This paper establishes a mathematical model to analyze the static and dynamic behaviors of functionally graded graphene reinforced composite (FG-GRC) beam with geometric imperfection subjected to thermo-electro-mechanical load. Three different geometric imperfections are considered. Four different distribution patterns of graphene nanoplatelets (GPLs) are taken into consideration. The effective properties of the geometrically imperfect FG-GRC beam are estimated by the modified Halpin-Tsai model and rule of mixture. The nonlinear partial differential governing equations are deduced based on first-order shear deformation theory, von Kármán nonlinear displacement-strain relationship and Hamilton principle, and discretized as ordinary differential forms through the differential quadrature (DQ) method. Newmark-β method and iteration method are employed to numerically solve the governing equations. The effects of geometric imperfection, GPLs and piezoelectric actuators on bending and vibration of the geometrically imperfect FG-GRC beam subjected to thermo-electro-mechanical load are comprehensively investigated. The results clearly demonstrate that the coupling effect of geometric imperfections and thermo-electric-mechanical loads can introduce an additional transverse load acting along the length of the geometrically imperfect FG-GRC beam, and hence makes a significant difference on its static and dynamic behaviors.

本文建立了一个数学模型来分析具有几何缺陷的功能梯度石墨烯增强复合材料（FG-GRC）梁在热机电载荷作用下的静态和动态行为。考虑了三种不同的几何缺陷。考虑了石墨烯纳米片 (GPL) 的四种不同分布模式。通过改进的 Halpin-Tsai 模型和混合规则估计几何不完美的 FG-GRC 梁的有效特性。基于一阶剪切变形理论、von Kármán非线性位移-应变关系和Hamilton原理推导出非线性偏微分控制方程，并通过微分求积(DQ)方法将其离散为常微分形式。纽马克-采用β法和迭代法对控制方程进行数值求解。全面研究了几何缺陷、GPLs和压电致动器对几何缺陷FG-GRC梁在热-机电载荷作用下弯曲和振动的影响。结果清楚地表明，几何缺陷和热电机械载荷的耦合效应可以引入沿几何缺陷FG-GRC梁的长度作用的附加横向载荷，从而对其静态和动态行为产生显着影响。