Nonlinear response of functionally graded plates under moving load

• Showing the importance of nonlinear analysis of thin FG plates under moving loads.
• Increasing the plate edge constraint reduces the effect of geometrical nonlinearity.
• Aspect ratio has significant affect on the nonlinear response of the FG plates.
• Increasing the load velocity, reduce the oscillatory behavior of nonlinear response.
• Benchmark solution for the future work is presented.

The nonlinear response of functionally graded (FG) plates under moving load is studied based on the classical plate theory (CPT). The geometrical nonlinearity due to large deformation is modeled using Green's strain tensor under von Kármán assumptions. The material properties vary continuously through the plate thickness and are obtained according to the rule of mixture. The finite element method (FEM) in conjunction with Newmark’s time integration scheme and Newton–Raphson method are employed to solve the nonlinear system of equations of motion subjected to the different boundary conditions. The formulation and method of solution are validated by studying their convergence behavior and performing the comparison studies with existing results in the literature in the limit cases. Finally, comparison studies between the nonlinear and linear response of FG plates under moving load are carried out and the influences of the material graded index, moving load velocity and plate aspect ratio are investigated.