Theoretical model of low-velocity impact on foam-core sandwich panels using finite difference method

In this article, a three-dimensional solution based on the Fourier's series and finite difference method has been presented to study the low-velocity impact on sandwich panels with foam core and composite face sheets. The Navier's equations are derived and displacements are substituted by their corresponding Fourier's series and three partial differential equations with coefficients of Fourier's series are obtained. The contact force has been considered as a Fourier's series of impactor displacement and deflection of top face sheet. Also, the model is verified by experiments performed on sandwich panel with epoxy/woven-fiberglass composites, face sheets and polyurethane foam core, and other researchers' works. The history of contact forces and lateral displacement of contact point has been obtained experimentally and compared with theoretical model. Finally, the effects of impact energy and geometrical parameters including in-plane dimension ratio, core thickness, and face sheet thickness on contact force and lateral deflection histories have been investigated.