中文摘要：

本文主要研究均匀涂层-功能梯度材料界面层-均匀半空间三层结构模型中均匀涂层与功能梯度材料层之间界面处的无摩擦轴对称接触问题的界面应力场。文中建立三层结构的理论计算模型，利用积分变换技术将数学模型转化为奇异积分方程，得到梯度材料夹层轴对称接触问题的表面位移解，再通过数值方法，得到梯度材料夹层的界面应力场。文中分析讨论了刚性圆柱形平压头作用下的均匀涂层与梯度材料夹层界面处的应力分布情况，探讨了剪切弹性模量比值、接触半径对界面处正应力、剪切应力分布的影响。研究表明，剪切弹性模量比值对界面处应力均产生重要的影响，随着剪切弹性模量比值的递增，界面层正应力呈递减趋势，而界面层剪切应力呈递增趋势，且接触半径的不同，也会改变影响的幅度。调整剪切弹性模量，是实现抑制裂纹萌生的一种有效途径。此外，作者主要从事新型功能材料接触力学的研究工作。

英文摘要：

The paper investigates the three -dimensional frictionless ax -symmetric contact problem of a functionally graded material under a rigid cylindrical indenter . The interfacial stress field between a homogeneous coating and a functionally graded layer are considered .A mathematical model is constructed to simulate the three layer structure which consisting of a homogeneous coating , a graded interlayer and a homogeneous half space .By using integral transform technique , the contact problem model is converted to a singular integral equation , which can obtain the surface displacement field; finally, by utilizing numerical methods, which can gain the interfacial stress field of the graded material interlayer structure .The paper analyzes the effect of the shear modulus ratio and contact radius on the interfacial stress field under a rigid cylindrical indenter .It is concluded that the shear modulus ratio and contact radius play an important part in the distribution of the interfacial stress .With the shear modulus ratio increasing , the interfacial normal stress shows a decreasing trend , but the interfacial shear stress shows an increasing trend .And the contact radius also changes the amplitude , which provides a new way to inhibit the contact damage and fracture .In addition, the authors are principally engaged in the research of the new functional materials contact mechanics .