功能梯度压电板柱面弯曲的弹性力学解  

Elasticity Solutions for Cylindrical Bending of Functionally Graded Piezoelectric Material Plates

作　　者：沈璐璐 蔡方圆 杨博[1] SHEN Lulu;CAI Fangyuan;YANG Bo(School of Civil Engineering,Zhejiang Sci-Tech University,Hangzhou 310018,P.R.China)

机构地区：[1]浙江理工大学建筑工程学院,杭州310018

出　　处：《应用数学和力学》2023年第3期272-281,共10页Applied Mathematics and Mechanics

基　　金：国家自然科学基金(11872336);机械结构强度与振动国家重点实验室开放课题(SV2020-KF-13)。

摘　　要：功能梯度压电材料(FGPM)同时兼具功能梯度材料和压电材料特性,可为多功能或智能化轻质结构设计提供支撑,在诸多领域有着广泛的应用前景.将Mian和Spencer功能梯度板理论由功能梯度弹性材料推广到功能梯度压电材料,解析研究了FGPM板的柱面弯曲问题,其中,材料弹性常数、压电和介电参数沿板厚方向可以任意连续变化.最终,给出了FGPM板受横向均布荷载作用下柱面弯曲问题的弹性力学解.通过算例分析,重点讨论了压电效应对FGPM板静力响应的影响.Functionally graded piezoelectric materials(FGPMs),combining the properties of functionally graded materials and piezoelectric materials,provides a new idea for multi-functional and intelligent lightweight components,and has broad application prospects in electronic devices.Based on the elastic and electric equilibrium equations,the Mian and Spencer functionally graded plate theory was extended from elastic materials to piezoelectric materials to study the cylindrical bending of FGPM plates,where the material elastic constants,piezoelectric and dielectric parameters were assumed to vary continuously and arbitrarily along the thickness direction.Accordingly,the elasticity solutions for cylindrical bending of FGPMs plates under the uniform transverse loading were obtained.Numerical examples were given to demonstrate the piezoelectric effects on the static responses of the presented FGPMs plates.

关 键 词：压电效应 Mian和Spencer板理论 柱面弯曲 弹性力学解 

分 类 号：O343.1[理学—固体力学]