Analysis of an anisotropic finite wedge under antiplane deformation

The antiplane deformation of an anisotropic wedge with finite radius is con sidered in this paper within the classical linear theory of elasticity. The traction-free condition is imposed on the circular segment of the wedge. T hree different cases of boundary conditions on the radial edges are conside red, which are: traction-displacement, displacement-displacement and tracti on-traction. The solution to the governing differential equation of the pro blem is accomplished in the complex plane by relating the displacement fiel d to a complex function. Several complex transformations are defined on thi s complex function and its first and second derivatives to formulate the pr oblem 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 Mel lin transforms of the first and second kinds. Closed form expressions are o btained for the displacement and stress fields in the entire domain. In all cases, explicit expressions for the strength of singularity are derived. T hese expressions show the dependence of the order of stress singularity on the wedge angle and material constants. In the displacement-displacement ca se, depending upon the applied displacement, a new type of stress singulari ty has been observed at the wedge apex.