Effect of flexoelectricity on the nonlinear static and dynamic response of functionally graded porous graphene platelets-reinforced composite plates integrated with piezoelectric layers

In this paper, the nonlinear free vibration and static bending of functionally graded porous graphene platelets-reinforced (FGP-GPLs) composite plates with discretized piezoelectric patches integrated on the upper and lower surfaces are numerically studied. For the first time, this research examines how the flexoelectric effect affects the stiffness of functionally graded graphene plates with piezoelectric laminates, and it explores the influence of porosity coefficient and graphene weight fraction on the strength of the flexoelectric effect. The material model of the composite layer comprises various porosity and GPLs distributions. Both porosity types and graphene patterns in the thickness direction are categorized into three distinct groups: uniform, symmetric, and asymmetric. The Halpin–Tsai micromechanical model, the rule of mixture, and the closed-cell Gaussian random field (GRF) scheme are used to determine the effective material properties of the composite layer. The computational model for piezoelectric smart structures is developed by considering the material characteristics, piezoelectric effect, flexoelectric effect, and von Kármán nonlinearity assumption. The nonlinear governing equations for the structures are derived by Hamilton principle combined with the first-order shear deformation theory (FSDT). The numerical model is discretized via the isogeometric analysis (IGA) technique and solved using a direct iterative method. The solution approach is validated against existing literature to confirm its accuracy and effectiveness. Finally, this paper thoroughly examines the effects of various parameters on the nonlinear static bending and free vibration of piezoelectric smart structures. These parameters include porosity and GPLs distribution patterns, porosity coefficients, GPLs weight fractions, load parameters, and the flexoelectric effect. Results indicate that the numerical model exhibits a stiffness-hardening mechanism under the flexoelectric effect.