This article investigates the nonlinear bending of functionally graded graphene platelet–reinforced composite plate with dielectric permittivity. Three functionally graded graphene platelet distribution patterns are considered in this study. Effective medium theory is adopted to determine tensile modulus and dielectric permittivity while rule of mixture is used to determine Poisson’s ratio of graphene platelet–reinforced composites. Governing equations for nonlinear bending of the functionally graded graphene platelet–reinforced composite plates are established based on Hamilton’s principle within the framework of first-order shear deformation plate theory and von Kármán geometrical nonlinearity. Through differential quadrature method, the governing equations are numerically solved and the nonlinear bending behaviors of the functionally graded graphene platelet–reinforced composite plates are obtained. The influences of functionally graded distribution pattern, graphene platelet volume fraction and the attributes of electrical loadings on the bending behaviors of the plates are comprehensively examined. It is demonstrated that the performances of the functionally graded graphene platelet–reinforced composite plates can be designed and actively tuned through adjusting several parameters, which will be helpful to develop graphene platelet–reinforced smart materials and structures.

中文翻译：

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具有介电性能的功能梯度石墨烯薄片增强复合板的静态响应

本文研究了具有介电常数的功能梯度石墨烯薄片增强复合板的非线性弯曲。本研究考虑了三种功能分级的石墨烯血小板分布模式。采用有效介质理论来确定拉伸模量和介电常数，而混合法则用于确定石墨烯薄片增强复合材料的泊松比。基于哈密顿原理，在一阶剪切变形板理论和冯卡门几何非线性的框架内，建立了功能梯度石墨烯片层增强复合板非线性弯曲的控制方程。通过微分正交法，对控制方程进行数值求解，得到功能梯度石墨烯薄片增强复合板的非线性弯曲行为。综合研究了功能梯度分布模式、石墨烯片体积分数和电负载属性对板弯曲行为的影响。结果表明，功能梯度石墨烯薄片增强复合板的性能可以通过调整几个参数来设计和主动调节，这将有助于开发石墨烯薄片增强智能材料和结构。石墨烯薄片体积分数和电负载对板弯曲行为的属性进行了全面检查。结果表明，功能梯度石墨烯薄片增强复合板的性能可以通过调整几个参数来设计和主动调节，这将有助于开发石墨烯薄片增强智能材料和结构。石墨烯薄片体积分数和电负载对板弯曲行为的属性进行了全面检查。结果表明，功能梯度石墨烯薄片增强复合板的性能可以通过调整几个参数来设计和主动调节，这将有助于开发石墨烯薄片增强智能材料和结构。