Because of geometric or material discontinuities, stress singularities can occur around the vertex of a V-notch. The singular order is an important parameter for characterizing the degree of the stress singularity. The present paper focuses on the calculation of the singular order for the anti-plane propagating V-notch in a composite material structure. Starting from the governing equation of elastodynamics and the displacement asymptotic expansion, an ordinary differential eigen equation with respect to the singular order is proposed. The interpolating matrix method is then employed to solve the established eigen equation to conduct the singular orders. The effects of the material principal axis direction, shear modulus, and propagation velocity and acceleration on the singular orders of the V-notch are respectively investigated, and some conclusions are drawn. The singular orders of the V-notches decrease with an increase in the material principal axis direction angle, except for the crack, whose singular orders do not change with the principal axis direction. The singular orders increase with an increase in the shear modulus $$G_{13} $$ , while they decrease with an increase in the shear modulus $$G_{23} $$ . The singular orders increase as the magnitude of the propagation velocity increases, while they decrease as the direction of the propagation velocity increases. The singular orders increase with an increase in the value of the propagation acceleration, while they decrease with an increase in the direction of the propagation acceleration. The singular orders become larger when the ratio of $$G_{13}^{(2)} /G_{13}^{(1)} $$ increases, while they become smaller when the ratio of $$G_{23}^{(2)} /G_{23}^{(1)} $$ increases, and they increase with an increase in the mass density ratio for the bi-material V-notch.

中文翻译：

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复合材料反面传播V型缺口奇异阶数的计算

由于几何或材料的不连续性，V 形槽口的顶点周围可能会出现应力奇点。奇异阶数是表征应力奇异程度的重要参数。本文重点研究复合材料结构中反平面传播V型缺口奇异阶次的计算。从弹性动力学控制方程和位移渐近展开出发，提出了关于奇异阶的常微分特征方程。然后采用插值矩阵法求解已建立的特征方程进行奇异阶次。分别研究了材料主轴方向、剪切模量、传播速度和加速度对V型缺口奇异阶数的影响，并得出一些结论。V型缺口奇异阶数随着材料主轴方向角的增加而减少，裂纹除外，其奇异阶数不随主轴方向变化。奇异阶数随着剪切模量 $$G_{13} $$ 的增加而增加，而它们随着剪切模量 $$G_{23} $$ 的增加而减少。奇异阶数随着传播速度幅度的增加而增加，而随着传播速度方向的增加而减少。奇异阶数随着传播加速度值的增加而增加，而随着传播加速度方向的增加而减少。当$$G_{13}^{(2)} /G_{13}^{(1)} $$的比值增加时，奇异阶数变大，