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使用超奇异积分方程方法对相材料中与界面垂直相触的I型三维平片裂纹问题进行了理论和数值分析 .在理论分析中 ,我们使用主部分析法分析了界面上裂纹端部应力奇性指数和I型应力强度因子 .在数值计算中 ,超奇异积分方程组中的未知函数裂纹表面位移差近似地表示为位移差的基本密度函数与多项式之积 .基本密度函数反映了裂纹端部应力奇性性态 .文章最后以矩形平片裂纹问题为例 ,给出了若干关于不同裂纹形状比和材料刚性比时的应力强度因子数值算例 .数值结果表明 ,本文提出的数值求解方法精度很高 .
In the theoretical analysis, we use principal component analysis (PCA) method to analyze the stress crack at the crack tip in the interface Sex index and stress intensity factor of type I. In numerical calculation, the displacement difference of crack surface on unknown function in the system of hypersonic singular integral approximation is expressed as the product of the basic density function of displacement difference and the polynomial. The basic density function reflects the crack tip Stress singularity state.Finally, a numerical example of the stress intensity factor at different crack shape ratios and material stiffness ratios is given by taking the rectangular plate crack as an example.Numerical results show that the accuracy of the numerical solution method proposed in this paper High.