Analysis of a Functionally Graded Finite Wedge Under Antiplane Deformation

The antiplane deformation of a wedge made of a functionally graded material (FGM) with finite radius has been investigated analytically in the present article. In relation to the boundary conditions imposed on the arc portion of the wedge, displacement or traction, two problems have been studied. In each of the problems three various kinds of boundary conditions (tractiondisplacement, displacement-displacement and traction-traction) have been applied to the radial edges of the wedge. The governing differential equations have been solved by employing finite Fourier transforms and Green’s function method. The closed form solutions for stress and displacement distribution have been achieved for the whole domain. Explicit relations have been extracted for the order of stress singularity in all cases. These relations indicated the dependence of the order of stress singularity on the boundary conditions, material property and wedge angle. In fact, despite of an isotropic wedge, for which the order of stress singularity depends only the geometry of the wedge, in an FG wedge the order of stress singularity depends both the geometry as well as the material property.