Equivalent single-layer theory for a complete stress field in sandwich panels under arbitrarily distributed loading

In single-layer theory, the displacement components represent the weighted-average through the thickness of the sandwich panel. Although discrete-layer theories are more representative of sandwich construction than the single-layer theories, they suffer from an excessive number of field variables in proportion to the number of layers. In this study, utilizing Reissner’s definitions for kinematics of thick plates, the displacement components at any point on the plate are approximated in terms of weighted-average quantities (displacements and rotations) that are functions of the in-plane coordinates. The equations of equilibrium and boundary conditions of the sandwich panel are derived by employing the principle of virtual displacements. The solution for an arbitrarily distributed load is obtained by employing Fourier series representations of the unknown field variables. This single-layer theory is validated against an analytical solution for simply supported square sandwich panels under pressure over a small region on the face sheet and is also compared with previous single-layer plate theories.