On the fully elastic adhesive layer and sandwich core model: a spectral decomposition/ method of weighted residuals solution

To accurately model the stress transfer through a square-ended sandwich structure core and/or a square-ended adhesive layer, a biharmonic Airy stress function solution is derived using a spectral decomposition and a collocation expansion. The solution satisfies the zero stress conditions at the traction-free surfaces and the matched displacement conditions at the top and bottom material interfaces. The stress field is investigated for an idealized state of pure shear. For this example case, the shear and normal stress fields are found to be finite and differentiable everywhere in the domain. This includes finite valued stresses at the sharp corners of an elastic medium. The resulting stress components are compared with the Goland—Reissner, the Closed Form Higher Order, and COMSOL finite element models. The Spectral/ Collocation model is found to be superior owing to the satisfaction of the differential equations of deformation compatibility. It is also demonstrated that highly refined structural mechanics finite element models are unable to handle the stress-free conditions at corners of the traction-free surfaces.