基于改进型XFEM的裂纹分析并行软件实现

Implementations of parallel software for crack analyses based on the improved XFEM

扩展有限元法(XFEM)目前已成为裂纹分析的主流数值方法.然而,在实际应用中该方法一直受到两方面的困扰:总体刚度矩阵高度病态以及动力学计算时额外自由度上的能量无法正确传递.前者导致在以迭代法求解为主的大规模计算中难以收敛,后者导致动力学求解精度低、实施困难.为解决这两大困扰,基于无额外自由度单位分解插值格式,提出改进型扩展有限元法(IXFEM).基于该方法,在高性能数值模拟软件开发框架JAUMIN上开发裂纹分析并行软件—PANDA_Fracture.实际算例表明, PANDA_Fracture软件具有如下特色:1)允许引入高精度裂尖加强,支持裂纹任意长度扩展; 2)同时支持动力学裂纹问题隐式求解与显式求解; 3)支持任意多裂纹问题高效求解; 4)支持上千CPU核高性能可扩展计算.

The extended finite element method （XFEM） has been a state-of-the-art tool for crack analyses. However, the method has been long hampered in engineering applications by two major issues. One is the global stiffness matrix in static analyses being highly ill- conditioned. The other one is the inconsistent energy transfer between the neighboring time steps in dynamic analyses. The first issue leads to bad convergence in large-scale engineering applications where iterative equation solvers are mainly used. The second issue causes poor accuracy and difficulties in implementations of dynamic analyses. In order to overcome these two issues, the improved XFEM is proposed, based on an extra-dof-free PU approximation. Thereby, parallel software for crack analyses, PANDA_Fracture, is developed based on the proposed method with an HPC framework for numerical applications--JAUMIN. As numerical examples indicate, the software PANDA_Fracture has several distinguished features. Firstly, it introduces highly accurate crack tip enrichment and supports arbitrary crack propagation. Secondly, it supports both implicit and explicit dynamic analyses. Thirdly, it supports multiple crack analyses with high efficiency. Fourthly, it scales up to one thousand CPU cores for high-performance simulations.