Size-dependent static response of a functionally graded nanobeam attached to a piezoelectric fibre-reinforced composite actuator

This study presents, for the first time, a theoretical investigation into the static bending behaviour of a functionally graded (FG) nanobeam integrated with a piezoelectric fibre-reinforced composite (PFRC) actuator. The model uniquely combines non-local strain gradient theory with electromechanical coupling to capture nanoscale effects accurately. In accordance with non-local strain gradient theory, a size-dependent functionally gradient nanobeam with a PFRC actuator formulation that includes extra material length size elements is designed. To model the FG nanobeam, we integrate the non-local strain gradient concept with a modified shear deformation beam theory. Three equations of equilibrium are built via the virtual work approach. The impacts of the outside electrical voltage, power law index, strain gradient parameter, non-local parameter, and length-to-thickness ratio on the static deformation of the nanobeam under electrical and mechanical loads are thoroughly investigated.