| 扩展有限元法的数值方面 |
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| 引用本文： | 余天堂.扩展有限元法的数值方面[J].岩土力学,2007,28(Z1):305-310. |
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| 作者姓名： | 余天堂 |
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| 作者单位： | 河海大学 土木工程学院 工程力学系，南京 210098 |
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| 基金项目： | 国家自然科学基金委员会、二滩水电开发有限责任公司雅砻江水电开发联合研究基金项目（No.50539030）和国家自然科学基金项目（No.50609004）。 |
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| 摘 要： | 扩展有限元法是一种在常规有限元框架内求解强和弱不连续问题的新型数值方法，其原理是在裂尖附近用一些奇异函数和沿裂纹面用阶跃函数加强传统有限元的基，以考虑跨过裂纹的位移场的不连续，该加强策略允许计算网格独立于不连续体几何。讨论了扩展有限元法的一些数值方面，主要包括：水平集法确定界面和加强节点与加强方式、裂尖加强范围的选择、J积分区域的确定和积分方案等。
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| 关 键 词： | 不连续问题 扩展有限元法 数值方面 |
| 收稿时间： | 2007-04-03 |
Numerical aspects of the extended finite element method |
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| YU Tian-tang.Numerical aspects of the extended finite element method[J].Rock and Soil Mechanics,2007,28(Z1):305-310. |
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| Authors: | YU Tian-tang |
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| Institution: | Department of Engineering Mechanics, College of Civil Engineering, Hohai University, Nanjing 210098, China |
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| Abstract: | The extended finite element method(XFEM) is a new numerical method of modeling strong as well as weak discontinuities within a standard finite element framework. The principle consists in enriching the basis of the classical finite element method by some singular functions around the crack tip and by a step function along the crack line to take into account the discontinuity of the displacement field across the crack. This enrichment strategy allows the use of a mesh independent of the discontinuity geometry. Numerical aspects of the XFEM are studied, including the representing of interface and the determination of enriched node and enriched model by level set method by level set method, the selection of enriched domain at the crack tip, the determination of quadrature domain for J integration and the quadrature scheme. |
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| Keywords: | discontinuous problem extended finite element method(XFEM) numerical aspects |
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