固结各向同性弹性薄层与无限长圆柱体的滑动接触问题  

Sliding contact problem of an infinite cylinder and the bonded elastic thin layer

作　　者：朱凯[1] 叶振环[1] 张旭[1] 熊飞峤[1] 孔丽[1] 

机构地区：[1]遵义师范学院,遵义563002

出　　处：《应用力学学报》2016年第6期982-988,1117,共7页Chinese Journal of Applied Mechanics

基　　金：基金项目:高速滚动轴承热力耦合分析基础方法研究(黔教合KY字[2014]294号)

摘　　要：基于Papkovich-Neuber势函数研究了受刚性基底固结作用下的弹性薄层的滑动接触问题。通过Fourier变换得出弹性薄层应力、位移表达式的Fourier形式。在边界条件的限定下,利用积分变换手段将平面应变问题的弹性方程转化为第一类奇异积分方程。运用Gauss-Chebyshev积分法将奇异积分方程进行离散,采取Chebyshev多项式零点作为Gauss节点,对边界压应力进行数值求解,最终求得接触压应力函数的量纲为一的量的表达式。数值算例结果表明:摩擦系数为影响最大压应力偏心率的主要因素;层厚对压应力分布的影响显著。The sliding contact problem for elastic thin layer is concerned based upon the Papkovich-Neuber potential function. Firstly, using the Fourier transform to get the stress and the displacement expressions of the elastic thin layer. Then, considering the boundary conditions, the elastic equation for plane stress problem is converted to a singular equation of the first kind by using integral transformation. Thirdly, using the zero point of Chebyshev polynomials as the Gauss node, the singular integral equation is reduced to a system of linear equations by utilizing the Gauss-Jacobi polynomials. Finally, the numerical solution for the contact pressure is obtained by solving the system of linear equations. Results obtained show that the main influence factor for the eccentricity of the maximum pressure is the friction coefficient, and the pressure is closely related to the layer's thickness changes.

关 键 词：弹性薄层 积分变换 第一类奇异积分方程 Guass-Chebyshev积分法 

分 类 号：O343.3[理学—固体力学]