A new finite element model for low-velocity impact analysis of sandwich beams subjected to multiple projectiles

In this paper, a new finite element formulation is presented for high-order impact analysis of sandwich beams with any boundary conditions subjected to simultaneous multiple small projectiles. The contact of the projectiles may occur on arbitrary places on both faces of the beam. Hamilton’s principle is used for driving the governing partial differential equations of motion. The effect of each projectile is modeled by a one degree of freedom spring-mass system with variable stiffness by assuming the Hertzian contact law. The appropriate elemental matrices are derived for a sandwich beam element that carrying four sprung masses on both face sheets. Based on the presented formulation, an FE code is developed using the Newmark method with direct iteration process. The various cases are used to validate the predictions of the presented higher order theory and FE formulation shows good agreement with available results in the open literature and exact solution. Furthermore, numerical examples are presented to investigate effects of various parameters on the response of the structure.