导电压头作用下的多层功能梯度压电材料涂层二维接触问题研究  

Investigation on the 2D Contact of Multilayer Functionally Graded Piezoelectric Material Coating Under Conducting Indenters

作　　者：代文鑫 刘铁军[1] DAI Wenxin;LIU Tiejun(School of Science,Inner Mongolia University of Technology,Hohhot 010051,P.R.China)

机构地区：[1]内蒙古工业大学理学院,呼和浩特010051

出　　处：《应用数学和力学》2023年第3期282-303,共22页Applied Mathematics and Mechanics

基　　金：国家自然科学基金(12062019);内蒙古自然科学基金(2020MS01022)。

摘　　要：考虑了材料参数可按照任意函数形式变化的功能梯度压电材料(FGPM)涂层在不同形状导电压头作用下的接触问题,研究了梯度系数对功能梯度压电涂层接触力学行为的影响.建立了多层功能梯度压电材料涂层模型,运用了Fourier积分变换和传递矩阵将多层功能梯度压电材料涂层的接触问题转化为奇异积分方程.利用Gauss-Chebyshev数值计算方法,得到了多层功能梯度压电材料涂层-基底结构在刚性导电平压头和圆柱形压头作用下的表面应力分布和电荷分布.利用数值解,分析了材料参数按照不同变化形式的FGPM涂层对最大压痕和电势的影响,还分析了功能梯度压电涂层内部的应力和电位移分布.研究结果表明,功能梯度压电材料参数的不同变化形式对结构的接触性能具有重要的影响.In view of the contact problem of functionally graded piezoelectric material(FGPM)coating under different kinds of conducting indenters,effects of the gradient index on the contact mechanical behavior of the FGPM coating were investigated.A model for the multilayer FGPM coating was established.The contact problem of the FGPM coating was transformed into singular integral equations by means of the Fourier integral transform technology and the transfer matrix method.The Gauss-Chebyshev quadrature formula was used to obtain the surface stress distribution and the charge distribution in the FGPM coating-substrate system under a rigid conducting flat indenter and a conducting cylindrical indenter.According to the numerical results,the effects of variations of the FGPM coating parameters on the indentation and electrical potential were analyzed.The distributions of stress and electrical displacement in the FGPM coating were obtained.The results show that,the variations of the FGPM coating parameters have an important influence on the contact behavior of the system.

关 键 词：接触问题 FGPM涂层 导电压头 Fourier积分变换 奇异积分方程 

分 类 号：O34[理学—固体力学]