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从弹性力学通解出发，借助积分变换将纤维和基体内的位移场和应力场表示成以裂纹面上位错函数为未知量的积分形式．由边界条件将纤维增强复合材料三维轴对称裂纹问题化成求解一组奇异积分方程的问题．应用奇异积分方程理论分析了裂纹尖端的应力奇异特性，确定了各种不同裂纹问题的奇异性指数．通过对奇异积分方程组的数值求解，计算了各种不同裂纹尖端的应力强度因子．
Based on the general solution of elastic mechanics, displacement field and stress field inside the fiber and matrix are represented by the integral transformation as an integral form of the dislocation function on the crack surface as an unknown quantity. The problem of three-dimensional axisymmetric crack in fiber-reinforced composites is solved by boundary conditions to solve a set of singular integral equations. The singular integral equation theory is used to analyze the stress singularity of the crack tip, and the singularity indices of various crack problems are determined. By solving the singular integral equations numerically, the stress intensity factors of different crack tip are calculated.