三维数值流形法块体切割技术研究

运用布尔碎片运算实现了简单的三维块体切割功能，形成覆盖整个求解域的六面体网格，再将六面体单元拆分生成48个四面体单元，从而生成四面体数学覆盖。运用布尔交运算将四面体单元与求解域求交集得到流形块体，再根据三维拓扑有向性原理和三维单纯形积分理论，形成了有向边、有向环、有向面和有向壳4种有向几何数据结构，用来构造生成封闭的有向三维流形单元。定义了有向流形单元的连通内面对和连通的有向流形单元的概念，利用有向流形单元的连通内面对搜索生成物理覆盖体系。概括总结了基于修正对称和反对称分解的三维数值流形元法的求解计算要点，在不考虑三维接触、三维裂纹尖端奇异场和三维裂纹扩展的假设下，模拟了三维节理面的有限塑性变形张拉过程，得到了比较合理的数值模拟结果，验证了前处理和计算求解算法的正确性。

A study on the block-cutting technique of three-dimensional numerical manifold method

Boolean fragment operation was used to develop a simple three-dimensional block-cutting technique. The hexahedral grid that covers the whole solution domain was generated, and then each hexahedron was divided into 48 tetrahedrons to produce the mathematical cover. Each tetrahedron unit was intersected with the solution domain using the Boolean intersection operation to generate the manifold block. Based on the oriented theory of topology and the three-dimensional simplex integration theory, four kinds of oriented geometry data structure including oriented edge, oriented wire, oriented face and oriented shell, were generated in each manifold block to construct enclosed and oriented three-dimensional manifold elements. The concepts of connected inner face pair and connected oriented manifold element were proposed, and then the physical covers were generated by searching the connected inner face pair of the oriented manifold elements. Furthermore, the key points for calculation of the modified symmetric and anti-symmetric decomposition-based three-dimensional numerical manifold method were summarized. A simulation on the tension process of finite plastic deformation on three-dimensional joints was performed without the consideration of three- dimensional contact, crack propagation and singular field at crack tips. Reasonable numerical simulation results were obtained, which justified the validation of the pre-processing module and calculation algorithm.