含裂纹复合材料的Cell-based光滑扩展有限元法

Cell-based Smoothed Extended Finite Element Method for Composite Materials with Cracks

为克服有限元法(FEM)某些固有的缺陷,提高计算精度,将Cell-Based光滑有限元法(CSFEM)与扩展有限元法(XFEM)相结合,提出光滑扩展有限元法(CS-XFEM).用该方法对含中心裂纹和斜裂纹的正交各向材料板进行模拟,并与FEM,XFEM和BXFEM(bimaterial extended finite element method)计算结果进行对比.数值算例结果表明,CS-XFEM兼具CSFEM和XFEM两者优点:单元网格与裂纹面相互独立,裂尖不必是单元节点,裂尖处网格也不需要加密,域内积分可转化为边界积分,形函数不需求导,对网格质量要求低;因此是分析断裂问题的简洁高效的数值计算方法.

To overcome some inherent flaws and improve accuracy of the finite element method（FEM）,a novel numerical method called cell-based smoothed extended finite element method（CS-XFEM） was presented.It combined the cell-based smoothed finite element method（CSFEM） and the extended finite element method（XFEM）.The CS-XFEMwas used to simulate an orthotropic plate containing center crack or inclined crack,and then was compared with FEM,XFEMand bimaterial extended finite element method（BXFEM）.The result shows that the CS-XFEMhas the advantages of both the CSFEMand XFEM： the meshes are independent to the crack surface; the end of crack needn＇t to be a node and the meshes around the end needn＇t to be fined; the CS-XFEMcan transform domain integration into boundary integration,therefore,the derivatives of the shape functions are not needed and the mesh size needn＇t to be regular.The CS-XFEMis a simple and efficient numerical method to analyze fracture problems.