On the static and dynamic responses of smart piezoelectric functionally graded graphene platelet-reinforced microplates

•A powerful and effective numerical model based on RPT, MCST and NURBS-based IGA is exploited.•Size-dependent effects for smart FG microplates with GPLs reinforcement are thoroughly presented.•Active control of static and dynamic responses via sensor and actuator layers is shown.•Structural damping effect of small-structures is taken into account.•The best composite reinforcement performance is explored. [Display omitted] Application of nano/micro structures has become popular in a wide range of advanced engineering systems in recent years. For a better insight, this paper presents an intensive numerical study on the static and dynamic responses of smart functionally graded microplates with graphene platelets (GPLs) reinforcement under concurrently mechanical and electrical loads. To this end, a powerful and effective numerical model based on refined plate theory (RPT), modified couple stress theory (MCST) and NURBS-based isogeometric analysis (IGA) is introduced to predict the complex behaviors of small-scale structures. Wherein, the MCST containing only one material length scale parameter is utilized to capture the size-dependent effects while the four-variable RPT-based IGA approach is exploited to describe the displacement field. The host microplate can be constituted by four different GPLs dispersions and integrated with two symmetric piezoelectric layers. A closed-loop control procedure based on displacement and velocity feedback gains is employed to actively control the static and dynamic responses of smart small-scale structures, which takes into account the structural damping effect. Several numerical examples are performed to examine the influence of some key parameters such as geometry, material length scale parameter, boundary condition, dynamic load, input electrical voltage as well as weight fraction and distribution of GPLs.