| 徐志民,谢伟,窦鹏鹏.光滑扩展有限元方法及其特点研究[J].计算力学学报,2020,37(5):567~576 |
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| 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 |
| 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. |
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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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