ANALYSIS OF 3-D NOTCHED/CRACKED STRUCTURES BY USING EXTENDED BOUNDARY ELEMENT METHOD

According to the theory of linear elasticity, the conventional numerical methods are difficult to calculate the singular stress fields of three dimensional V-notched/cracked structures because of the stress singularity in the V-notch/crack tip region. In this paper, the extended boundary element method (XBEM) is first proposed to calculate the whole displacement and stress fields of three dimensional V-notch/crack structures. Firstly, the three dimensional V-notched/cracked structure is divided into two parts, which are a small sectoral column around the notch/crack tip and the outer region without the tip sectorial column. The displacement and stress components in the small sector column are expressed as the asymptotic series expansions with respect to the radial coordinate from the tip. The stress singular orders and the associated displacement and stress eigen-functions in the tip region are determined by the interpolating matrix method. The amplitude coefficients in the asymptotic series expansions are taken as the basic unknowns. Secondly, the boundary element method is used to analyze the three dimensional V-notched/cracked structure removed the small sector column. Hence, the whole displacement and stress fields of both the tip region and outer region are obtained by combining the boundary element analysis and the asymptotic series expansions of the displacement and stress fields in the notch/crack tip region, where the XBEM has the characteristics of the semi-analytic approach. The XBEM is suitable for the displacement and stress analysis of the three dimensional V-notched/cracked structures, and its solution can accurately describe the displacement and stress fields from the notch/crack tip to the whole region of the V-notched/cracked structures. Finally, two typical examples are given to demonstrate the effectiveness and accuracy of the extended boundary element method.