中文摘要：

数值流形方法是一种能统一处理连续和不连续问题的有效数值方法．该方法采用的数学覆盖系统可完全独立于物理域，能很好地求解各类裂纹问题，而n边形单元（n〉4）则具有网格划分灵活，求解精度高等优点．论文基于数值流形方法，采用正六边形数学单元求解线弹性复杂裂纹问题．在导出相关方程的基础上对典型裂纹问题进行了分析，通过互能积分法得到了裂尖的应力强度因子，计算结果与参考解吻合得较好．除此之外，文中还对不同单元上的求解精度进行了比较，结果表明采用正六边形单元的求解精度较正四边形单元和正三角形单元上的精度均更高．

英文摘要：

The numerical manifold method （NMM） can tackle both continuous and discontinuous with high efficiency and accuracy. Due to the independence of the mathematical cover system and the physical domain,the NMM is very suitable for crack problems. At the same time,the n-sided elements （n〉4） are also very attractive due to their greater flexibility in meshing and higher accuracy, compared with the fre quently used triangular and quadrilateral elements. In the present paper,the NMM,combined with the regular hexagonal mathematical elements, is applied to solve linear elastic complex crack problems. Through the interaction integral, the stress intensity factors at concerned crack tips are computed in typical numerical examples, and the results agree well with the reference solutions. In addition, the accuracy on different mathematical elements is also investigated and the results show that the accuracy on hexagonal elements is higher than that on regular triangular and quadrilateral elements.