Low velocity impact modeling of functionally graded carbon nanotube reinforced composite (FG-CNTRC) plates with arbitrary geometry and general boundary conditions

The full dynamic response of FG-CNT reinforced composite plates with arbitrary geometry subjected to impact loading is considered in the present paper. The CNT reinforcement distribution is considered either uniform or functionally graded along the plate thickness and the equivalent mechanical properties of reinforced composite plates are estimated according to the extended rule of mixtures. The derived governing equations are based on high-order shear deformation theory, using Hamilton's principle. An integration scheme appropriate for calculating double integral with variable limits is developed based on the Simpson's rule to evaluate the components of Hamilton's equation. A two-dimensional Ritz formulation appropriate for general boundary conditions is incorporated in the nonlinear Hertzian contact law to establish the equations of motion. A well-known fourth-order Runge-Kutta method is employed to solve the resulting equations in time domain. The validation of the proposed model is accomplished by comparing its results and those published in the literature and good agreement is achieved. A comprehensive sensitivity analysis is conducted to study the effect of various involved parameters such as CNT volume fraction and its distribution profile along the thickness, boundary conditions, temperature rising and in-plane loading on impact characteristics of both circular and triangular plates.