Effect of flexoelectricity on the nonlinear static and dynamic response of functionally graded porous graphene platelets-reinforced composite plates integrated with piezoelectric layers

IF 3.6 3区材料科学 Q2 ENGINEERING, MECHANICAL

International Journal of Mechanics and Materials in Design Pub Date : 2025-05-24 DOI:10.1007/s10999-025-09765-5

Xinjie Zhang, Xie Zhao, Yanqing Li, Hongtao Wang, Shijie Zheng

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Abstract

In this paper, the nonlinear free vibration and static bending of functionally graded porous graphene platelets-reinforced (FGP-GPLs) composite plates with discretized piezoelectric patches integrated on the upper and lower surfaces are numerically studied. For the first time, this research examines how the flexoelectric effect affects the stiffness of functionally graded graphene plates with piezoelectric laminates, and it explores the influence of porosity coefficient and graphene weight fraction on the strength of the flexoelectric effect. The material model of the composite layer comprises various porosity and GPLs distributions. Both porosity types and graphene patterns in the thickness direction are categorized into three distinct groups: uniform, symmetric, and asymmetric. The Halpin–Tsai micromechanical model, the rule of mixture, and the closed-cell Gaussian random field (GRF) scheme are used to determine the effective material properties of the composite layer. The computational model for piezoelectric smart structures is developed by considering the material characteristics, piezoelectric effect, flexoelectric effect, and von Kármán nonlinearity assumption. The nonlinear governing equations for the structures are derived by Hamilton principle combined with the first-order shear deformation theory (FSDT). The numerical model is discretized via the isogeometric analysis (IGA) technique and solved using a direct iterative method. The solution approach is validated against existing literature to confirm its accuracy and effectiveness. Finally, this paper thoroughly examines the effects of various parameters on the nonlinear static bending and free vibration of piezoelectric smart structures. These parameters include porosity and GPLs distribution patterns, porosity coefficients, GPLs weight fractions, load parameters, and the flexoelectric effect. Results indicate that the numerical model exhibits a stiffness-hardening mechanism under the flexoelectric effect.

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柔性电对集成压电层的功能梯度多孔石墨烯片增强复合材料非线性静动态响应的影响

本文对上下表面集成离散压电片的功能梯度多孔石墨烯片增强（FGP-GPLs）复合材料板的非线性自由振动和静态弯曲进行了数值研究。本研究首次考察了挠曲电效应对压电层压板功能梯度石墨烯板刚度的影响，并探讨了孔隙率系数和石墨烯重量分数对挠曲电效应强度的影响。复合层的材料模型包含不同的孔隙率和gpl分布。在厚度方向上，孔隙类型和石墨烯模式可分为三种不同的类型：均匀、对称和不对称。采用Halpin-Tsai微观力学模型、混合规律和闭孔高斯随机场（GRF）格式确定复合材料层的有效材料性能。考虑材料特性、压电效应、挠曲电效应和von Kármán非线性假设，建立了压电智能结构的计算模型。利用Hamilton原理结合一阶剪切变形理论（FSDT）推导了结构的非线性控制方程。数值模型采用等几何分析（IGA）技术离散化，采用直接迭代法求解。通过对现有文献的验证，验证了求解方法的准确性和有效性。最后，深入研究了各种参数对压电智能结构的非线性静态弯曲和自由振动的影响。这些参数包括孔隙度和gpl分布模式、孔隙度系数、gpl重量分数、载荷参数和挠曲电效应。结果表明，该数值模型在挠曲电效应下表现出一种刚度硬化机制。

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来源期刊

International Journal of Mechanics and Materials in Design ENGINEERING, MECHANICAL-MATERIALS SCIENCE, MULTIDISCIPLINARY

CiteScore

6.00

自引率

5.40%

发文量

审稿时长

>12 weeks

期刊介绍： It is the objective of this journal to provide an effective medium for the dissemination of recent advances and original works in mechanics and materials'' engineering and their impact on the design process in an integrated, highly focused and coherent format. The goal is to enable mechanical, aeronautical, civil, automotive, biomedical, chemical and nuclear engineers, researchers and scientists to keep abreast of recent developments and exchange ideas on a number of topics relating to the use of mechanics and materials in design. Analytical synopsis of contents: The following non-exhaustive list is considered to be within the scope of the International Journal of Mechanics and Materials in Design: Intelligent Design: Nano-engineering and Nano-science in Design; Smart Materials and Adaptive Structures in Design; Mechanism(s) Design; Design against Failure; Design for Manufacturing; Design of Ultralight Structures; Design for a Clean Environment; Impact and Crashworthiness; Microelectronic Packaging Systems. Advanced Materials in Design: Newly Engineered Materials; Smart Materials and Adaptive Structures; Micromechanical Modelling of Composites; Damage Characterisation of Advanced/Traditional Materials; Alternative Use of Traditional Materials in Design; Functionally Graded Materials; Failure Analysis: Fatigue and Fracture; Multiscale Modelling Concepts and Methodology; Interfaces, interfacial properties and characterisation. Design Analysis and Optimisation: Shape and Topology Optimisation; Structural Optimisation; Optimisation Algorithms in Design; Nonlinear Mechanics in Design; Novel Numerical Tools in Design; Geometric Modelling and CAD Tools in Design; FEM, BEM and Hybrid Methods; Integrated Computer Aided Design; Computational Failure Analysis; Coupled Thermo-Electro-Mechanical Designs.