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提出了一种分析横观各向同性纤维增强复合材料轴对称界面端的奇异应力场的特征值法。基于横观各向同性弹性材料空间轴对称问题的基本方程和一阶近似假设,利用分离变量形式的位移函数和无网格算法,导出了关于应力奇异性指数和应力角函数的奇异性特征方程。对于纤维/基体轴对称界面端模型,特征值法给出的应力奇异性指数、相应的位移和应力角函数,与通过有限元分析得到的结果非常吻合。利用有限元计算得到的奇异应力场,结合特征值法给出的应力奇异性指数和应力角函数,通过线性外插得到了相应的应力强度系数。特征值法结合有限元分析,可以完全确定横观各向同性纤维增强复合材料轴对称界面端的奇异应力场。
An eigenvalue method for analyzing the singular stress field at the axisymmetric interface of transversely isotropic fiber-reinforced composites is proposed. Based on the basic equations and the first-order approximation assumption of the axisymmetric problem of transversely isotropic elastic materials, the singularity characteristic equations of stress singularity and stress angle functions are derived by using the displacement function and the meshless algorithm in the form of discrete variables . For the fiber / matrix axisymmetric interface model, the stress singularity index, corresponding displacement and stress angle functions given by the eigenvalue method are in good agreement with the results obtained by finite element analysis. By using the singular stress field calculated by finite element method and combining the stress singularity index and stress angle function given by eigenvalue method, the corresponding stress intensity coefficient is obtained by linear extrapolation. Eigenvalue method combined with finite element analysis can completely determine the singular stress field at the axisymmetric interface of transversely isotropic fiber-reinforced composites.