Modeling complex crack problems using the three-node triangular element fitted to numerical manifold method with continuous nodal stress

摘要

A three-node triangular element fitted to numerical manifold method with continuous nodal stress, called Trig3-CNS（NMM）element, was recently proposed for linear elastic continuous problems and linear elastic simple crack problems. The Trig3-CNS（NMM） element can be considered as a development of both the Trig3-CNS element and the numerical manifold method（NMM）.Inheriting all the advantages of Trig3-CNS element, calculations using Trig3-CNS（NMM） element can obtain higher accuracy than Trig3 element without extra degrees of freedom（DOFs） and yield continuous nodal stress without stress smoothing. Inheriting all the advantages of NMM, Trig3-CNS（NMM） element can conveniently treat crack problems without deploying conforming mathematical mesh. In this paper,complex problems such as a crucifix crack and a star-shaped crack with many branches are studied to exhibit the advantageous features of the Trig3-CNS（NMM） element. Numerical results show that the Trig3-CNS（NMM） element is prominent in modeling complex crack problems.