An adaptive local mesh refinement strategy in numerical manifold method

Abstract

The numerical manifold method (NMM) is a powerful numerical analysis method based on the partition of unity, which is very suitable for the simulation of jointed rock mass. In order to achieve high accuracy and efficiency in simulating problems with large stress gradient such as stress concentration area and crack tip, an adaptive local mesh refinement algorithm based on the analysis-suitable T-spline (AS T-spline) is proposed in this paper. Specifically, the AS T-spline is applied to locally refine the mathematical cover of NMM in such regions as crack tips where stress concentration exists. The basis function of the cubic AS T-spline is derived and used as the weight function in the NMM to conduct the local refinement for a feasible adaptive procedure. Several numerical examples are given to demonstrate the accuracy and efficiency of the proposed method.