In this paper, we propose an effective computational approach to analyze and active control of geometrically nonlinear responses of functionally graded (FG) porous plates with graphene nanoplatelets (GPLs) reinforcement integrated with piezoelectric layers. The key concept behind this work is to utilize isogeometric analysis (IGA) based on B\'ezier extraction technique and $C^0$-type higher-order shear deformation theory ($C^0$-HSDT). By applying B\'ezier extraction, the original Non-Uniform Rational B-Spline (NURBS) control meshes can be transformed into B\'ezier elements which allow us to inherit the standard numerical procedure like the standard finite element method (FEM). In this scenario, the approximation of mechanical displacement field is calculated via $C^0$-HSDT whilst the electric potential field is considered as a linear function across the thickness of each piezoelectric sublayer. The FG plate includes internal pores and GPLs dispersed into metal matrix either uniformly or non-uniformly along plate's thickness. To control responses of structures, the top and bottom surfaces of FG plate are firmly bonded with piezoelectric layers which are considered as sensor and actuator layers. The geometrically nonlinear equations are solved by Newton-Raphson iterative procedure and Newmark's integration. The influence of porosity coefficient, weight fraction of GPLs as well as external electrical voltage on geometrically nonlinear behaviors of plate structures with various distributions of porosity and GPLs are thoroughly investigated. A constant displacement and velocity feedback control approaches are then adopted to actively control geometrically nonlinear static and dynamic responses, where structural damping effect is taken into account, based on a closed-loop control with sensor and actuator layers.

翻译：本文提出了一种高效的计算方法，用于分析并主动控制集成压电层的功能梯度（FG）多孔板（含石墨烯纳米片（GPLs）增强）的几何非线性响应。该工作的核心思路是采用基于Bézier提取技术和$C^0$型高阶剪切变形理论（$C^0$-HSDT）的等几何分析（IGA）。通过应用Bézier提取，原始的非均匀有理B样条（NURBS）控制网格可转换为Bézier单元，从而继承如标准有限元法（FEM）般的标准数值流程。在此框架下，机械位移场通过$C^0$-HSDT近似计算，而电势场则视为沿每个压电子层厚度方向的线性函数。FG板包含内部孔隙及均匀或非均匀分散于金属基体中的GPLs，其分布沿板厚方向变化。为控制结构响应，FG板的上下表面牢固粘接压电层，分别作为传感器层和作动器层。几何非线性方程通过Newton-Raphson迭代法和Newmark积分法求解。系统研究了孔隙率系数、GPLs质量分数以及外部电压对不同孔隙和GPLs分布板结构几何非线性行为的影响。随后，基于传感器与作动器层的闭环控制，采用恒定位移和速度反馈控制方法，在考虑结构阻尼效应的前提下，主动控制几何非线性静态与动态响应。