考虑挠曲电与温度效应的Mindlin-Medick板理论及其应用  

The Mindlin⁃Medick Plate Theory and Its Application Under Flexoelectricity and Temperature Effects

作　　者：鲁双 李东波[1] 陈晶博 席勃 LU Shuang;LI Dongbo;CHEN Jingbo;XI Bo(School of Science,Xi’an University of Architecture and Technology,Xi’an 710055,P.R.China)

机构地区：[1]西安建筑科技大学理学院,西安710055

出　　处：《应用数学和力学》2023年第9期1122-1133,共12页Applied Mathematics and Mechanics

基　　金：国家自然科学基金项目(51878547,51641809,52378195)。

摘　　要：基于Hamilton变分原理,推导了挠曲电纳米板的二维场方程和边界条件,然后将本构关系和几何关系代入场方程中,得到了相应的控制方程.研究了非均匀温度变化引起的挠曲电纳米板面内拉伸变形、厚度伸缩变形、对称厚度-剪切变形及其耦合的挠曲电极化.位移场和电势场用双重Fourier级数解求解.结果表明,所有场都对温度载荷敏感,这为利用温度场控制挠曲电纳米板的力学和电学行为提供了前景.对比分析了温度场和机械场对位移场的影响,拓展了考虑挠曲电效应和温度效应的Mindlin-Medick板结构分析理论,其可为微纳米尺度器件的结构设计提供参考.Based on the Hamiltonian variational principle,the 2D field equations and boundary conditions for flexoelectricity were derived,and the corresponding governing equations were obtained through substitution of the constitutive relation and geometric equations into the field equation.The in⁃plane tensile deformation,thick⁃ness⁃stretch deformation,symmetric thickness⁃shear deformation,and their coupled flexoelectric polarization of flexoelectric nanoplates caused by inhomogeneous temperature changes,were studied.The displacement fields and electric potential fields were solved with the double Fourier series method.The results demonstrate that,all fields are sensitive to the temperature load,which raises the prospect of controlling the mechanical and electrical behaviors of flexoelectric nanoplates by means of the temperature field.The effects of the thermal field and mechanical field on the displacement field were compared and examined.The work extends the Mind⁃lin⁃Medick plate structure analysis theory in view of the flexoelectric and temperature effects,and provides a reference for the structural design of micro⁃and nano⁃scale devices.

关 键 词：Mindlin-Medick理论 挠曲电效应 温度效应 温度调控 机械调控 

分 类 号：O34[理学—固体力学]