Title: Applications of a novel general solution to the inhomogeneous spatial axisymmetric problem in functionally graded materials

Abstract

The axisymmetric problem has always been a typical problem in the theory of elasticity, and the inhomogeneous spatial one has an especially wider range of applications. In this work, we present a novel analytical elastic general solution to the inhomogeneous spatial axisymmetric problem. The specific descriptions of inhomogeneity are: Young’s modulus of the material is an arbitrary function of both radius and thickness coordinates, and Poisson’s ratio is considered as a constant. The elastic stress method is applied to obtain a general stress solution and a relatively concise analytical displacement solution, the degenerate forms of which are both consistent with the existing results. Based on the general elastic solution, we study an axisymmetric bending problem of functionally graded circular plates subjected to a transverse loading q_0 r^n (n is an even number, and r is the radius coordinate) and give explicitly analytical elastic solutions to the case of uniform loadings under simply supported and two types of clamped supported conditions respectively. The final analytic solutions correspond well to the existing numerical results. The distributions of explicit elastic fields related to the inhomogeneous parameter reveal the influence of inhomogeneity on the stress and displacement in FGM circular plates intuitively, which makes it possible to control the elastic performance of FGM plates more accurately.