ON THE ELASTIC FIELDS OF AN ELLIPTIC INHOMOGENEITY UNDER PLANE DEFORMATION

A generalized and unified approach is presented for the two-dimensional plane problem of an elliptical inhomogeneity in an isotropic elastic medium. The analysis is based upon the use of conformal mapping and Laurent series expansion of Muskhelishvili's complex potentials. The resulting elastic fields are derived explicitly in both transformed and physical planes for the inhomogeneity and the surrounding matrix. The associated expressions are universal in the sense of being applicable to generalized geometries and applied loads. The application of the general solution is illustrated by several examples and the resulting solutions are verified with those existing in the literature. The results advanced here can be used as building blocks for dealing with more complex problems involving a wide variety of geometry and loading conditions.