光滑扩展有限元方法及其特点研究

将光滑有限元法S-FEM（Smoothed Finite Element Method）的子域光滑应变技术和边域光滑应变技术同时引入到扩展有限元XFEM（Extended Finite Element Method）中，提出一种新的光滑扩展有限元法S-XFEM（Smoothed Extended Finite Element Method）。在单元选取及扩充结点选取时采用ES-FEM的光滑域划分方式，在数值积分计算刚度矩阵时采用基于三角形子域的CS-FEM积分思路，并给出了高斯点的积分策略。设计了S-XFEM程序架构并利用Matlab语言编制了S-XFEM计算程序。通过几个经典算例研究对比了XFEM和S-XFEM的特点，验证了S-XFEM的精确性和适用性。结果表明，XFEM和S-XFEM均具有很高的计算精确性和收敛性，XFEM计算精度略高于S-XFEM，而S-XFEM在网格独立性上则明显优于XFEM。

Study on Smoothed Extended Finite Element Method and its characteristics

In this paper,a new smoothed extended finite element method (S-XFEM) was proposed by simultaneously introducing the cell-based and edge-based strain smoothing technique of the Smoothed Finite Element Method (S-FEM) into the Extended Finite element method (XFEM).The S-XFEM adopted the smooth domain partition of the ES-FEM in the selection of elements and accepted the extension nodes and the integration strategy of the CS-FEM based on triangular subdomain in the numerical integration calculation of stiffness matrix with the new integration strategy of Gaussian points.And then the S-XFEM calculation program was designed and programmed with Matlab.The characteristics of the S-XFEM were compared in several classical examples to verify the accuracy and applicability.The results show that both the XFEM and the S-XFEM have high computational accuracy and convergence.The computational accuracy of the XFEM is slightly higher than that of the S-XFEM,while the S-XFEM is obviously superior to the XFEM in mesh independence.