The present article investigates frictional contact mechanics between a moving punch possessing sharp ends and a finite-thickness functionally graded layer resting on the rigid foundation. The rigid punch has either flat or semi-circular profiles, and it moves over the functionally graded layer at a steady subsonic speed. The tangential load developed by the moving punch is proportional to the normal applied load since Coulomb’s friction law is adopted. Variations of shear modulus and mass density through the thickness of the layer are expressed by exponential functions, whereas the variation of the Poisson’s ratio is neglected. Governing partial differential equations are derived considering two-dimensional theory of elastodynamics, and these equations are solved analytically utilizing Galilean and Fourier transformations. Equations are reduced to a singular integral equation of the second kind. Singular integral equation is solved, and results of analytical approach are compared with those obtained by means of the finite element method in elastostatic case. A very good agreement is achieved between analytical and computational results. Parametric analyses are performed to observe the influences of punch speed, material inhomogeneity and coefficient of friction upon contact stresses of a finite-thickness graded layer resting on the rigid foundation. Stresses observed for relatively thin softening layers are much sensitive to the variation in punch speed.

本文研究了具有尖锐末端的移动冲头与位于刚性基础上的有限厚度功能梯度层之间的摩擦接触力学。刚性冲头具有平坦或半圆形的轮廓，并且以稳定的亚音速在功能渐变层上移动。由于采用了库仑摩擦定律，因此移动冲头产生的切向载荷与法向施加的载荷成比例。剪切模量和质量密度在层厚度上的变化用指数函数表示，而泊松比的变化则被忽略。考虑弹性力学的二维理论，导出了控制偏微分方程，并利用伽利略和傅立叶变换对这些方程进行了解析求解。方程被简化为第二种奇异积分方程。求解奇异积分方程，并将分析方法的结果与通过弹性有限元方法获得的结果进行比较。在分析和计算结果之间达成了很好的协议。进行参数分析，以观察冲头速度，材料不均匀性和摩擦系数对位于刚性基础上的有限厚度渐变层的接触应力的影响。相对较薄的软化层观察到的应力对冲压速度的变化非常敏感。在分析和计算结果之间达成了很好的协议。进行参数分析，以观察冲头速度，材料不均匀性和摩擦系数对位于刚性基础上的有限厚度渐变层的接触应力的影响。相对较薄的软化层观察到的应力对冲压速度的变化非常敏感。在分析和计算结果之间达成了很好的协议。进行参数分析，以观察冲头速度，材料不均匀性和摩擦系数对位于刚性基础上的有限厚度渐变层的接触应力的影响。相对较薄的软化层观察到的应力对冲压速度的变化非常敏感。