METHOD OF TRANSLATIONS FOR A MODE-I ELLIPTIC CRACK IN AN INFINITE BODY - PART-I - POLYNOMIAL LOADING

A method has been proposed for determining the displacement of the ell iptic crack faces in an infinite body and consequently stress intensit y factors under the action or polynomial loading. The method is based: on the Rice integral formula which relates the stress and displacemen t fields for two different states of a body; on Dyson's theorem which defines the form of the displacement field for the prescribed law of t he action of the polynomial loading; on the theory of the elliptic cra ck translations in a nonuniform stress field developed in the present study; and finally on the known solution for a uniform loading. The me thod proposed does not require the solution of boundary problem and ac tually represents itself the recurrent procedure for step by step dete rmination of the displacement field for higher and higher degrees of p olynomial loading. In its structure, objectives and complexity the met hod corresponds to the weight function methods known in the literature whose main feature is the use of the known particular solutions for t he given body in order to obtain new solutions. (C) 1998 Elsevier Scie nce Ltd. All rights reserved.