Thermo-electro-elastic coupled modeling and simulation of functionally graded piezoelectric structures

压电梯度板壳结构热电弹耦合建模与仿真

¹ School of Energy Engineering, Yulin University, Yulin 719000
² School of Mechatronic Engineering and Automation, Shanghai University, Shanghai 200444
³ School of Mechanical Engineering, Northwestern Polytechnical University, Xi'an 710072

Received: 4 November 2022

Abstract

Compared with the composite materials, the functionally graded materials can not only provide better specific stiffness but also reduce the risk of layered damage. Therefore, the graded distribution forms have become the development trend of advanced structures. An efficient finite element (FE) modeling method and numerical simulation of plate and shell with nonlinear temperature gradient coupling are developed based on the FOSD hypothesis for thermo-electro-elastic coupled functionally graded piezoelectric material (FGPM) integrated with smart structures in this paper. The constitutive model for thermo-electro-elastic coupled FGPM is derived. Assuming that the temperature gradient distribution changes secondarily through the thickness, two nonlinear physical models for temperature change are constructed. Based on the FOSD hypothesis, the multi-field coupled FE equation of plate and shell is derived. The accuracy of the present FE model is verified by the commercial calculation structures. The parametric simulation of FGPM shells is carried out based on the FE model.

摘要

相比于复材层合结构, 功能梯度材料不但能提供良好的比刚度, 而且降低了分层损伤风险, 结构梯度化是高性能结构发展的趋势。针对热电弹耦合下压电梯度结构, 基于一阶剪切变形假设, 构建了非线性温度梯度耦合下的压电梯度薄壁结构板壳有限元模型, 实现高效的压电梯度结构"热-电-弹"耦合数值模拟。推导了压电梯度材料的"热-电-弹"耦合本构模型; 假设温度梯度沿厚度方向呈二次变化, 构建了2种非线性温度变化物理模型; 基于一阶剪切变形假设, 推导了多物理场耦合下的板壳有限元方程; 采用商业有限元计算结构对本模型的准确性进行了验证, 对压电梯度壳体结构进行了参数化仿真。