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

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。

Based on the idea of extended finite element method, a new enrichment displacement functionthe 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.