Solution for Eshelbyʹs elastic inclusions in a finite plate using boundary integral equation method

This paper provides a solution for Eshelbyʹs elastic inclusions in a finite plate based on the complex variable boundary integral equation (CVBIE) method. In the formulation, an inclusion with Eshelbyʹs eigenstrains is embedded in an elliptic plate, and the exterior boundary is applied by some static loading. Two BIEs are suggested in the present study. One of BIEs is used for the finite inclusion region, and the other is used for region bounded by interface and the exterior boundary. After the discretization of BIEs, a numerical solution is suggested. In the solution, an inverse matrix technique is suggested which can eliminate one unknown vector in advance. Three numerical examples under different generalized loadings are provided. Interaction between the prescribed eigenstrains and the static loading along the exterior boundary is studied in detail.