Abstract
In this paper, we derive a general solution for an isotropic elastic medium (matrix) with nonconcentric multilayered circular inclusions. Inner inclusions are perfectly bonded to the outer inclusions and matrix that is infinite extent under anti-plane deformation. The inclusions have different elasticity, radii and central points. The matrix is subjected to arbitrary loading, for examples, by uniform anti-plane shear stresses at infinity, as well as a concentrated force or screw dislocation at an arbitrary point. The solution is obtained through iterations of the Mebius transformation as a series with an explicit general term involving the complex potential of the corresponding homogeneous problems. The procedure is referred to as heterogenization. Using there solutions, several numerical examples are presented graphically.
