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徐志民,谢伟,窦鹏鹏.光滑扩展有限元方法及其特点研究
Study on Smoothed Extended Finite Element Method and its characteristics[J].计算力学学报,2020,37(5):567~576
光滑扩展有限元方法及其特点研究
Study on Smoothed Extended Finite Element Method and its characteristics
Study on Smoothed Extended Finite Element Method and its characteristics
投稿时间:2019-11-05  修订日期:2020-01-06
DOI:10.7511/jslx20191105001
中文关键词:  扩展有限元法  光滑有限元法  光滑扩展有限元法  应力强度因子  裂纹
英文关键词:XFEM  S-FEM  S-XFEM  stress intensity factor (SIF)  crack
基金项目:国家自然科学基金面上项目(11672238);陕西省自然科学基金(2017JM1027;2020JZ-06)资助项目.
作者单位E-mail
徐志民 西北工业大学 航空学院, 西安 710072  
谢伟 西北工业大学 航空学院, 西安 710072 nwpuxiewei@nwpu.edu.cn 
窦鹏鹏 西北工业大学 航空学院, 西安 710072  
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中文摘要:
      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。
英文摘要:
      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.
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