关键词: 数值流形法, T样条, 局部加密算法, 等几何分析

Abstract: The accuracy requirements of numerical manifold method (NMM) can be reached by changing the density of mathematical covers and the order of cover functions. In this study, NMM coupled with nonuniform rational B-splines (NURBS) and T-splines in the context of isogeometric analysis is proposed. Computational formula for a 9-node NMM based on quadratic B-splines is derived. For the case of crack propagation problems where singular fields around crack tips exist, local refinement technique by the application of T-spline discretizations is incorporated into NMM, which facilitates a truly local refinement without extending the entire row of control points. A local refinement strategy for the 4-node mathematical cover mesh based on T-splines and Lagrange interpolation polynomial is proposed. The results from numerical examples show that the 9-node NMM based on NURBS has higher accuracies. The local mesh refinement using T-splines reduces the number of degrees of freedom while maintaining calculation accuracy at the same time, and T-splines refinement method is a natural truly local refinement algorithm.

Key words: numerical manifold method, T-splines, local refinement algorithm, isogeometric analysis