Winkler地基模型上功能梯度材料涂层的摩擦接触问题

研究Winker地基模型上功能梯度材料涂层在一刚性圆柱形冲头作用下的摩擦接触问题。功能梯度材料涂层表面作用有法线向和切线向集中作用力。假设材料非均匀参数呈指数形式变化,泊松比为常量,利用Fourier积分变换技术将求解模型的接触问题转化为奇异积分方程组,再利用切比雪夫多项式对所得奇异积分方程组进行数值求解。最后,给出了功能梯度材料非均匀参数、摩擦系数、Winker地基模型刚度系数及冲头曲率半径对接触应力分布和接触区宽度的影响情况。

A frictional contact problem of a functionally graded layer resting on a Winkler foundation

This paper presents the investigation to the frictional contact problem for a functionally graded layer under the action of a rigid circular stamp supported by a Winkler foundation.A segment of the top surface of the graded layer is subject to both normal and tangential traction while rest of the surface is devoid of traction.The graded layer is assumed to be an isotropic nonhomogeneous medium with an exponentially varying shear modulus and a constant Poisson''s ratio.The problem is reduced to a Cauchy-type singular integral equations with the use of Fourier integral transform technique and the boundary conditions of the problem.The singular integral equations is solved numerically using Chebychev polynomials.The main objective of this paper is to study the effect of the material non-homogeneity factor,stiffness of the friction coefficient,Winkler foundation and punch radius on the contact pressure distribution and the size of the contact region.