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. (15th January 2022) - Adhikari, Balakrishna; Singh, B.N.
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. Graphical abstract: Highlights: A simple Mori-Tanaka model has been presented for the CNT reinforced composites by considering size dependent parameters for different elastic modulus. The study of the different types of randomness of the CNT fiber in the matrix phase has been performed by employing the Mori-Tanaka mean field homogenization procedure and FEM RVE approach. The nonlinearity of all the field variables are considered using the Green-Lagrange strain field. Two new type of higher order shear strain function have been proposed.