为保证在裂纹尖端具有最佳的逼近，裂纹尖端的解析解与其周边数值解联合应用的新型流形法用来求解应力强度因子，但仅限于平面问题的Ⅰ型和Ⅱ型裂纹。沿用解析解与数值解联合应用的思路，以三维穿透直裂纹为研究对象，在裂纹尖端引入Williams解析解级数，应用解析覆盖与周边数值覆盖联合求解三维应力强度因子，相对于其他数值方法而言计算精度高。推导相应的刚度矩阵和应变矩阵的具体表达式，通过典型算例验证了解决三维应力强度因子精确求解的有效性。

A new method is presented to compute the Stress Intensity Factors(SIF) by combining analytical solutions with numerical solutions in previous studies based on numerical manifold method, which obtains optimal approximation at the crack tip but only for the type Ⅰ and typeⅡ cracks in planar. Following the idea of combined application, Williams series is introduced at the crack tip and 3D SIF for three-dimensional straight through cracks is completed via combining analytical covers with numerical covers, which obtains higher computational precision than other numerical methods. Meanwhile, the corresponding formulas of the stiffness matrix and the strain matrix are deduced，and numerical examples shows the validity of the method in solving the exact solution of 3D stress intensity factor.

O343.2

国家自然科学基金（51779019、51809017）；中央级公益性科研院基本科研业务费（CKSF2020065/CL）