The novelty here comes from not only the perfect nonlinear three-dimensional (3D) electro-elasticity investigation but also the mixed material itself. The literature widely showed mechanical assessments on the piezoelectric structures; however, a lack of nonlinear three-dimensional elasticity studies has been witnessed on these kinds of smart materials. Therefore, a nonlinear 3D elasticity-piezoelectricity coupling is considered in this study. What is more, this research brings about an era in the field of sensing manufacturing such as sensors and actuators by proposing the construction of these devices in an advanced composite framework. The piezoelectric medium can be electro-mechanically improved with the aggregation of graphene platelets/nanoplatelets (GPLs/GNPs) based on the functionally graded (FG) composition. The assumption for such a smart composite has been made to provide higher flexibility smart tools while their elastic strength can also get further. To accomplish this, the derivation of a rigorous mathematical model has come out for a transversely isotropic inhomogeneous FG-piezoelectric beam-like sensor/actuator using 3D kinematic displacements, geometrically nonlinear strains, Lagrange technique, 3D stress-strains tensors, linear elastic material, and in particular Halpin-Tsai micro-mechanic model. Numerical modeling has been built by the generalized differential quadrature (GDQ) technique. A comprehensive parametric study has also been established for intelligent FG beams.

中文翻译：

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GNPs增强两相非均匀FG压电复合材料的非线性三维电弹性数值建模


这里的新颖性不仅来自完美的非线性三维 （3D） 电弹性研究，还来自混合材料本身。文献广泛展示了压电结构的机械评估;然而，已经证明了对这类智能材料缺乏非线性三维弹性研究。因此，本研究考虑了非线性三维弹性-压电耦合。更重要的是，这项研究通过提出在先进的复合框架中构建传感器和执行器等传感制造领域，开创了一个时代。压电介质可以通过基于功能分级 （FG） 组成的石墨烯片/纳米片 （GPL/GNP） 的聚集进行机电改进。对这种智能复合材料的假设是为了提供更高的灵活性 智能工具 同时它们的弹性强度也可以进一步提高。为了实现这一目标，使用 3D 运动位移、几何非线性应变、拉格朗日技术、3D 应力应变张量、线弹性材料，特别是 Halpin-Tsai 微观力学模型，为横向各向同性非均匀 FG 压电束状传感器/执行器推导出了一个严格的数学模型。数值建模是通过广义微分正交 （GDQ） 技术构建的。此外，还为智能 FG 梁建立了全面的参数化研究。