A screw dislocation near one open inhomogeneity and another closed inhomogeneity both permitting constant interior stresses

We prove that the interior stresses within both a non-parabolic open in-homogeneity and another interacting non-elliptical closed inhomogeneity can still remain constant when the matrix is simultaneously under the action of a screw dislocation and uniform remote anti-plane stresses. The constancy of interior stresses is realized through the construction of a conformal mapping function for the doubly connected domain occupied by the surrounding matrix. The mapping function is endowed with the information describing the screw dislocation via the incorporation of two specifically defined logarithmic terms. The constant interior stress fields are observed to be independent of the specific open and closed shapes of the two inhomogeneities and the existence of the screw dislocation. In contrast, the existence of the neighboring screw dislocation significantly affects the open and closed shapes of the two inhomogeneities.