Galerkin-Vlasov approach for bending analysis of flexoelectric doubly-curved sandwich nanoshells with piezoelectric/FGP/piezoelectric layers using the nonlocal strain theory  

使用非局部应变理论对双曲率夹层纳米壳结构(压电/FGP/压电)进行弯曲电效应分析的Galerkin-Vlasov方法

作　　者：Tran Van Ke Do Van Thom Nguyen Thai Dung Nguyen Van Chinh Phung Van Minh Van Ke Tran;Van Thom Do;Dung Nguyen Thai;Van Chinh Nguyen;Van Minh Phung

机构地区：[1]Faculty of Mechanical Engineering,Le Quy Don Technical University,Hanoi 100000,Vietnam [2]Faculty of Special Equipment,Le Quy Don Technical University,Hanoi 100000,Vietnam

出　　处：《Acta Mechanica Sinica》2025年第2期7-40,共34页力学学报(英文版)

基　　金：This work was supported by the Le Quy Don Technical University Research Fund(Grant No.23.1.11).

摘　　要：Flexoelectricity refers to the link between electrical polarization and strain gradient fields in piezoelectric materials,particularly at the nano-scale.The present investigation aims to comprehensively focus on the static bending analysis of a piezoelectric sandwich functionally graded porous(FGP)double-curved shallow nanoshell based on the flexoelectric effect and nonlocal strain gradient theory.Two coefficients that reduce or increase the stiffness of the nanoshell,including nonlocal and length-scale parameters,are considered to change along the nanoshell thickness direction,and three different porosity rules are novel points in this study.The nanoshell structure is placed on a Pasternak elastic foundation and is made up of three separate layers of material.The outermost layers consist of piezoelectric smart material with flexoelectric effects,while the core layer is composed of FGP material.Hamilton’s principle was used in conjunction with a unique refined higher-order shear deformation theory to derive general equilibrium equations that provide more precise outcomes.The Navier and Galerkin-Vlasov methodology is used to get the static bending characteristics of nanoshells that have various boundary conditions.The program’s correctness is assessed by comparison with published dependable findings in specific instances of the model described in the article.In addition,the influence of parameters such as flexoelectric effect,nonlocal and length scale parameters,elastic foundation stiffness coefficient,porosity coefficient,and boundary conditions on the static bending response of the nanoshell is detected and comprehensively studied.The findings of this study have practical implications for the efficient design and control of comparable systems,such as micro-electromechanical and nano-electromechanical devices.弯曲电效应是指压电材料中电偶极矩与应变梯度场之间的联系,特别是在纳米尺度上.本研究旨在全面关注基于弯曲电效应和非局部应变梯度理论的压电夹层功能性梯度多孔(FGP)双曲浅纳米壳的静态弯曲分析.本研究考虑了两个包含非局部参数和长度尺度参数并沿纳米壳厚度方向变化的系数.这两个系数可以降低或增加纳米壳刚度.本研究还提出了三种不同的孔隙率规则.纳米壳结构由三层不同的材料组成并放置在Pasternak弹性基底上.最外层是由具有弯曲电效应的压电智能材料构成,而核心层则由功能性梯度多孔材料组成.结合Hamilton原理与改进的高阶剪切变形理论(RPT),本文可以推导出具有更精确结果的通用平衡方程.采用Navier和Galerkin-Vlasov方法,得到不同边界条件下的纳米壳的静态弯曲特性.通过将具体案例与已发表结果进行比较,验证了程序正确性.此外还全面研究了诸如弯曲电效应、非局部和长度尺度参数、弹性基础刚度系数、孔隙率系数和边界条件等参数对纳米壳静态弯曲响应的影响.本研究的发现对于例如微机电和纳机电设备等同类系统的有效设计和控制具有实际意义.

关 键 词：Analytical solution Flexoelectric effect Nonlocal strain gradient theory Static bending of nanoshell 

分 类 号：O343.9[理学—固体力学] O343.1[理学—力学]