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

Yavar Anani,Gholamhossein Rahimi

doi:10.1590/1679-78252386

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.

Highlights

The principal problem in the elasticity theory is to find the relation between the stress and the strain in a body under certain external forces
A hollow thick sphere with an inner radius A and an outer radius B made of transversely isotropic Functionally Graded (FG) rubber like materials is considered
In each arbitrary radius, magnitude of normalized radial stress increases by increasing external pressure

Summary

INTRODUCTION

The principal problem in the elasticity theory is to find the relation between the stress and the strain in a body under certain external forces. Shells are general structural elements in many engineering applications, including pressure vessels, sub-marine hulls, ship hulls, wings and fuselages of airplanes, automobile tires pipes, exteriors of rockets, missiles, concrete roofs, chimneys, cooling towers, liquid storage tanks, and many other structures They are found in nature in the form of leaves, eggs, inner ear, bladder, blood vessel, skulls, and geological formations (Reddy 2007), the main concern of this paper is transversely isotropic thick spherical shell made of Functionally Graded (FG) rubber like materials. Exact analytical solution is derived for stresses and displacements of pressurized thick spheres made of transversely isotropic functionally graded rubber like materials (FGM) with power law variation material properties in radial direction

PROBLEM FORMULATION

A R B 0 Θ 2π

Formulation for

Case Study: Reinforced Neo-Hookean Model Function

AND DISCUSSION

CONCLUSION