Effectiveness of the stress solutions of 3-D V-notched/cracked structures by using extended boundary element method

In this paper, the extended boundary element method (XBEM) is proposed to calculate the stress fields of the three-dimensional (3-D) V-notched/cracked structure based on the linear elasticity theory. The 3-D V-notched/cracked structure contains two parts, a small sector column around the 3-D V-notch/crack tip and the outer region without the tip region. The stress fields in a small sector column are firstly expressed by asymptotic series expansions. Then the expressions of the small sector column are embedded into the boundary integral equation for the outer region. Finally, the whole displacement and stress fields of the 3-D V-notched/cracked structure are obtained by the XBEM. Two numerical examples are given to demonstrate the effectiveness and accuracy of the proposed 3-D XBEM.