关键词: 三维数值流形元法, 有向三维流形单元, 连通内面对, 物理覆盖搜索, 修正对称和反对称分解

Abstract: 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.

Key words: three-dimensional numerical manifold method, oriented three-dimensional manifold element, connected inner face pair, physical cover searching, modified symmetric and anti-symmetric decomposition