Effects of graded-index and Poisson's ratio on elastic-solutions of a pressurized functionally graded material thick-walled cylinder

Abstract

In this study, the effect of graded-index and Poisson's ratio on the elastic-numerical solutions of an axisymmetric functionally graded material (FGM) thick-walled cylinder under internal pressure in-plane strain condition is presented. We assumed that the cylinder is made up of two different linear elastic materials and the volumetric fraction varied continuously and gradually through the radial direction. The thermo-mechanical properties are considered to be temperature-independent (TID) and defined by using the rule of mixture. The effects of the graded-index and Poisson's ratio on the stresses, strains and radial displacement are presented. The governing equations of an FGM cylinder are solved by using the non-linear shooting method and the Runge-Kutta fourth-order algorithm. The numerical solutions are obtained by writing the code of the governing equation in python open-access environment software package. The analytical solutions of a homogeneous cylinder are performed to validate the numerical solutions of an FGM cylinder. The results are presented in graphical form. The results show that the graded-index and Poisson's ratio have remarkable influences on the response of stresses, strains, and displacement distributions across the radial direction. But, both graded-index and Poisson's ratios have insignificant impacts on the radial stress of a pressurized FGM cylinder. Furthermore, the graded-index has a great significant effect on the material properties variations through the radial direction.

Keywords

• Graded-index
• Functionally graded material
• Thick-walled cylinder
• Poisson's ratio
• Volumetric fraction