Isogeometric modeling and analysis of piezoelectric laminated shells

LIU Tao; XU Wenxiang; JIANG Yafen; HU Xiaolei; ZHANG Shunqi

doi:10.16579/j.issn.1001.9669.2026.04.014

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Isogeometric modeling and analysis of piezoelectric laminated shells

·Design·Calculation· | 更新时间：2026-04-15

- Isogeometric modeling and analysis of piezoelectric laminated shells
- Journal of Mechanical Strength Vol. 48, Issue 4, Pages: 122-133(2026)
- 作者机构：
  
  1.安徽工业大学机械工程学院，马鞍山 243032
  2.安徽工业大学创新创业学院（工程师学院）、工程实训中心，马鞍山 243032］
  3.上海大学机电工程与自动化学院，上海 200444
- 作者简介：
  
  LIU Tao, E-mail: lt_ahut@126.com
- 基金信息：
  
  National Natural Science Foundation of China(11972020);Key Research Projects of Natural Science in Colleges and Universities of Anhui Province(KJ2021A0404;KJ2021A0368)
- DOI：10.16579/j.issn.1001.9669.2026.04.014
  CLC： TB333
- Received：13 July 2024，
  
  Published：15 April 2026
- 稿件说明：
移动端阅览
刘涛，许文祥，蒋雅芬，等. 压电层合壳体等几何建模及分析［J］. 机械强度，2026，48（4）：122-133.

LIU Tao，XU Wenxiang，JIANG Yafen，et al. Isogeometric modeling and analysis of piezoelectric laminated shells［J］. Journal of Mechanical Strength，2026，48（4）：122-133.
刘涛，许文祥，蒋雅芬，等. 压电层合壳体等几何建模及分析［J］. 机械强度，2026，48（4）：122-133. DOI： 10.16579/j.issn.1001.9669.2026.04.014.

LIU Tao，XU Wenxiang，JIANG Yafen，et al. Isogeometric modeling and analysis of piezoelectric laminated shells［J］. Journal of Mechanical Strength，2026，48（4）：122-133. DOI： 10.16579/j.issn.1001.9669.2026.04.014.

摘要

目的

传统有限元法在建模过程中存在几何不精确性和单元阶次较低的问题，在处理含有曲线或曲面的复杂几何模型时，会引入逼近误差。相较而言，等几何分析方法将非均匀有理B样条（Non-Uniform Rational B-Splines

NURBS）基函数作为形函数，具备几何精确、高阶连续、高精度和无需传统网格划分过程等优势。因此，基于等几何分析方法和一阶剪切变形理论建立了一种能够精确预测压电层合壳体结构力-电行为的等几何分析模型，并进行相应分析。

方法

首先，利用NURBS基函数推导了Reissner-Mindlin壳单元的位移离散方程；其次，考虑材料的纤维角度，建立了从局部坐标系到全局坐标系的压电本构方程的转换关系，并采用Hamilton变分原理构建了压电层合壳体的等几何分析模型；然后，利用构建的等几何分析模型对经典壳体问题进行了分析，并将等几何分析模型的结果与已有文献和有限元软件仿真的结果进行了对比，验证了模型的精确性和高效性；最后，对机-电载荷作用下压电层合壳体的静力学和动力学响应进行了分析。

结果

数值结果表明，所建立的压电层合壳体的等几何分析模型具有较高的计算精度，并且同时适用于普通单层壳体、层合壳体及压电层合壳体等结构的分析。

Abstract

Objective

The traditional finite element method suffers from geometric inaccuracy and low element order during modeling

which introduces approximation errors when dealing with complex geometric models with curves or curved surfaces. In contrast

the isogeometric analysis method employs the non-uniform rational B-splines (NURBS) basis functions as shape functions and offers advantages such as exact geometry representation

high-order continuity

high accuracy

and elimination of the traditional meshing process. Therefore

an isogeometric analysis model capable of accurately predicting the electromechanical behavior of piezoelectric laminated shell structures is to be proposed based on the isogeometric analysis method and the first-order shear deformation theory

and the corresponding analysis is to be carried out.

Methods

Firstly

the displacement discretization equations of the Reissner-Mindlin shell element were derived using NURBS basis functions. Secondly

considering the fiber orientation of the material

the transformation relation of the piezoelectric constitutive equations from the local coordinate system to the global coordinate system was established

and the isogeometric analysis model of piezoelectric laminated shells was constructed via Hamilton’s variational principle. Thirdly

the established isogeometric analysis model was used to analyze classical shell problems

the results of isogeometric analysis model were compared with results in the existing literature and simulation results of finite element software

and the accuracy and efficiency of the model were verified. Finally

the static and dynamic responses of piezoelectric laminated shells under electromechanical loading were investigated.

Results

Numerical results demonstrate that the established isogeometric analysis model for piezoelectric laminated shells achieves high computational accuracy and is simultaneously applicable to the analysis of structures such as conventional single-layer shells

laminated shells

and piezoelectric laminated shells.

关键词

Keywords

references

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