岩土力学2012，Vol.33Issue(11)：3447-3453,7.
水平集和无网格耦合法在裂纹扩展中的应用
Coupling of level set and meshless method and its application to crack propagation
摘要
Abstract
A new method which couples the level set method with meshless method to simulate crack growth is presented. The coupling of level set and meshless method can achieve naturally because they all set up based on the discrete nodal data. Two level sets that are orthogonal to one another at the crack tip are used to represent the geometry of crack and the location of crack tip, and to construct the Heaviside skip function and the Westergaard enriched function near the crack tip in the element-free Galerkin method (EFGM) discontinuous approximation. New crack tips are defined by the update algorithm of level set easily when the crack is growing. The coupling method does not use the visibility method, the diffraction method or the transparency method. The √r singularity is reproduced very well; and the convergence for elastic problems is improved. The passage of crack has no influence on the nodal domain. Smaller domain is used to calculation, which keeps the band and sparsity of the over all stiffness matrix. In addition, the level set makes the selection of enriched nodes and the establishment of additional function simply; and its update process needs no evolution equations. The numerical results show that the presented method has higher computational accuracy; and the simulated expanding path of crack is coincided with the tested curve. So, the results verify the validity and accuracy of the presented method.关键词
裂纹扩展/无网格伽辽金法/水平集法/不连续近似Key words
crack propagation/ element-free Galerkin method/ level set method/ discontinuous approximation分类
数理科学引用本文复制引用
马文涛,师俊平,李宁..水平集和无网格耦合法在裂纹扩展中的应用[J].岩土力学,2012,33(11):3447-3453,7.基金项目
国家自然科学基金(No.10972180,No.61001156,No.51269024) （No.10972180,No.61001156,No.51269024）
宁夏自然科学基金(No.NZ1030). （No.NZ1030）
