Abstract: “By applying the equivalent inclusion method and utilizing ellipsoidal harmonic functions, the stress fields of an infinite body which contains an ellipsoidal inhomogeneity were solved and given in closed form. Since ellipsoidal coordinates are used, the stresses along the principal axes and on the surface of the ellipsoid are easily calculated. The exact solution is presented for an infinite elastic medium which contains an ellipsoidal inhomogeneity subjected to principal stresses at infinity. The equivalent inclusion method is applied to obtain the stress field of ellipsoidal inhomogeneity that is used to solve the stress fields outside the inhomogeneity. The difference of this approach and the Eshelby’s method is that in our analysis the ellipsoidal coordinates are employed and the corresponding harmonic functions, Lamé functions are used as Boussingesq stress functions. This paper provides an alternative solution for the stresses outside ellipsoidal inhomogeneity other than Eshelby’”

Keywords: tress, Fields , Outside, Ellipsoidal, Inhomogeneity, Ellipsoidal, Potentials