In this study, the frictional moving contact problem for an orthotropic layer bonded to an isotropic half plane under the action of a sliding rigid cylindrical punch is considered. Boundary conditions of the problem include the normal and tangential forces applied to the layer with a cylindrical punch moving on the surface of the layer in the lateral direction at a constant velocity V. It is assumed that the contact area is subjected to the sliding condition where Coulomb’⣙s law is used to relate the tangential traction to the normal traction. Using the Fourier integral transform technique and Galilean transformation, the plane contact problem is reduced to a singular integral equation in which the unknowns are the contact stress and the contact width. The singular integral equation is solved numerically using Gauss–Jacobi integration formulae. Numerical results for the contact widths and the contact stresses are given as a solution.

中文翻译：

---

关于移动刚性圆柱冲头在与各向同性半平面结合的正交各向异性层上滑动的接触问题

在这项研究中，考虑了在滑动刚性圆柱冲头的作用下粘合到各向同性半平面的正交各向异性层的摩擦移动接触问题。问题的边界条件包括圆柱冲头以恒定速度 V 沿横向在层表面上移动时施加到层上的法向力和切向力。 假设接触区域受到滑动条件，其中库仑定律用于将切向牵引力与法向牵引力联系起来。使用傅里叶积分变换技术和伽利略变换，将平面接触问题简化为奇异积分方程，其中未知数为接触应力和接触宽度。奇异积分方程使用 Gauss-Jacobi 积分公式进行数值求解。