改进型XFEM中基于精确几何描述的非连续单元分割算法研究

扩展有限元法(XFEM)在裂纹模拟中取得空前成功，但在实际工程应用中仍存在精度和性能上的极大挑战：(1)空间裂纹几何描述的非光滑性，将导致应力强度因子计算存在较大震荡，进而影响裂纹扩展路径的精确预测；(2)裂纹与非连续单元之间的精确几何分割存在实现复杂、计算量大、鲁棒性差的困难；(3)三维裂纹精确分析要求裂纹前缘处网格较为精细，从而使得计算代价极大。.为克服上述挑战，本项目将在现有改进型XFEM和二维裂纹分析并行软件PANDA_Fracture基础之上开展下列研究：(1)裂纹精确几何描述—研究基于解析性质的空间曲面裂纹描述方法；(2)非连续单元高效分割—发展基于标准分割模板库的非连续单元快速分割和子剖分方法；(3)三维裂纹分析并行软件—实现基于JAUMIN并行编程框架的三维裂纹分析并行软件。所研发的改进型XFEM并行软件，将为PBX炸药裂纹模拟、航空发动机零部件疲劳裂纹分析提供技术支撑。

The extended finite element method (XFEM) has achieved unprecedented success in crack simulation, but great challenges still remain in practical applications in the aspects of accuracy and performance: (1) The non-smoothness of the geometric description of cracks will cause large oscillations in the extraction of stress intensity factors, and thus results in inaccurate prediction of crack propagation paths; (2) The accurate geometric intersection between crack surfaces and discontinuous elements is difficult to implement, computationally expensive, and insufficiently robust; (3) Accurate crack analysis in three dimensions requires a very fine mesh at the crack front, which is extremely time-consuming..In order to overcome the above-mentioned challenges, the following research will be carried out on the basis of the improved XFEM and the parallel software for two-dimensional crack analysis, PANDA_Fracture: (1) Accurate geometric description of cracks — A crack description method with analytic nature will be employed for three-dimensional arbitrary cracks; (2) Efficient partitioning of discontinuous elements — A templated partitioning method will be established for fast partitioning and subdivision of discontinuous elements; (3) Implementation of parallel software for three-dimensional crack analysis — a parallel software package for crack analysis in three dimensions will be developed based on the parallel programming infrastructure JAUMIN. The parallelized improved XFEM will provide technical support for crack simulation of PBX explosives and for fatigue crack analysis of aero-engine parts.