模量面内变化的梯度功能弹性薄层接触应力分析

针对材料均匀去除要求，提出了一种基于梯度功能研抛盘的加工新方法，研究了模量面内变化的梯度功能弹性薄层接触应力问题。用半逆解法推导出梯度功能弹性薄层无摩擦接触应力方程，引入补偿函数来补偿平面位移的影响，简化了解析过程；利用ANSYS建立了梯度功能研抛盘无摩擦接触模型，得到位移加载下试样表面的等效应力分布；通过与应力方程拟合，获得了应力预测方程解析式及相应的补偿函数关系。最后，建立了试验平台，试验对比结果显示误差在10%以内，验证了接触应力预测方程解析式的正确性。

Contact Stress Analysis of Functionally Graded Elastic Thin Layers with In-plane Variation of Modulus

To attain the requirements for uniform removal of materials, a new processing method was proposed based on functionally graded lapping and polishing plate. Also, the contact stress of functionally graded elastic thin layers with in-plane variation of modulus was studied. Firstly, the frictionless contact stress equation of functionally graded elastic thin layers was derived by semi-inverse method, and the compensation function was introduced to compensate the effects of plane displacement, which simplified the analytical processes. Then, the frictionless contact model of functionally graded lapping and polishing plate was established by ANSYS, the equivalent stress distribution on the specimen surface under displacement loading was obtained. By fitting with the stress equation, the analytical formula of stress prediction equation and the corresponding compensation function were obtained. Finally, a experimental platform was established and the experimental and predicted values were compared. The results show that the errors are within 10%, which verifies the correctness of the analytical formula of contact stress prediction equation.