Abstract
In the present paper, based on the general solution for an elliptical crack in an infinite solid, subjected to arbitrary tractions (the VNA solution), the analytical solution of the first order variation of displacement field due to geometrical changes in the shape of an elliptical crack is derived. The analytical solution is related to the partial derivatives of the displacement field with respect to the lengths of the major and minor axes of the ellipse, respectively. Since the VNA solution involves the generic elliptic integrals. The partial derivatives of the generic elliptic integrals with respect to the lengths of the major and minor axes of the ellipse are required. A systematic procedure for the evaluation of these derivatives is also developed in this paper. The presently developed analytical solution will be effectively utilized to establish the three-dimensional weight function method for elliptical crack problems, in the forthcoming paper.
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