtained results show that the inhomogeneity properties of FGMs structure parameter have a significant influence on the displacement, stretch and stresses distribution along the radial direction.

Keywords:
Transversely isotropic hyperelastic material; thick-walled spherical shells; finite deformation; functionally graded material