三维数值流形法覆盖系统生成算法研究

Study on algorithm of cover system generation in three-dimensional numerical manifold method

覆盖系统生成效率低是当前制约三维数值流形法在大型实际工程中应用的瓶颈问题。通过改进三维覆盖系统的生成算法,提出了改进的布尔交运算生成三维覆盖系统的算法,并采用C++语言编写了相应的程序。根据数学网格与物理域的拓扑几何关系,确定采用传统布尔交运算还是由数学网格直接生成流形块体,并对生成的流形块体进行三维块体有效性检查,满足要求后即可生成新的三维流形单元,进而生成所有前处理三维覆盖系统。选取两个简单算例和一个边坡工程问题来说明所提方法的可行性和计算程序的正确性,并通过对比分析说明方法的计算效率。计算结果表明,改进的布尔交运算比传统布尔交运算更高效;随着网格密度的增加,生成一个单元的平均耗时逐渐减少;随着物理域边界复杂程度增加,所提方法计算效率逐渐降低。为今后采用数值流形法进行结构分析奠定基础,具有较强的实际应用价值。

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.