中文摘要：

扩展有限元法（xFEM）是一种新的求解不连续问题的数值方法，由于该方法建立在传统有限元法框架内，而且避免了不连续界面扩展时的网格重新划分，所以，近年来扩展有限元法是工程力学领域里的一个研究热点。本文基于Zi和Belytschko新近提出的一种不连续位移场假设，推导了求解粘着裂纹扩展问题的矩形扩展有限元公式和离散方程。提出了基于位移加载的直接迭代的算法来求解非线性有限元方程，并给出了详细的过程。编写了Fortran程序，模拟了三点弯曲梁开裂问题，得到的结果与已知文献结果吻合，验证了方法、公式和所编写的程序的正确性。

英文摘要：

The extended finite element method （XFEM） is a new numerical method for modeling discontinuity problems. As the method is established in a standard finite element framework, and remeshing is not necessary during the growth of discontinuous faces, it has become one of the hot research topics in engineering mechanics area in recent years. Rectangular extended finite element formulations and the discretized equations for analysis of the cohesive crack growth were derived based on the newly proposed dis- continuous displacement field by Zi and Belytschko. The direct iteration algorithm with displacement loading was proposed for solving the non-linear finite element equations. Details were given. A Fortran program was written to analyze the fracture of a three-poini; bending beam. The results agree well with existing data in the literature, thus, prove the correctness of the proposed method, derived formulations and the written program.