Three-layered sandwich plate: Exact mathematical model

Abstract

The subject of this paper is the plate composed of two relatively stiff outer layers (skins) and a more compliant inner layer (soft interlayer, called core), i.e., three-layered (sandwich) plate. This system may represent composite and laminated plates, e.g., sandwich panels and decks. This paper presents a model that describes the behavior of three-layered plate by a system of exact analytical (explicit) equations, derived from the Kirchhoff–Love plate assumptions. Accordingly, this system of equations corresponds to the Kirchhoff–Love equation of the plate.The pie-chart of research on sandwiches allots only a slight slice to analytical modeling, while it allots the largest slice to approximate prediction methods. In particular, the three-layered plate lacked the two-dimensional governing equations. Empirical or semi-empirical formulations, finite element models, a priori formulas based on simplified or rough theories may represent more accessible research topics; however, they suffer from high layer-to-interlayer stiffness ratios, which impinge on their results. Thus, these approximate prediction methods provide unsatisfactory results for the continuously increasing ratios that the industry is developing, and will be developing, to increase ever more the stiffness-to-density and strength-to-density ratios of the sandwiches. Conversely, this model, whose formulation is exact, does not suffer whatsoever from high skin-to-core elastic modulus ratios, and therefore it is specifically dedicated to modern, advanced, and innovative sandwich plates.To apply this exact model is less time consuming than to generate any finite element mesh or to apply any approximate method. Consequently, approximate methods become completely unnecessary for the three-layered plates that comply with Kirchhoff–Love plate assumptions. On the contrary, for the three-layered plates that do not comply with these assumptions, the finite element models continue to represent a viable means, provided that beforehand their reliability is checked and their free parameters are calibrated. To facilitate check and calibration, exact results from the model are provided in the paper, which finite element results can be compared to.