Nonlinear eccentric low-velocity impact analysis of a highly prestressed FGM rectangular plate, using a refined contact law

In the present paper, a nonlinear analysis is presented for response prediction of a low-velocity eccentric impact between a functionally graded rectangular plate and a rigid sphere or a projectile with a spherical nose. Some of the novelties of the present paper are (i) considering the more general case of eccentric impact, (ii) investigating effects of the initial in-plane loads on the impact responses of the functionally graded plates, especially for compressive loads that are comparable but not equal to the buckling loads, (iii) using a contact law that incorporates influences of the transverse variations of the material properties of the substrate layers and the plate thickness, and (iv) using nonlinear strain-displacement relations instead of using the traditional infinitesimal deformations assumption for assessment of influences of the initial preloads. Due to using von Karman strain-displacement relations and a nonlinear contact law, the governing equations are highly nonlinear. For this reason, an iterative solution scheme is employed. A sensitivity analysis is performed to investigate influences of the specifications of the plate and the indenter, the eccentric value, and the in-plane preloads on the indentation and force time histories. Results reveal that due to the resulting increase in the contact force, slightly higher damages may be expected for impacted FGM plates subjected to initial compressive in-plane loads.