An Innovative Solution in Closed Form and Numerical Analysis for Dissimilar Elliptical Inclusion in Plane Elasticity

Abstract

This paper provides a closed form solution for dissimilar elliptical inclusion in plane elasticity. A dissimilar elliptical inclusion is embedded in the infinite matrix with different elastic properties. The infinite matrix is applied by the constant remote loading. Complex variable method is used and two sets of the complex potentials are assumed in the analysis. One set is used for the matrix portion, and other for the inclusion portion. Catching the idea from the eigenstrain problem, we can assume the stresses in the inclusion to be constant. From the continuity conditions for stresses and displacements along the interface, we can get the two sets of the complex potentials in a closed form. In the analysis, an adequate form of the complex potential defined in the elliptical inclusion portion is analyzed in detail.