Two-Dimensional Stress Analysis of Thick Hollow Functionally Graded Sphere Under Non-Axisymmetric Mechanical Loading

Sandeep Kumar Paul,Manoj Sahni

doi:10.33889/ijmems.2021.6.4.066

Abstract

In this paper, a functionally graded thick hollow sphere is considered for the analysis of two-dimensional steady state mechanical stress in the radial and circumferential directions under mechanical loading. Modulus of elasticity is varying with continuous nonlinear variation along the radial direction and Poisson’s ratio is kept as constant. The Legendre series and Euler differential equation are used to solve Navier equations. Geometry of the sphere is assumed in spherical coordinate system. Applying mechanical boundary conditions at inner and outer radii, we have carried out the analytical solutions for stresses, strains and displacements. In the numerical example, only internal pressure is varying along circumferential direction and external pressure is kept as zero. Displacements and mechanical stresses are presented graphically and the results are discussed numerically.

Highlights

In the beginning, Functionally Graded Materials (FGMs) were used to design heat resisting material in the aerospace industry
Assume the inner and outer radii of the sphere, respectively as r1 = 1.2, r2 = 1.4 in meters; Poisson’s ratio v = 0.3 and constant Young’s modulus Y0 = 200GPa for a FGM thick hollow cylinder and mechanical boundary conditions are defined as σrr(r1, θ) = 200 cos 4 θMPa, σrθ(r1, θ) = 0, u(r2, θ) = 0, w(r2, θ) = 0 (29)
This paper presents an analytical solution for mechanical response of functionally graded thickwalled spherical pressure vessel

Summary

Introduction

Graded Materials (FGMs) were used to design heat resisting material in the aerospace industry. Prediction is made for the partial behaviour of stresses of thick-walled functionally graded cylinder subjected to uniform inner and outer pressure along thickness direction by Nejad and Fatehi (2015). Using Frobenius series method, a cylindrical pressure vessel made of functionally graded material is investigated as elasticity problem by Gharibi et al (2017).

Results

Conclusion