扩展有限元中非连续区域的一种积分方案  

An integration scheme for discontinuities in the extended finite element method

作　　者：喻葭临[1] 张其光[1] 于玉贞[1] 孙逊[1] 

机构地区：[1]清华大学水利水电工程系,水沙科学与水利水电工程国家重点实验室,北京100084

出　　处：《清华大学学报（自然科学版）》2009年第3期351-354,共4页Journal of Tsinghua University(Science and Technology)

基　　金：国家自然科学基金资助项目(50779024,50639060)

摘　　要：为促进和推广扩展有限元在实际复杂问题中的应用,提出一种适用于扩展有限元非连续区域积分的简易积分方案。利用基于该积分方案的扩展有限元程序,结合粘聚裂纹模型实现了对三点弯梁开裂过程的模拟。结果表明,由此积分方案得出的结果与常规分片积分法方案得到的结果以及已有研究结果十分吻合。与已有积分方案相比,此简易积分方案既能保证精度和收敛性,同时无需复杂的分片积分过程,也无需考虑零能模式的控制措施,大大地降低了建模的复杂性和成本。A simple integration scheme is presented for numerical quadrature of discontinuous zones in the extended finite element method （XFEM）. This integration scheme is used in an XFEM analysis to model the fracture of a three-point bending beam using the cohesive crack model. The results agree well with those obtained from two other conventional subdomain integration schemes. In contrast to previous integration schemes, this scheme guarantees accuracy and convergence, simplifies the integration procedure, and needs no hour-glass control, so the modeling complexity and cost are sharply reduced.

关 键 词：扩展有限元 虚结点 积分方案 三点弯梁 

分 类 号：TU411.93[建筑科学—岩土工程]