Application of HT finite element method to multiple crack problems of mode I, II and III

The paper presents a multiple fracture analysis of mode I, n and III problems by Hybird-Trefftz (HT) finite element element. Since the approach employs regular T-complete functions that satisfy the governing equation, the procedure is much simpler and its accuracy should be better than that of general finite element. HT method can be viewed as a powerful computational tool in dealing with the singular crack problems. The paper focus on the applications of HT finite element method to mode I, II and III fracture problems in elastic field. In particular, a series of special element models are presented to represent those elements containing a crack, which can accurately satisfy the fracture behavior of elements on crack faces. Furthermore, auxiliary functions are adopted near crack tips to improve computing accuracy at the same time. The performance of the proposed finite element formulations is assessed by an case of arbitrary elastic three-dimension mass with an arbitrary side crack, which can be simplified as pure mode I, II and III fracture problems, respectively. In contrast with conventional finite or boundary element model, the effect of numbers of T-complete functions, the mesh density, the number of Gauss points and the auxiliary functions near crack tips on the accuracy of the solution are discussed. The numerical assessment indicates that the proposed HT finite element formulation is ideally suitable for the analysis of mode I, n and n fracture problems, and may be applied to engineering problem as well.