A new analytical solution and novel energy formulations for non-linear eccentric impact analysis of composite multi-layer/sandwich plates resting on point supports

In the present research, an analytical solution based on a new idea of superposition of two kinematic descriptions is presented for dynamic response analysis of a multi-layer/sandwich composite plate with point supports subjected to an eccentric low-velocity impact. Direct and virtual-work-based novel energy formulations are proposed for the problem that take into account the potential energy of the indentation region. The nonlinear governing equations of motions are found based on minimization of the total potential energy of the whole mass-plate system, including work of the inertia forces, employing Ritz technique and transformation of the time-dependent nonlinear system of governing equations to a non-linear algebraic one through a novel concept. In contrast to the available researches, influence of the lower layers on the stiffness of the contact region is incorporated. Time-dependent responses of a sandwich composite plate with simply supported edges are compared with those of a plate resting on point supports. Verification of the results has been accomplished based on results of ABAQUS computer code. In the results section, the significant effects of the point supports (in comparison to the complete edge supports), initial velocity of the indenter, aspect ratio of the plate, and material properties of the layers on time histories of the contact force and lateral deflection of the plate are investigated.