A higher-order sandwich plate theory accounting for 3-D stresses

In this paper we extend a layerwise higher-order shear-deformation theory to model a sandwich plate impacting with an elastic foundation at a low velocity. A new concept of sublaminates is introduced, and the new sandwich plate theory satisfies the continuity conditions of interlaminar shear and normal stresses, accommodates the normal and shear stresses on the bonding surfaces, and accounts for non-uniform distributions of transverse shear stresses in each layer. Moreover, the use of sublaminates enables the modeling of shear warpings that change with the spatial location, vibration frequency, and loading and boundary conditions. A finite-element model based on this sandwich plate theory is derived for performing direct transient analyses to predict the initiation and location of critical matrix crack and the threshold of impact damage. Moreover, analytical shear warping functions, shear coupling functions, and normal strain functions due to in-plane stretching, bending, transverse shearing, and surface loading are presented.