| 夏晓舟,章青.含两类附加函数的扩展等参有限元法[J].计算力学学报,2008,25(1):41~47 |
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| 含两类附加函数的扩展等参有限元法 |
| Extended isoparametric finite element method including two class of enrichment functions |
| 修订日期：2006-09-26 |
| DOI：10.7511/jslx20081011 |
| 中文关键词: 扩展等参有限元,附加自由度,附加位移函数,指数型间断函数,三角基函数 |
| 英文关键词:extended isoparametric finite element,enriched freedom degree,enriched displacement function,exponent discontinuous function,trigonometric basic function. |
| 基金项目:国家自然科学基金、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重点项目
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国家自然科学基金
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国家重点基础研究发展计划(973计划) |
| 夏晓舟 章青 |
| 河海大学工程力学系 江苏南京210098 |
| 摘要点击次数: 1540 |
| 全文下载次数: 25 |
| 中文摘要: |
| 基于扩展有限元的基本思想,提出一类指数型间断函数来模拟。由于裂纹或节理等非连续结构所导致的位移不连续现象,该附加函数是以到间断处的垂直距离为自变量,且随距离的增大而呈指数衰减,同时,在非连续结构末端引入能反映其奇异场特性的三角基函数。本文用弱解形式推导了扩展有限元格式,并论证了两类附加函数在单元公共边上能够保持位移连续性这一要求。最后,编制了二维4节点和三维8节点的扩展等参有限元程序,并分别给出了算例,结果表明在模拟裂纹追踪时,扩展有限元法可行且有效。 |
| 英文摘要: |
| Based on the idea of extended finite element method,a new enrichment displacement function-the exponent discontinuous function is presented to stimulate the discontinuous character resulted from discontinuity such as crack or joint.This enrichment function uses the vertical distance to discontinuity as the independent variable.It has of exponent attenuation characteristic with the increment of the vertical distance from discontinuity.Simultaneously,at the end of discontinuity,the trigonometric basic function is introducced to embody its singularity.The weak form of extended finite element discrete equation is deduced and the displacement continuity for the share edge of elements can be kept.Finally,the programs for 2-D four nodes and 3-D eight nodes isoparametric finite element are made and the numerical experiments are provided to demonstrate the utility and robustness of the proposed technique. |
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