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.