Effect of internal load and temperature on graded spherical shell

Abstract

In this work, the effect of internal pressure in a functionally graded hollow spherical shell is theoretically studied. The material properties through the graded direction are assumed to be non-linear with power law distribution. In order to obtain the effect of internal pressure and temperature on the design of pressure vessel, Navier and heat conduction equations are solved by direct method. The pressure variation and the mechanical stress distribution such as radial stress distribution and hoop stress distribution along the radial direction are presented in a sequential manner. The radial distribution of temperature has also been depicted in the result and discussion section. As a result of which it may be concluded that the material which has lower power law index is beneficial in terms of generation of lower thermal stress. The study also aims to understand the influence of autofrettage on stress distribution and load bearing capacity in thick spherical shells. Analytical equations, based on the Maximum Shear Stress theory and Distortion Energy theory, are derived to determine the optimum radius of the elastic-plastic juncture, known as 𝐶𝑜𝑝𝑡 in autofrettage technology. The results demonstrate that autofrettage increases the pressure inside the shell, enhancing its ability to withstand higher internal pressures.