Nonlocal Strain Gradient Approach for Static Behavior of Cross-Ply Laminated Nanoplates with Piezoelectric Fiber-Reinforced Composite Layer

This study examines the bending of cross-ply laminated composite nanoplates coupled to a piezoelectric fiber-reinforced composite layer via the nonlocal strain gradient theory. The aim is to accurately capture size-dependent impacts and electromechanical interaction in nanoscale composite structures. The mechanical response is modeled utilizing a refined four-variable shear deformation theory, with the governing equilibrium equations developed using the virtual work assumption. The nanoplate is examined under simply supported boundary conditions exposed to both mechanical loading and applied electric voltage. A detailed parametric investigation is done to assess the contribution of non-local and strain gradient factors, imposed voltage, and geometric ratios on the bending behavior. The results show that the nonlocal parameter generates a softening result, increasing deflection, whereas the strain gradient parameter raises stiffness and minimizes deformation. Moreover, the applied voltage successfully controls the bending response by electromechanical actuation, underlining the potential of PFRC-integrated nanoplates in smart nanoscale systems.