基于布尔交运算的三维流形单元生成研究

三维流形单元的生成是进行三维数值流形分析的首要问题之一。详细研究了三维流形单元的生成过程，并采用C++语言编写了相应的程序。借鉴二维流形单元的形成技术，基于拓扑学的“有向性”原理，将点、有向边、有向环、有向面和有向壳等作为三维块体的基本数据结构。将材料体和数学网格进行布尔交运算，并对形成的流形块体进行有效性检测，满足要求后即形成新的三维流形单元。每个数学网格的顶点作为新流形单元的数学覆盖，再对数学覆盖进行细分，形成流形单元的物理覆盖。分别选取凹形体、空心体和包含有限结构面的材料体与数学网格进行布尔交运算，并选取一个典型工程来检查该方法和程序的可行性。计算结果表明，该方法可以对复杂块体（凹形体、空心体和包含有限结构面的体）进行处理，为今后进行复杂结构计算和分析奠定基础，具有较强的适应性和可靠性。

Generation of three-dimensional manifold element based on Boolean intersection operations

The generation of three-dimensional (3D) manifold element is a critical problem for analyzing with 3D numerical manifold method (NMM). The aim of this paper is to investigate the generation of 3D manifold element and then develop the corresponding program with the C++ programming language. With the method of generation of 3D manifold element, the vertices, oriented edges, loops, faces and shells are considered as the fundamental data structure of 3D block based on the oriented theorem of topology. The Boolean intersection operations of blocks and mathematical meshes are conducted to validate new blocks. The manifold elements are generated once the validity of new blocks is satisfied. The vertices of each mathematical mesh are considered as the mathematical covers of new manifold elements, and then the physical covers are generated by subdivision of mathematical covers. Case studies for blocks with concaves, hollow or finite structural surfaces are conducted by using Boolean intersection operations with corresponding mathematical meshes. Moreover, a selected rock slope with many finite discontinuities is used to verify the developed method, with which shows that complicated block with concaves, hollow or finite structural surfaces can be well dealt. This study provides an effective and reliable way to analyze complicated structures.