含正交各向异性夹层的Kirsch问题的弹性解

Elastic Solutions of Kirsch Problem with Orthogonal Anisotropic Interlayer

针对含有正交各向异性圆环的Kirsch问题,利用级数展开求解材料内部的弹性控制方程,获得了两种不同荷载下各向异性圆环嵌入无限基体的位移/应力解析表达式,其中圆环材料的形态分别考虑为径向各向异性、环向各向异性、横观各向同性。在该理论退化验证良好的基础上,对各向异性材料进行力学分析。结果表明:不同形态的圆环对孔口周围的应力分布有较大的影响。另外,随着各向异性圆环的厚度增大,圆环和基体之间界面处的应力值也增大。

The elastic governing equations within the material are solved through the utilization of a series expansion for the Kirsch problem,incorporating an orthogonal anisotropic hollow layer.Analytical expressions for the displacement/stress of anisotropic hollow layers embedded in an infinite matrix are obtained for two different loads.The material morphology of the hollow layer is considered to be radially anisotropic,circumferentially anisotropic,and transversely isotropic.A mechanical analysis of the anisotropic materials is performed based on the well-verified theoretical degradation.The results show that the various configurations of the hollow layers have a great effect on the stress distribution around the orifice.In addition,as the thickness of the anisotropic circular hole increases,the stress value at the interface between the circular hole and the substrate increases.