含裂纹复合材料的Cell-based光滑扩展有限元法

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.

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

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-XFEM was used to simulate an orthotropic plate containing center crack or inclined crack， and then was compared with FEM， XFEM and bimaterial extended finite element method (BXFEM). The result shows that the CS-XFEM has the advantages of both the CSFEM and 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-XFEM can 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-XFEM is a simple and efficient numerical method to analyze fracture problems.