Abstract
We derive a solution for many circular cylindrical holes that are free boundary to an elastic medium (matrix) of infinite extent under in-plane problem. These many holes have different radii and different central points. When there are many holes in the matrix, we consider the matrix as a poroelastic matrix. The matrix is subjected to arbitrary loading, for example, by uniform stresses. 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 problem. This procedure is referred to as heterogenization. Using these solutions, we observe the stress concentration factor around the holes from this solution and analysis of FEM (ANSYS). Several numerical examples are presented graphically.
