Modeling and analyze of behaviors of functionally graded graphene reinforced composite beam with geometric imperfection in multiphysics

This paper establishes a mathematical model to analyze the static and dynamic behaviors of functionally graded graphene reinforced composite (FG-GRC) beam with geometric imperfection subjected to thermo-electro-mechanical load. Three different geometric imperfections are considered. Four different distribution patterns of graphene nanoplatelets (GPLs) are taken into consideration. The effective properties of the geometrically imperfect FG-GRC beam are estimated by the modified Halpin-Tsai model and rule of mixture. The nonlinear partial differential governing equations are deduced based on first-order shear deformation theory, von Kármán nonlinear displacement-strain relationship and Hamilton principle, and discretized as ordinary differential forms through the differential quadrature (DQ) method. Newmark-β method and iteration method are employed to numerically solve the governing equations. The effects of geometric imperfection, GPLs and piezoelectric actuators on bending and vibration of the geometrically imperfect FG-GRC beam subjected to thermo-electro-mechanical load are comprehensively investigated. The results clearly demonstrate that the coupling effect of geometric imperfections and thermo-electric-mechanical loads can introduce an additional transverse load acting along the length of the geometrically imperfect FG-GRC beam, and hence makes a significant difference on its static and dynamic behaviors.