Investigation of Stress Behavior in the Vicinity of Singular Points of Elastic Bodies Made of Functionally Graded Materials

Abstract

This paper presents the results of analytical and numerical investigations into stress behavior in the vicinity of different types of singular points on two-dimensional (2D) elastic bodies made of functionally graded materials (FGMs). A variant of constructing eigensolutions for plane FGM wedges, where the elastic properties are represented as a series expansion with respect to the radial coordinates, was considered. It was shown that, in the vicinity of singular points, the stress behavior is determined by solving the problem for the corresponding homogeneous wedge, where the elastic characteristics coincide with the characteristics of FGMs at the wedge vertex. Numerical investigations were carried out to evaluate the stress state of elastic bodies containing FGM elements at singular points, where the type of boundary conditions changes or where dissimilar materials come into contact. The results of the calculations showed that the behavior of stresses in FGMs in the vicinity of singular points can also be determined from an analysis of the eigensolutions for the corresponding homogeneous wedges, where the elastic properties coincide with the elastic constants of FGMs at singular points and that the functionally graded properties are dependent on one or two polar coordinates.