压电涂层-功能梯度压电界面层-基底结构的二维接触问题研究

在多层压电元件中，由于界面处材料成分和性质的突变，常常导致界面处应力集中，使得界面处出现开裂或蠕变现象，从而大大缩短了压电元件的使用寿命。功能梯度压电材料作为界面层，可有效的缓解界面材料不匹配导致的破坏。本文主要研究利用功能梯度压电材料界面层连接压电涂层和基底，分析三层结构在圆柱型压头作用下的力电响应。利用傅里叶积分变换技术，本文将压电涂层-功能梯度压电层-基底结构在刚性圆柱压头作用下的二维平面应变接触问题转化为带有柯西核的奇异积分方程。运用高斯-切比雪夫积分公式，将奇异积分方程转化为线性方程组并对其进行数值求解，得到压电涂层-功能梯度压电层-基底结构在圆柱形压头作用下的应力分布和电位移分布。数值结果表明，梯度压电材料参数的变化对结构中的力电响应具有重要的影响。本文研究结果对于利用功能梯度压电界面层消除界面处的应力不连续导致的界面破坏具有重要的理论指导意义，研究结果可为功能梯度压电材料界面层的设计提供帮助。

Study on two-dimensional contact problem for piezoelectric coating - functionally graded piezoelectric interface layer - substrate system

The sudden change of material composition and properties at the interface of multilayer elements often leads to stress concentration at the interface, resulting in cracking or creep of the interface layer, which greatly shortens the service life of piezoelectric elements.As an interface layer, functionally graded piezoelectric materials can effectively alleviate the damage caused by interface material mismatch.This paper mainly studies the electromechanical response of the structure under the action of cylindrical indenter when the interface layer of functionally graded piezoelectric material is used to connect the piezoelectric coating and substrate.Using Fourier integral transform technique, the two-dimensional plane strain contact problem of piezoelectric coating functionally graded piezoelectric layer substrate structure under the action of rigid cylindrical indenter is transformed into a singular integral equation with Cauchy kernel.Using Gauss Chebyshev integral formula, the singular integral equation is transformed into linear equations and solved numerically. The stress distribution and potential shift distribution of piezoelectric coating functionally graded piezoelectric layer substrate structure under the action of cylindrical indenter are obtained.The numerical results show that the variation of gradient piezoelectric material parameters has an important influence on the electromechanical response of the structure.The research results of this paper have important theoretical guiding significance for using functionally graded piezoelectric interface layer to eliminate the interface failure caused by stress discontinuity at the interface. The research results can provide help for the design of functionally graded piezoelectric interface layer.