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

A three-node triangular element fitted to the numerical manifold method with continuous nodal stress called Trig3-CNS (NMM) element for accurately modeling two-dimensional linear elastic fracture problems is presented. By adopting two cover systems, namely, the mathematical cover and physical cover, the numerical manifold method (NMM) could easily solve continuous and discontinuous problems in a unified way. In contrast to the three-node triangular element (Trig3), the Trig3-CNS element has higher order of 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 based methods with high order approximations. The purpose of the present work is to synergize the advantages of both the recently developed Trig3-CNS element and the NMM to precisely model two-dimensional linear elastic fracture problems. A number of numerical examples indicate the accuracy and robustness of the present Trig3-CNS (NMM) element.