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In the present paper, we derive a solution for two circular holes or rigid inclusions that are perfectly bonded to an elastic medium (matrix) of infinite extent under in-plane deformation. These two holes or rigid inclusions have different radii and different central points. The matrix is subjected to arbitrary loading, for example, by uniform stresses, as well as a concentrated force at an arbitrary point. The solution is obtained through iterations of the Möbius transformation as a series with an explicit general term involving the complex potential of the corresponding homogeneous problem. This procedure is referred to as heterogenization. Using these solutions, several numerical examples are presented graphically.

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This paper presents the general solutions for many circular elastic inclusions that are perfectly bonded to an elastic medium(matrix) of infinite extent under the in-plane deformation. These many elastic inclusions have different radii, central points and possess different elastic properties. The matrix is subjected to arbitrary loading, for example, by uniform stresses at infinity. This solution is obtained through iterations of the Möbius transformation as a series with an explicit general term involving the complex potential functions of the corresponding homogeneous problem. This procedure is referred to as heterogenization. Using these solutions, several numerical examples are presented by the graphically.

In this paper, we derive the general solutions for many cylindrical holes or rigid inclusions perfectly bonded to an elastic medium(matrix) of infinite extent, under In-Plane deformation. These many holes or rigid inclusions have different radii and different central points.The solution is potential functions of the corresponding homogeneous problem.Using these solutions, several numerical examples are shown by the graphical representation.

In the present paper, we derive a solution for two circular elastic inclusions that are perfectly bonded to an elastic medium (matrix) of infinite extent under in-plane deformation. These two inclusions have different radii, central points, and elasticities. The matrix is subjected to arbitrary loading by, for example, uniform stresses, as well as to a concentrated force at an arbitrary point. In this paper, we present a solution under uniform stresses at infinity as an example. The solution is obtained through iterations of the Möbius transformation as a series with an explicit general term involving the complex potential of the corresponding homogeneous problem. This procedure is referred to as heterogenization. Using these solutions, several numerical examples are presented graphically.

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