Nonlinear bending analysis of FG-CNTRC plate resting on elastic foundation by natural element method

A nonlinear numerical analysis is addressed for a functionally graded carbon nanotube-reinforced composite (FGCNTRC) plate on elastic foundation. The large deflection bending problem is formulated according to the von K ' arm ' an nonlinear theory and the (1,1,0)* hierarchical model. And, it is numerically solved by 2-D (twodimensional) natural element method (NEM) which is characterized by a high accuracy even for coarse grid. The derived nonlinear matrix equations are iteratively calculated by combining the load increment scheme and the Newton-Raphson iteration method. The present method was verified through the benchmark test, where the present method shows excellent agreement with the reference solutions. The nonlinear behavior of FG-CNTRC plate on elastic foundation is evaluated in terms of the non-dimensional deflection and bending moment. These non-dimensional quantities are examined with respect to the foundation stiffness, the volume fraction and gradient pattern of CNT, the aspect and width-thickness ratios of plate and the boundary condition. From the parametric experiments, it is found that both non-dimensional quantities are significantly influenced by such parameters.