Abstract：According to the theory of linear elasticity, the numerical methods are difficult to calculate the singular stress field in a V-notch/crack tip region. In this paper, the extended boundary element method (XBEM) is proposed to determine the singular stress field near a V-notch/crack tip. Firstly, a small sector around the V-notch/crack tip is dug out from the V-notch/crack structures. The displacement and stress components in the small sector are expressed as the asymptotic series expansions with respect to the radial coordinate from the tip. The amplitude coefficients in the series expansions are taken as the basic unknowns. Secondly, the boundary element method is used to analyze the V-notch/crack structure removed the small sector. Consequently, the complete displacement and stress fields of the V-notched/cracked structure are solved by combining the boundary element analysis and the asymptotic series expansions of the stress field, where the extended boundary element method has the characteristics of the semi-analytic approach. The XBEM is suitable for the stress analysis of general V-notched/cracked structures, and its solution can accurately describe the displacement and stress field from the notch/crack tip to the whole region. Finally, two numerical examples are given to demonstrate the effectiveness and accuracy of the XBEM.
2018, Vol. 39 
