基于层合板模型求解功能梯度压电材料涂层的二维接触问题  

Solving the 2-D contact problem of functionally graded piezoelectric material coating based on laminated plate model

作　　者：余慧芳 刘铁军[1] YU Hui-fang;LIU Tie-jun(Department of mechanics,School of science,Inner Mongolia University of technology,Hohhot 010051,China)

机构地区：[1]内蒙古工业大学理学院,呼和浩特010051

出　　处：《内蒙古工业大学学报（自然科学版）》2021年第4期247-255,共9页Journal of Inner Mongolia University of Technology：Natural Science Edition

基　　金：内蒙古自然科学基金项目(2020MS01022)。

摘　　要：压电材料具有良好的机电耦合效应,被广泛应用在传感器、执行器等智能结构中.由于功能梯度压电材料可以克服压电材料易发生断裂且难以输出较大的电位移等缺点,因而受到研究者的广泛关注.本文应用层合板模型模拟材料参数可以任意变化的功能梯度压电材料涂层,研究了梯度压电涂层在圆柱形压头作用下的二维无摩擦接触问题.利用Fourier积分变换和传递矩阵技术,本文将功能梯度压电材料涂层的二维无摩擦接触问题转化为奇异积分方程组,并利用数值方法对其进行求解.数值结果表明,功能梯度压电材料的梯度指数变化对接触力学行为产生重要的影响.其研究结果对于利用功能梯度压电涂层抑制接触损伤和变形具有重要指导意义.Piezoelectric materials have good electromechanical coupling effects and are widely used in smart structures such as sensors and actuators.As functionally graded piezoelectric materials can overcome the shortcomings of piezoelectric materials such as being prone to fracture and difficult to output large electrical displacements,they have received extensive attention from researchers.In this paper,the laminated plate model is used to simulate the functionally graded piezoelectric material coatings whose material parameters can be changed arbitrarily,and the two-dimensional frictionless contact problem of the gradient piezoelectric coating under the action of a cylindrical indenter is studied.Using Fourier integral transformation and transfer matrix technology,this paper transforms the two-dimensional frictionless contact problem of functionally graded piezoelectric material coatings into singular integral equations,and uses numerical methods to solve them.The numerical results show that the change of the gradient index of the functionally graded piezoelectric material has an important influence on the contact mechanical behavior.The research results have important guiding significance for the use of functionally graded piezoelectric coatings to suppress contact damage and deformation.

关 键 词：功能梯度压电材料 层合板模型 接触 傅里叶积分变换 奇异积分方程 

分 类 号：TB34[一般工业技术—材料科学与工程]