关键词: 数值流形方法, 规则网格, 局部加密算法, 适合分析T样条

Abstract: Generally, a finite element mesh or a regular mesh is used as the mathematical covering system in the numerical manifold method (NMM). The advantage of the regular mesh is that it has no requirement to conform to the boundary of the solution domain and various discontinuities. In this paper, the regular rectangular mesh was used as the mathematical mesh in NMM, and the analysis-suitable T-spline was introduced into NMM to realize the local refinement. As the analysis-suitable T-spline was defined over a mildly restricted T-mesh, it presents many important mathematical properties, such as linear independence, partition of unity and highly localized refinement capability. However, after an analysis-suitable T-mesh was locally refined, the generated new T-spline was not analysis-suitable. Therefore, a simple local refinement algorithm was developed in this paper to make sure that the refined mathematical mesh was still analysis-suitable. Moreover, the results from numerical examples show that the algorithm has strong applicability in large-stress gradient areas such as stress concentration area and crack tips.

Key words: numerical manifold method, regular mesh, local refinement, analysis-suitable T-spline