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论文主要研究刚性圆柱形压头作用下,涂层-梯度层-半空间结构的无摩擦光滑接触问题.假设均匀表面和半空间具有不同的力学性能,梯度层剪切模量沿厚度方向呈指数函数变化,泊松比为一常数.通过Hankel变换及其逆变换求解微分方程,将接触问题转化为奇异积分方程,通过数值分析方法得到均匀表层的位移和应力基本解.利用该基本解,求解刚性圆柱形压头作用下的接触应力分布,并研究了接触半径一定,剪切模量比值变化对应力分布的影响.结果表明,接触半径变化会对应力分布产生影响;同时可以发现,厚度对接触应力分布具有一定的影响.
In this thesis, we study the frictionless smooth contact problem of the coating-gradient layer-half-space structure under the action of a rigid cylindrical indenter.It is assumed that the uniform surface and the half-space have different mechanical properties.The gradient modulus of the gradient layer shows an exponential The change of function and the Poisson’s ratio are constant.Hankel transform and its inverse transform are used to solve the differential equation and the contact problem is transformed into the singular integral equation.The displacement and stress basic solution of uniform surface are obtained by numerical analysis.Using this basic solution, The results show that the change of contact radius will have an impact on the stress distribution. At the same time, it can be found that the influence of thickness on the distribution of stress Contact stress distribution has a certain impact.