无网格与有限元的耦合在动态断裂研究中的应用

提出将无网格Galerkin法与有限元耦合的方法用于分析动态裂纹扩展问题,只在裂尖附近区域沿裂纹扩展方向布置无网格结点,而在其他区域采用一般的有限元,区域交界处的结点采用MLS方法插值,然后将求得的结点值再分配到有限单元的相关结点上,保证了无网格区域和有限元区域的交界处位移的连续。避免了网格的再生成,同时也克服了单纯使用无网格Galerkin法所带来的边界条件难处理及计算效率较低的缺点。数值算例显示这种方法是有效的。

Coupled Finite Element-Element-Free Galerkin Method for Dynamic Fracture

Element-free Galerkin method(EFGM) and the traditional finite element method(FEM) are coupled for analyzing the dynamic fracture.The EFGM is only used near the crack tip for modelling the crack propagation,while FEM in the remaining part including the boundary.In the interface region,the functions at the nodes are evaluated with moving least square interpolation and then assigned to the FE nodal set.The proposed method is applied to calculate the mode I dynamic energy release rate in a two-dimensional cracked structure,where remeshing gets unnecessary,and the boundary conditions are treated directly as usual FEM.