文档介绍：基于互补理论的扩展有限元接触问题实现
网络出版时间:2011-12-12 16:50 网络出版地址:s/detail/
第 32 卷第 12 期 2011 年 12 月
文章编号:1000-7598 (2011) 12-3805-08
岩土力学 Rock and Soil Mechanics
Dec. 2011
基于互补理论的扩展有限元接触问题实现
石露 1,李小春 1,王伟 2,白冰1
(,武汉 430071;,石家庄 050043)
摘要:在处理含有裂隙这类不连续问题时,常规有限元方法需要对裂隙尖端部位进行局部网格加密,当裂隙扩展时还需要进行网络重构。基于单位分解思想的扩展有限元成功解决了常规有限元难以处理的裂隙类不连续问题。在研究复合裂隙时, 通常需要考虑裂隙的接触问题。基于互补理论,建立了裂隙面上相对位移和接触力的互补方程,并采用牛顿法求解,无需开闭迭代,且能够快速收敛。最后,对含裂隙平板进行受压数值试验,计算结果表明,基于互补理论的扩展有限元接触算法能够有效地阻止裂隙两端网格的相互嵌入,且获得裂隙面上的应力分布与实际一致。关键词:扩展有限元;互补理论;接触问题中图分类号:O 文献标识码:A
Implementation of XFEM’s contact problem based plementary law
SHI Lu1, LI Xiao-chun1, WANG Wei2, BAI Bing1
(1. State Key Laboratory of Geomechanics and Geotechnical Engineering, Institute of Rock and Soil Mechanics, Chinese Academy of Sciences, Wuhan 430071, China; 2. School of Civil Engineering, Shijiazhuang Tiedao University, Shijiazhuang 050043, China)
Abstract: When dealing with discontinuous issues such as fracture and crack in geo-engineering, conventional finite element method (CFEM) need to refine mesh in the local zone including crack tip; furthermore, the mesh must be reconfigured and re-partitioned once the crack propagation happened. The extended finite element method (XFEM), based on the idea of partition of unit method, can essfully solve these problems easily, which may hardly be deposed by CFEM. Usually, contact problem of crack surface must be considered when studying pound fracture. Based on plementary theory, plementary equation between relative displacement and contact force of the crack surface can be established, and solved by Newton's method without considering opening and closing iteration. Finally, as a numerical example, a plate with crack pressed to indicate the effectiveness of this method. The results indicate that the method can prevent mesh ration from one side of the crack into the other side effectively; and also obtain the st