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 引用本文: 王效贵 王美. 考虑尺寸效应的双材料轴对称界面端应力奇异性[J]. 力学学报, 2010, 42(3): 448-455.
Xiaogui Wang, Mei Wang. Stress singularity at axisymmetric interface wedge of bonded dissimilar materials considering dimension effects[J]. Chinese Journal of Theoretical and Applied Mechanics, 2010, 42(3): 448-455.
 Citation: Xiaogui Wang, Mei Wang. Stress singularity at axisymmetric interface wedge of bonded dissimilar materials considering dimension effects[J]. Chinese Journal of Theoretical and Applied Mechanics, 2010, 42(3): 448-455.

## Stress singularity at axisymmetric interface wedge of bonded dissimilar materials considering dimension effects

• 摘要: 提出了一种分析双材料轴对称界面端的应力奇异行为的特征值法.基于弹性力学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的离散形式的奇异性特征方程.由奇异性特征方程的特征值和特征向量,即可确定应力奇异性指数、位移角函数和应力角函数.数值求解了纤维/基体轴对称界面端模型的奇异性特征方程, 结果表明:尺寸效应参数δ(奇异点与轴对称轴的距离和应力奇异性支配区域大小的比值)影响着应力奇异性的强弱与阶次, 准一阶近似解析解只是δ>>1时的一个特例.

Abstract: An eigenvalue method was proposed to study the stresssingularity behavior at the axisymmetric interface wedge of the bondeddissimilar isotropic materials. Based on the fundamental equations of thespacial axisymmetric problem and the assumption of first-orderapproximation, the discrete characteristic equation on the stresssingularity was derived by making use of the displacement functions in theform of separated variables and the technique of meshless method. Thephysical eigenvalue is associated with the order of the stress singularity,and the corresponding eigenvector is related to the displacement and stressangular variations. A dimensionless parameter δ, which was definedas the ratio between the distance from the singular point to theaxisymmetric axis and the dimension of the singularity-dominated region, wasused to characterize the dimension effects on the stress singularitybehavior. The characteristic equation of the fiber/matrix axisymmetricinterface wedge model was solved numerically, and the order of stresssingularity, the associated displacement and stress angular variations wereobtained. It was found that the parameter δ influenced both thestrength and the order of the stress singularity, and the analyticalsolutions derived by the quasi first-order approximation was just a specialcase while δ>>1.

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