The finite element method by employing the singular element with concordant displacement at the crack tip

A new regular polygon singular element is presented here. Its displacement is divided into two parts—linear and singular, the latter including the stress intensity factors vanishes on the boundary of the singular element, so the continuity of the displacement is satisfied. Furthermore, each element in the singular stiffness matrix can be expressed in some more simple analytic formulas. The procedure of analysing and reasoning of this technique is given in this paper, with which the intensity factors of the three kinds of loading system—uniform tension, three-point bending and shearing—are calculated. The results of the calculation show that this method is successful.