Method of translations for a mode I elliptic crack in an infinite body. Part I: polynomial loading

method has been proposed for determining the displacement of the elliptic crack faces in an infinite body and consequently stress intensity factors under the action of polynomial loading. The method is based : on the Rice integral formula which relates the stress and displacement fields for two different states of a body ; on Dysonʹs theorem which defines the form of the displacement field for the prescribed law of the action of the polynomial loading; on the theory of the elliptic crack translations in a nonuniform stress field developed in the present study; and finally on the known solution for a uniform loading. The method proposed does not require the solution of boundary problem and actually represents itself the recurrent procedure for step by step determination of the displacement field for higher and higher degrees of polynomial loading. In its structure, objectives and complexity the method corresponds to the weight function methods known in the literature whose main feature is the use of the known particular solutions for the given body in order to obtain new solutions. © 1998 Elsevier Science Ltd. All rights reserved.