Method of translations for a mode I elliptic crack in an infinite body. Part II: expansion of the fundamental solution into a series

Abstract The present paper considers the consequences of the application of the theory of crack translation in a nonuniform stress field to the analysis of an elliptic crack in an infinite body, developed in Part I of the present paper, which are more important for practical calculations. On the basis of trigonometrical cosines and sinuses the system of orthogonal on the ellipse contour functions ce i ( t ) and se i ( t ) are introduced. The application of these functions together with the technique of weight function method allows the general procedure for determination of terms of the weight function expansion and then for obtaining the fundamental solution of the elasticity theory to be proposed.