基于层合板模型的梯度压电涂层Reissner-Sagoci问题研究  

Investigation on Reissner-Sagoci Problem for Functionally Graded Piezoelectric Coating Based on Laminate Model

作　　者：马占洲 刘铁军[1] MA Zhanzhou;LIU Tiejun(College of Science,Inner Mongolia University of Technology,Hohhot O10051,Inner Mongolia,China)

机构地区：[1]内蒙古工业大学理学院,内蒙古呼和浩特010051

出　　处：《力学季刊》2022年第4期876-888,共13页Chinese Quarterly of Mechanics

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

摘　　要：为了研究具有任意变化材料特性的功能梯度压电涂层在刚性圆柱压头作用下的Reissner-Sagoci问题,建立层合板模型对涂层表面的接触行为进行分析.利用Hankle积分变换技术和传递矩阵方法,将功能梯度压电涂层的扭转接触问题转化为包含柯西奇异核的积分方程.借助高斯-雅可比数值积分方法,将该奇异积分方程转换为线性方程组,通过求解线性方程组,计算得到材料参数按照任意形式变化的梯度压电涂层表面处的应力、位移以及电位移.研究结果表明,梯度压电涂层材料参数的梯度变化对功能梯度压电材料的Reissner-Sagoci问题求解有显著影响.研究结果为通过设计功能梯度压电材料参数而改善压电元件的力学性能、抑制接触损伤和破坏的方案提供依据.In order to study the Reissner-Sagoci problem for the functionally graded piezoelectric coating with arbitrarily varying material properties under a rigid cylindrical indenter, a laminate model is established to analyze the contact behavior on the coating surface. The Hankle integral transform technique and the transfer matrix method are used to convert the torsional contact problem of functionally graded piezoelectric coatings into the integral equation(s) involving Cauchy singular kernels. The Gauss-Jacobi numerical integration method is used to convert this singular integral equation into a system of linear equations. The stress,displacement and electrical displacement on the surface of the gradient piezoelectric coating with arbitrarily varying material parameters can be obtained by solving the linear equations. The results show that the variation of the gradient functionally graded piezoelectric coating parameters has a significantly impact on the electromechanical response of the Reissner-Sagoci problem. The present results provide a foundation for improving the mechanical properties and suppressing the contact damage and failure of piezoelectric components by designing materials parameters of functional graded piezoelectric materials.

关 键 词：功能梯度压电材料 Reissner-Sagoci问题 层合板模型 奇异积分方程 Hankle积分变换 

分 类 号：O343.3[理学—固体力学]