中文摘要：

扩展有限元是一种以单位分解思想为基础,在常规有限元位移中加入跳跃函数和渐近位移场函数,以处理不连续问题的数值方法。将水平集算法应用到裂纹界面的描述及加强单元类型的判别,并与扩展有限元相结合,用于分析材料断裂问题。相比传统有限元,有限元网格与裂纹面位置相互独立,不需满足裂纹为单元边、裂尖为单元节点和在裂纹附近进行高密度的网格划分的要求。通过算例分析了单元积分方案,裂尖积分区域对应力强度因子计算精度的影响。

英文摘要：

The Extended Finite Element Method（XFEM）,which is based on the partition of unitym,is a novel numerical approach to solve discontinuous problems.It employs jump function and asymptotic crack tip displacement field function in Classical Finite Element Method,and applies the Level Set algorithm to describe the crack interface and judge the element types.It can be used to analyze the problem of material fracture.Compared with the classical finite element method,where the finite element mesh and the location of crack are mutual independent,the XFEM does not need to construct a mesh which conforms to the crack surface,and thus achieves fine granularity partition around the crack tip.The results from the case analysis demonstrate the impact of the scheme of element integration and the integral region of crack tip on the calculation accuracy of stress intensity factor.