A singular element of shape-free hybrid stress-function finite elements in anisotropic materials

Abstract In this paper, the analytical solutions of the stress function around crack tip in the 2D anisotropic material are proposed. Further, a new singular element based on hybrid stress-function (HSF) model is developed and tested. Compared with other well-known methods, such new scheme exhibits two advantages: (i) for the singular element, the shape and the number of nodes can be flexibly adjusted as required; (ii) high precision for stress intensity factors (SIF) can be obtained due to the advantages of the HSF method, with very small computational cost. It demonstrates that the proposed scheme is an effective technique for dealing with crack problems.