Elastodynamic solution for plane-strain response of functionally graded thick hollow cylinders by analytical method

Abstract

An elastodynamic solution for plane-strain response of functionally graded thick hollow cylinders subjected to uniformly-distributed dynamic pressures at boundary surfaces is presented. The material properties, except Poisson's ratio, are assumed to vary through the thickness according to a power law function. To achieve an exact solution, the dynamic radial displacement is divided into two quasi-static and dynamic parts, and for each part, an analytical solution is derived. The quasi-static solution is obtained by means of Euler's equation, and the dynamic solution is derived using the method of the separation of variables and the orthogonal expansion technique. The radial displacement and stress distributions are plotted for various functionally graded material (FGM) hollow cylinders under different dynamic loads, and the advantages of the presented method are discussed. The proposed analytical solution is suitable for analyzing various arrangements of hollow FGM cylinders with arbitrary thickness and arbitrary initial conditions, which are subjected to arbitrary forms of dynamic pressures distributed uniformly on their boundary surfaces.

Analysis of complicated one‐dimensional stress oscillation behaviour in a functionally graded material plate

“…The radial displacements were then divided into the quasi-static term and the series of dynamic terms, each of which was expressed by the product of a space-variable function and a time-variable function. Applying a similar method, investigations on one-dimensional elastodynamic behaviours of FGM hollow circular cylinders were conducted [10,11]. A two-dimensional problem of an FGM hollow circular cylinder was solved with FEM in the case where material properties varied in both radial and axial directions [12].…”