A Coupled Mori–Tanaka model and FEM RVE approach for the geometrical nonlinear dynamic response of the FG-CNTRC plate based on a novel shear strain function using isogeometric finite element procedure

Abstract

In this study, Mori–Tanaka micromechanical model has been coupled with finite element representative volume element (RVE) approach to model functionally graded CNT reinforced (FG-CNTRC) plate. The coupled model also termed as extended Mori–Tanaka (E-MT) effectively determines the mechanical properties of the CNT reinforced composite plates. The E-MT model has the provision to consider different types orientation of the CNT fibers in matrix phase with the incorporation of second order orientation tensor matrix. The solution of the E-MT model has been propagated to the FG-CNTRC structural model to obtain the geometrically nonlinear response. The nonlinear governing equations of motions are obtained using the Green–Lagrange strain field and solved using nonlinear Newmark’s time integration method. The effect of various parameters like aspect ratio of CNT reinforcement, orientation of the CNT fibers, span thickness ratio of the plate, different type of edge constraint, and the gradation of the CNT fiber across the thickness of the plate have been studied in this paper.