Analytical and Numerical Analysis of Solid Cylinder Made of Radially Nonuniform Material Under Extension

Abstract

Functionally graded materials are inhomogeneous composite materials, composed of two or more constituents selected to achieve desirable properties for specific applications. In this work, a solid cylindrical tube made of inhomogeneous composite materials under tensile action was analyzed within the context of three-dimensional elasticity theory. An analytical solution was obtained for computing the displacement and stress fields. It has been assumed that the elastic stiffness is varying through the functionally graded material according to radial variation laws: linear, power, and exponential laws, while Poisson's ratio is considered as constant. In order to check the relevance of the analytical solution, a finite element model of the cylindrical tube was constructed, taking into account variations in Young's modulus. Very good agreement has been found between the numerical results and the predictions of the analytical solution, which confirms the accuracy of our model. Numerous curves were plotted by adjusting the inhomogeneity parameter and the elongation value, revealing a significant effect. Thus, the inhomogeneity in material properties can be exploited to optimize stress distribution. Indeed, by tailoring the material properties to match the stress distribution in a specific load scenario, stress concentrations can be minimized in high-stress areas.