A four-node quadrilateral element fitted to numerical manifold method with continuous nodal stress for crack analysis

Formulations of a four-node quadrilateral element fitted to numerical manifold method (NMM) with continuous nodal stress called Quad4-CNS (NMM) element for two-dimensional (2D) crack analysis are presented. This Quad4-CNS (NMM) element can be considered as a development of the recently published four-node quadrilateral element with continuous nodal stress (Quad4-CNS). In contrast to the four-node iso-parametric quadrilateral element (Quad4), the Quad4-CNS element has higher order of global approximations, much better accuracy and continuous nodal stress. Moreover, it is free from the “linear dependence” which otherwise cripples many of the partition of unity (PU) based methods with high order global approximations. Due to the adoption of two cover systems, namely, the mathematical cover and physical cover, the NMM is capable of solving continuous and discontinuous problems in a unified way. The purpose of this paper is to synergize the advantages of both the Quad4-CNS element and the NMM to precisely model linear elastic fracture problems. A number of numerical examples indicate the accuracy and robustness of the present Quad4-CNS (NMM) element.