Local refinement strategy and implementation in the Numerical Manifold Method (NMM) for two-dimensional geotechnical problems

Complex geometric features contained in rock masses and its induced continuous-discontinuous deformation field pose great challenges for Finite Element Analysis to generate high-quality fitting meshes. Proposing the splitting of physical covers, the Numerical Manifold Method (NMM) simulates the complex geometries and the continuous-discontinuous deformation using a simply generated structured mesh. Locally refining the NMM’s structured mesh to meet different accuracy needs of various engineering part, or to solve stress concentrations (singularities) is, therefore, a critical issue for large scale engineering simulation. In this work, a multi-level local refinement is realized on a structured mesh with square elements. To ensure the continuity between the large and small elements, the degree of freedoms (DOFs) are present at the hanging node’s physical covers, and the mean value coordinates are employed as the weight functions of the hanging node’s mathematical cover. Different from the conventional recursive quadtree/octree algorithm, the mathematical group composed of one or more square elements is introduced to generate the 1-irregular mesh. The proposed approach features concise algorithm, simple data structure and convenient numerical implementation, which automatically realizes a local refinement with arbitrary level for complex geotechnical problems. Three numerical examples demonstrate the correctness, convergence and efficiency of the present NMM.