Finite element modeling and analysis of flexoelectric plates using gradient electromechanical theory
Finite element modeling and analysis of flexoelectric plates using gradient electromechanical theory
复制标题
DOI：
10.1007/s00161-023-01252-6
复制
发表时间：
2023-09
影响因子：
2.6
通讯作者：
Y. S. Joshan;S. Santapuri
中科院分区：
文献类型：
--
作者：
Y. S. Joshan;S. Santapuri
本文从三维梯度机电理论出发，发展了双向耦合挠性电极板理论。梯度机电理论考虑了三个机械长度刻度参数和两个电动长度刻度参数，同时考虑了机械和电气尺寸效应。在考虑Kirchhoff假设的情况下，利用变分公式推导了板的控制方程和边界条件。建立了一种计算效率高的连续非协调有限元来求解所得的板方程。为了评估非协调有限元框架的精度，将计算结果与简支挠性电板的Navier型解析解进行了比较。有限元框架也用现有文献中的实验结果对被动微板进行了验证。计算结果与理论分析和实验结果吻合较好。此外，还比较了非协调单元和标准协调单元的计算效率，标准协调单元具有更大的自由度和跨所有单元边界的连续性。观察到，非协调单元的速度几乎是协调单元的两倍，而精度没有明显的损失。在此基础上，利用二维有限元方法分析了柔性电复合板在传感器模式和执行器模式下的尺寸相关响应。通过各种参数研究，分析了边界条件、长度尺度参数、板的尺寸、挠性电层厚度比等对挠性电板型传感器和执行器响应的影响。结果表明，由于尺寸效应，挠曲电板中的有效机电耦合在微尺度上增加，并且比标准压电材料的板厚要高。
This work presents the development of a two-way coupled flexoelectric plate theory starting from a 3D gradient electromechanical theory. The gradient electromechanical theory considers three mechanical length scale parameters and two electric length scale parameters to account for both mechanical and electrical size effects. Variational formulation is used to derive the plate governing equations and boundary conditions considering Kirchhoff’s assumptions. A computationally efficientcontinuous non-conforming finite element is developed to solve the resulting plate equations. To assess the accuracy of the non-conforming finite element framework, the results are compared with Navier-type analytical solution for a simply supported flexoelectric plate. The finite element framework is also validated with experimental results in the existing literature for a passive micro-plate. The results show excellent agreement with both analytical and experimental results. Furthermore, computational efficiency of the non-conforming element is compared with the standard conforming element, which contains greater degrees of freedom and continuity across all elemental edges. It was observed that the non-conforming element is almost twice as fast as the conforming element without a significant loss of accuracy. The 2D finite element formulation is subsequently used to analyze the size-dependent response of flexoelectric composite plates operating in both sensor and actuator modes. Various parametric studies are performed to analyze the effect of boundary conditions, length scale parameters, size of the plate, flexoelectric layer thickness ratio, etc., on the response of flexoelectric plate-type sensors and actuators. It is found that the effective electromechanical coupling increases in a flexoelectric plate at microscale (due to the size effects), and it is higher than standard piezoelectric materials for plate thicknessm.