A polytree-based adaptive scheme for modeling linear fracture mechanics using a coupled XFEM-SBFEM approach

摘要

In this paper, an adaptive mesh refinement, namely polytree is presented to increase the resolution of polygonal meshes. Conforming to elements with hanging nodes from the process of generating polytree meshes by commonly using polygonal basic functions is inaccurate because their derivatives are singular in the vicinity of these nodes. Scaled boundary finite element method (SBFEM) is an excellent candidate to overcome such shortcomings. For crack simulations by using extended finite element method (XFEM), enrichment functions of discontinuous and asymptotic fields which get involved with high gradients are necessary to be solved by local mesh refinements. The idea of coupling XFEM with SBFEM is thus designed as an effective numerical technique to solve the negative effects of hanging nodes in adaptive mesh scheme and to raise the computational capability of XFEM in modeling crack problems over polygonal meshes. In addition, a modification of enriched nodes around the crack tip and a treatment of blending elements are introduced to improve the accuracy of XFEM analysis. Several numerical examples are examined to prove the computational efficiency of the present method for modeling crack problems in comparison with the uncoupled counterpart and previous published results.