固结各向同性弹性薄层与无限长圆柱体的滑动接触问题
发布时间：2019-03-20 21:27
【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。
[Abstract]:Based on the Papkovich-Neuber potential function, the sliding contact problem of elastic thin layer subjected to consolidation of rigid basement is studied. The Fourier form of the expression of stress and displacement of elastic thin layer is obtained by Fourier transform. Under the boundary conditions, the elastic equations of plane strain problems are transformed into singular integral equations of the first kind by means of integral transformation. The singular integral equation is discretized by Gauss-Chebyshev integral method, and the zero point of Chebyshev polynomial is used as the Gauss node to solve the boundary compressive stress numerically. Finally, the expression of the dimension of the contact compressive stress function is obtained. The numerical results show that friction coefficient is the main factor affecting the maximum compressive stress eccentricity and the thickness of the layer has a significant effect on the distribution of the compressive stress.
【作者单位】： 遵义师范学院;
【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)
【分类号】：O343.3
[Abstract]:Based on the Papkovich-Neuber potential function, the sliding contact problem of elastic thin layer subjected to consolidation of rigid basement is studied. The Fourier form of the expression of stress and displacement of elastic thin layer is obtained by Fourier transform. Under the boundary conditions, the elastic equations of plane strain problems are transformed into singular integral equations of the first kind by means of integral transformation. The singular integral equation is discretized by Gauss-Chebyshev integral method, and the zero point of Chebyshev polynomial is used as the Gauss node to solve the boundary compressive stress numerically. Finally, the expression of the dimension of the contact compressive stress function is obtained. The numerical results show that friction coefficient is the main factor affecting the maximum compressive stress eccentricity and the thickness of the layer has a significant effect on the distribution of the compressive stress.
【作者单位】： 遵义师范学院;
【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)
【分类号】：O343.3
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