عنوان مقاله [English]
Available low-velocity impact analyses have mainly been presented for isotropic or laminated composite (especially those with transversely isotropic material properties) structures. In the mentioned models, only the stiffness of the impacted region is considered and the influence of the stiffness of the underneath layers on the impact responses is discarded. It is evident that the stiffness of the substrate layers may considerably affect the contact stiffness of the contact region. In some other papers, the nonlinear Hertz-type contact law has been replaced by a linear one. In the present paper, in addition to overcoming the mentioned shortcomings, it is intended to extend the previous research to functionally graded plates, whose material properties vary in the transverse direction according to a power law. The apparent contact stiffness is determined through calculation of the volume mean of the material properties and by employing Turners procedure. Among other superiorities, the solution is presented in a semi-analytical form. The governing equations of the plate are derived based on the classical plate theory, and the analytical solution is of a Navier-type. \ The \ proposed \ solution is \ adopted, according to the boundary condition of simply supported edges. Therefore, \ the \ plate is \ modeled as a continuous \ rather \ than \ discrete \ system. The \ resulted \ nonlinear time-dependent equations are solved using the Runge-Kutta numerical time integration method. In the present research, effects of various parameters of the indenter (radius, mass, velocity) and the functionally graded plate (power law exponent or the so-called volume fraction index and thickness of the plate) on the low-velocity responses (indentation, contact force, and lateral deflection) are investigated in the elastic region, employing non-linear Hertzs contact law. Since the present results are extracted based on an analytical method, modeling, linearization, and common numerical errors are prevented. Results of the present research are verified by results reported by other researchers for special cases.