We present a rigorous analysis of the plane problem of an elastic half-plane with a fixed cycloid wavy boundary under biaxial tension using Muskhelishvili’s complex variable method. A closed-form expression for the pair of analytic functions characterizing the stresses and displacements in the elastic body is derived by means of analytic continuation. Furthermore, elementary expressions for the interfacial and hoop stresses along the cycloid interface and stress distributions along the right of an interface valley are obtained. For a cusped cycloid interface, the stresses exhibit the square root singularity at the cusp tips. The mode I stress intensity factor at a cusp tip is expediently extracted from the resulting analytic functions. The interfacial normal stress and hoop stress are constant along a cusped cycloid interface except at the isolated cusp tips.

我们使用Muskhelishvili的复变量方法，对双轴拉伸下具有固定摆线波浪边界的弹性半平面的平面问题进行了严格的分析。通过解析连续性，得出了表征弹性体中应力和位移的一对解析函数的闭式表达式。此外，获得了沿摆线界面的界面应力和环向应力以及沿界面谷部右侧的应力分布的基本表达式。对于针尖摆线界面，应力在针尖处显示平方根奇异点。合宜地从所得的分析函数中提取出尖峰处的模式I应力强度因子。