压电智能薄壁结构电致材料和几何非线性建模与分析

doi:10.12066/j.issn.1007-2861.2014

上海大学学报(自然科学版) ›› 2020, Vol. 26 ›› Issue (1): 58-68.doi: 10.12066/j.issn.1007-2861.2014

压电智能薄壁结构电致材料和几何非线性建模与分析

张顺琦^1,²(), 张书扬³, 陈敏⁴, 赵国忠²

^1. 上海大学机电工程与自动化学院, 上海 200444
^2. 大连理工大学工业装备结构分析国家重点实验室, 辽宁大连 116024
^3. 西北工业大学机电学院, 西安 710072
^4. 西交利物浦大学工业设计系, 江苏苏州 215123

收稿日期:2018-02-28 出版日期:2020-02-29 发布日期:2020-03-22
通讯作者: 张顺琦 E-mail:zhangsq@shu.edu.cn
基金资助:
国家自然科学基金青年科学基金资助项目(11602193);大连理工大学工业装备结构分析国家重点实验室开放课题资助项目(GZ1709);陕西省自然科学基础研究计划-青年资助项目(2017JQ1027);江苏省自然科学青年基金资助项目(BK20170418)

Analysis and modeling of piezoelectric laminated smart structures with both geometric and electroelastic material nonlinearities

Shunqi ZHANG^1,²(), Shuyang ZHANG³, Min CHEN⁴, Guozhong ZHAO²

^1. School of Mechatronic Engineering and Automation, Shanghai University, Shanghai 200444, China
^2. State Key Laboratory of Structural Analysis for Industrial Equipment, Dalian University of Technology, Dalian 116024, Liaoning, China
^3. School of Mechanical Engineering, Northwestern Polytechnical University, Xi'an 710072, China
^4. Department of Industrial Design, Xi'an Jiaotong-Liverpool University, Suzhou 215123, Jiangsu, China

Received:2018-02-28 Online:2020-02-29 Published:2020-03-22
Contact: Shunqi ZHANG E-mail:zhangsq@shu.edu.cn

摘要/Abstract

摘要：

随着压电智能薄壁结构在航空航天领域的广泛应用,对计算模型准确性的要求也越来越高.压电智能结构在强致动电压下会同时发生电致材料非线性和几何非线性,为了给压电智能薄壁结构的设计和应用提供更准确的模型,基于一阶剪切变形假设,同时考虑压电材料非线性本构关系以及多种几何非线性理论 (包括冯卡门非线性、中等转角非线性以及大转角非线性),建立了压电智能薄壁结构在强致动电压下的几何非线性有限元模型,并通过已有研究的实验数据验证了模型的准确性. 最后,基于电致材料非线性和不同几何非线性模型,进行了平板结构和半圆形压电壳体结构的仿真和分析,显示了同时考虑电致材料和几何非线性的必要性.

关键词: 压电智能结构, 强致动电压, 电致材料非线性, 几何非线性, 有限元模型

Abstract:

Piezoelectric smart structures under strong driving voltages will result in large displacements and rotations, in which electroelastic material and geometric nonlinearities affect simultaneously the structural response. In order to provide a precise model for design and application of piezoelectric smart structures, geometrically nonlinear finite element (FE) models with strong driving voltages are developed based on the first-order shear deformation hypothesis. The proposed models consider both geometric and material nonlinearities, in which the geometrically nonlinear effects include von Kármán type nonlinear, moderate rotation nonlinear and large rotation nonlinear. The present models are validated effectively and accurately through comparison with the experimental data from the literature. Finally, simulations and validations have been conducted through a plate structure and a cantilevered semicircular cylindrical piezoelectric shell structure in terms of the proposed different models to verify the necessity and precision.

Key words: piezoelectric smart structure, strong driving voltage, electroelastic material nonlinear, geometrically nonlinear, finite element model

中图分类号:

O343.5

张顺琦, 张书扬, 陈敏, 赵国忠. 压电智能薄壁结构电致材料和几何非线性建模与分析[J]. 上海大学学报(自然科学版), 2020, 26(1): 58-68.

Shunqi ZHANG, Shuyang ZHANG, Min CHEN, Guozhong ZHAO. Analysis and modeling of piezoelectric laminated smart structures with both geometric and electroelastic material nonlinearities[J]. Journal of Shanghai University（Natural Science Edition）, 2020, 26(1): 58-68.

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压电智能薄壁结构电致材料和几何非线性建模与分析

Analysis and modeling of piezoelectric laminated smart structures with both geometric and electroelastic material nonlinearities

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