Modeling strong/weak discontinuities by local mesh refinement variable-node XFEM with object-oriented implementation

摘要

In this paper, we present a Matlab object-oriented implementation of the variable-node extended finite element method (XFEM), which is enhanced by local mesh refinement technique, for modeling strong and weak discontinuities such as cracks, inclusions, and voids. An easy-to-use local mesh refinement scheme is thus proposed, in which the variable-node elements play an important role as they are integrated into the model for the purpose of connecting/linking different scale meshes. For efficiency, the fine-scale mesh is generated near discontinuities, and the refinement is controlled by three parameters: the number of extension layers, the number of subdivision scales, and the number of refinement levels. We detail the implementation of integrating the variable-node elements into the local mesh refinement XFEM codes in a seamless way. The concept of object-oriented programming (OOP) and strategy design pattern promote the extensibility of computer codes. We consider several numerical examples to show the applicability and accuracy of the current computer codes for mutiple crack growths, crack-hole interactions, multiple inclusions, and a rock slope with one interface and two faults.