A multi-physical coupling NURBS-based isogeometric analysis for nonlinear electrodynamics of three-directional poroelastic functionally graded circular nanoplate: Introducing deep neural network algorithm for nonlinear electrodynamics problems

Abstract

For the right design of nanosystems with integrated piezoelectric transducers and materials, it is crucial to understand the electro-mechanical coupling factor. Considering this, this work determines the influence of placement and dimension of piezoelectric patch on the vibrations of circular sandwich sector nanoplate coupled with an electrically layer. The core of the current nanostructure is made of three-directional poroelastic functionally graded material (3D-PFGM). The quasi-3D sinusoidal shear deformation theory (Q-3DSSDT) considering the effect of thickness stretching, compatibility conditions, and Hamilton's principle are coupled with each other regarding discovering the general motion equations and boundary domains related to the circular sector sandwich nanoplate. For considering the size effect, nonlocal quasi-3D sinusoidal strain gradient theory (NQSSGT) by employing both hardening and softening effects is considered. The NURBS-based isogeometric analysis is applied to answer the partial differential coupled equations (PDCE). In addition, the finite element method is implemented for more verification and presenting important outcomes. The novelties of this work are considering the effects of NQSSGT, placement, and dimension of the piezoelectric patch in addition to considering 3D-PFGM of the circular sector sandwich nanoplate. After obtaining the datasets of the mathematics simulation, a deep neural network algorithm is presented to test, train, and validate the presented nonlinear electrodynamics response of the current circular sector sandwich nanoplate. The results of the current nanostructure can be used in related industries of nano-robots and nano-electronic devices for future works. The findings highlight the significant influence of material gradation, poroelastic effects, and piezoelectric coupling on the vibration characteristics, offering valuable insights for the design and optimization of smart materials and structures in microelectromechanical systems (MEMS), sensors, and actuators. This research paves the way for future innovations in the field of advanced functional materials and their applications in high-precision technologies.