Nonlinear Displacement Analysis of Functionally Graded Flexoelectric-Piezoelectric Nanobeams

Articles in Press

Document Type : Research Paper

Authors
Issam ABED 1
Sami ABDELKHALEK 2
Fehmi NAJAR 3
1 Applied Mechanics and Systems Research Laboratory (LR03ES06), Ecole Polytechnique de Tunisie, University of Carthage, B.P. 743, Al Marsa 2078, Tunis, Tunisia
2 Transvalor, 950 Avenue Roumanille, CS 40237 Biot, 06904 Sophia Antipolis Cedex, France
3 Department of Mechanical Engineering, College of Engineering at Al Kharj, Prince Sattam bin Abdulaziz University, Al-Kharj 16273, Saudi Arabia
10.22055/jacm.2026.49034.5685
Abstract
The integration of flexoelectricity with piezoelectricity has recently attracted considerable interest due to its ability to enhance electromechanical coupling at the nanoscale. This paper presents a nonlinear finite element framework for the static analysis of functionally graded piezoelectric–flexoelectric nanobeams undergoing nonlinear displacements. The governing equations are derived using Hamilton’s principle and incorporate nonlinear von Kármán strains, flexoelectric and piezoelectric effects, and power-law distributions of constituent materials along the nanobeam’s longitudinal and transverse axes. The weak form is discretized using a mixed finite element formulation with the penalty method. Validation against homogeneous nanobeam cases demonstrates the accuracy and robustness of the proposed formulation. Comprehensive parametric studies are conducted to explore the influence of gradient indices, boundary conditions, and material composition on beam deflections. Results reveal that compliant polymer-ceramic combinations, such as PVDF-BaTiO3, exhibit significantly larger deflections compared with purely ceramic configurations, highlighting the role of low-modulus constituents in enhancing flexibility. In contrast, stiffer ceramics such as SrTiO3 and PbTiO3 increase overall rigidity and reduce deflections. The developed framework provides new insights into the coupled electromechanical behavior of graded piezoelectric-flexoelectric nanobeams, offering valuable guidelines for the design of next-generation nanoelectromechanical systems. Applications include highly sensitive sensors, ultra-precise actuators, and nanoscale energy harvesters, where optimized material distributions can maximize electromechanical efficiency.
Keywords
Piezoelectricity
Flexoelectricity
Nanobeam
FGM
ANM
FEM
Subjects

Publisher’s Note Shahid Chamran University of Ahvaz remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

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