不连续问题的扩展有限元法分析

改进的扩展有限元不需要经过后处理可以直接求得应力强度因子,从而为动态不连续问题的分析提供了便利.研究表明:不连续区域附近的积分方案,特别是裂尖区域的积分方案,对结果精度影响很大.文中采用一种新的积分方案对裂尖和裂缝贯穿单元进行积分,既方便积分,又可以减少计算量.采用改进的扩展有限元模拟了裂纹扩展.对于闭合裂缝,必须考虑缝面间的接触条件;裂缝面间若采用完全接触,得到的结点加强自由度近似为零.由于避免了传统有限元方法中的网格重构,改进的扩展有限元在静态和动态不连续问题分析方面具有广阔的应用前景.

Extended finite element method analysis of discontinuities

The stress intensity factors can be evaluated without post-processing with the improved extended finite element method,so it is convenient to analyze the dynamic discontinuities.The study shows that the integration scheme for the domain including the discontinuity has very important effects on the accuracy,especially the integration scheme for the domain including the crack tip.A new numerical integration scheme is used for crack-tip element and element intersected by the discontinuity,and it is convenient and can save time.Crack growth is simulated with the improved extended finite element.The contact conditions must be considered for closed crack interfaces.If the perfect contact between the crack interfaces is considered,the enriched degrees of freedom of nodes are almost equal to zero.Because the geometry of crack is independent of the computation mesh,the method is very appealing and has considerable potential for problems with stationary and dynamic discontinuities.