中文摘要：

文章旨在研究功能梯度中厚板中切口尖端的奇性问题。从柱坐标系下平衡方程出发,基于切口尖端位移场的级数渐近展开假设,推导出了关于功能梯度中厚板切口尖端奇性指数的特征微分方程组,并将切口的径向边界条件表达为奇性指数和特征角函数的组合,从而将功能梯度中厚板切口尖端奇性指数的计算转化为相应边界条件下特征常微分方程组的求解问题。该文采用插值矩阵法求解该特征微分方程组,可以一次性地计算出功能梯度中厚板切口的各阶奇性指数和相应的特征角函数,并通过算例验证了文中所提算法是有效的。

英文摘要：

The singularity of the V-notch located in the functionally graded plate whose material con- stants vary along the thickness direction is analyzed. Based on the assumption of the asymptotic ex- pansion of the displacement fields close to the vertex of the V-notch, the equilibrium equations are transformed into a set of characteristic ordinary differential equations with respect to the singularity order. The radial boundary conditions are expressed as the combination of singularity order and char- acteristic angular functions. The evaluation of the singularity order for the V-notch in the functionally graded plate is transformed into the solution of a set of characteristic ordinary differential equations under the corresponding boundary conditions. The interpolation matrix method is introduced to solve the characteristic equations for obtaining the singularity order and characteristic angular functions. The effectiveness of the proposed algorithm is verified by the numerical examples.