Analysis of an Anisotropic Finite Wedge under Antiplane Deformation

Abstract

The antiplane deformation of an anisotropic wedge with finite radius is considered in this paper within the classical linear theory of elasticity. The traction-free condition is imposed on the circular segment of the wedge. Three different cases of boundary conditions on the radial edges are considered, which are: traction-displacement, displacement-displacement and traction-traction. The solution to the governing differential equation of the problem is accomplished in the complex plane by relating the displacement field to a complex function. Several complex transformations are defined on this complex function and its first and second derivatives to formulate the problem in each of the three cases of the problem corresponding to the radial boundary conditions, separately. These transformations are then related to integral transforms which are complex analogies to the standard finite Mellin transforms of the first and second kinds. Closed form expressions are obtained for the displacement and stress fields in the entire domain. In all cases, explicit expressions for the strength of singularity are derived. These expressions show the dependence of the order of stress singularity on the wedge angle and material constants. In the displacement-displacement case, depending upon the applied displacement, a new type of stress singularity has been observed at the wedge apex.