关键词: 数值流形法, 覆盖系统, 布尔交运算, 三维流形单元, 数学网格

Abstract: The low efficiency of cover system generation is a bottleneck problem that restricts the application of 3D numerical manifold method in large-scale practical engineering. By improving the generation algorithm of 3D cover system, an improved algorithm of generating 3D cover system based on Boolean intersection operation is proposed, and the corresponding program with C++ is developed. According to the topological geometric relationship between mathematical mesh and physical domain, the manifold block is generated by the conventional Boolean intersection operation or the mathematical mesh directly. The manifold elements are generated when new blocks satisfy the validity, and then all preprocessing 3D cover systems are generated. Two simple examples and a slope engineering problem are selected to illustrate the feasibility of the present method and the correctness of the calculating program, and the calculating efficiency of the present method is also analyzed by comparison. The results show that the improved Boolean intersection operation is more efficient than the conventional Boolean intersection operation. With the increase of mesh density, the average generating time consumption of one element decreases gradually. With the increasing complexity of physical domain’s boundary, the computational efficiency of the present method is gradually reduced. It provides a foundation, with strong practical application value, for future structural analysis with the numerical manifold method.

Key words: numerical manifold method, cover system, Boolean intersection operation, three-dimensional manifold element, mathematical mesh