Abstract

In this article, a fundamental solution for the field equation of functionally graded (FG) circular planes is developed via generalization of the Michell solution for non-axisymmetric elasticity problems. The FG plane as a special case is assumed to have a constant Poisson’s ratio, while the elasticity modulus varies exponentially in the radial direction from a metal base to a ceramic base. The generalized form of the Frobenius method is extended and employed to solve the governing equations and investigate both plane-stress and plane-strain states. The target structural application of this solution has included circular solid or hollow FG cylinders, in which both inner and outer surfaces may be prescribed tractions. To this end, the stress field is first extracted and validated by available solutions for isotropic plane in the literature. Next, the stress field in an intact annular plane under a constant, as well as an …