Petrov-Galerkin zonal free element method for piezoelectric structures

authored by: Yi Yang, Bing Bing Xu, Jun Lv, Miao Cui, Huayu Liu, Xiaowei Gao
Abstract: This paper presents a novel Petrov-Galerkin free element method (PGPZ-FREM) based on a combination of the strong form free element method (FREM), sub-domain mapping technique, and Petrov-Galerkin method for analyzing piezoelectric structures. This is a brand new numerical method that combines the ideas of isogeometric method and meshless method. Similar to the isogeometric method, the computational domain is divided into a lot of patches or subdomains firstly. In each subdomain, local collocation Lagrangian elements are generated according to the location of the nodes. Additionally, the Heaviside step function is selected as the weight function to simplify the calculations. By constructing equations point by point, a set of linear algebraic equations is established to solve the piezoelectric problem. Finally, the accuracy and stability of the piezoelectric zonal Petrov-Galerkin free element method are verified by numerical examples, including a symmetric piezoelectric block, a piezoelectric tuning fork, a dual-material MFC sensor, and the wing skin pressure sensing system.
Organisation(s): Institute of Continuum Mechanics
External Organisation(s): Dalian University of Technology
Type: Article
Journal: Applied mathematical modelling
Volume: 143
No. of pages: 15
ISSN: 0307-904X
Publication date: 07.2025
Publication status: Published
Peer reviewed: Yes
ASJC Scopus subject areas: Modelling and Simulation, Applied Mathematics
Electronic version(s): https://doi.org/10.1016/j.apm.2025.116057 (Access: Open)
: Details in the research portal "Research@Leibniz University"

BibTeX

@article{f990f00771d64998a09cba5c58a9b395,
title = "Petrov-Galerkin zonal free element method for piezoelectric structures",
abstract = "This paper presents a novel Petrov-Galerkin free element method (PGPZ-FREM) based on a combination of the strong form free element method (FREM), sub-domain mapping technique, and Petrov-Galerkin method for analyzing piezoelectric structures. This is a brand new numerical method that combines the ideas of isogeometric method and meshless method. Similar to the isogeometric method, the computational domain is divided into a lot of patches or subdomains firstly. In each subdomain, local collocation Lagrangian elements are generated according to the location of the nodes. Additionally, the Heaviside step function is selected as the weight function to simplify the calculations. By constructing equations point by point, a set of linear algebraic equations is established to solve the piezoelectric problem. Finally, the accuracy and stability of the piezoelectric zonal Petrov-Galerkin free element method are verified by numerical examples, including a symmetric piezoelectric block, a piezoelectric tuning fork, a dual-material MFC sensor, and the wing skin pressure sensing system.",
author = "Yi Yang and Xu, {Bing Bing} and Jun Lv and Miao Cui and Huayu Liu and Xiaowei Gao",
note = "Publisher Copyright: {\textcopyright} 2025 The Author(s)",
year = "2025",
month = jul,
doi = "10.1016/j.apm.2025.116057",
language = "English",
volume = "143",
journal = "Applied mathematical modelling",
issn = "0307-904X",
publisher = "Elsevier Inc.",
}