INTERACTING CIRCULAR INHOMOGENEITIES IN PLANE ELASTOSTATICS

This paper provides a general series solution to the problem of interacting circular inhomogeneities in plane elastostatics. The analysis is based upon the use of the complex stress potentials of Muskhelishvili and the Laurent series expansion method. The general forms of the complex potentials are derived explicitly for the circular inhomogeneity problem under arbitrary plane loading. Using the superposition principle, these general expressions were subsequently employed to treat the problem of an infinitely extended matrix containing any number of arbitrarily located inhomogeneities. The above procedure reduces the problem to a set of linear algebraic equations which are solved with the aid of a perturbation technique. The current method is shown to be capable of yielding approximate closed-form solutions for multiple inhomogeneities, thus providing the explicit dependence of the solution upon the pertinent parameters.