On the decoupled biharmonic airy stress function for the square-end adhesive layer and sandwich structure core

Abstract

To accurately model the stress transfer through a square ended sandwich structure core or a square ended adhesive layer, a Decoupled Biharmonic Airy stress function solution is derived. This solution satisfies the zero stress natural boundary conditions at the traction free surfaces and the matched displacement essential boundary conditions at the top and bottom material interfaces. This model asymptotically satisfies the biharmonic equation on the Airy stress function that arises from simultaneous imposition of point equilibrium and displacement field compatibility. For an example case, the stress field is investigated for an idealized state of pure shear. In this case, the shear and normal stress fields are found to be finite and differentiable throughout the domain. This includes finite valued through-thickness normal stresses at the sharp corners of an elastic medium. The resulting stress components are compared with the Goland–Reissner model and the Closed Form Higher Order (CFHO) model and it is found that the Goland–Reissner model and the CFHO model significantly underestimate the peak stress values as compared to the Decoupled Biharmonic model.