A structural model for plane sandwich beams including transverse core deformability and arbitrary boundary conditions
Ornella Mattei and Lorenzo Bardella
DICATAM, University of Brescia, Via Branze 43, Brescia 25123, Italy
In order to model the effect of arbitrary boundary conditions on plane linear elastic sandwich beams, we develop a structural theory relying on a zigzag warping: each layer, of arbitrary thickness and modulus, is described by the Timoshenko kinematics and, for the core, we further consider the transverse strain, which measures the normal deformability along the core thickness. This structural model, dependent on six functions of the beam axis coordinate, builds on the theory put forward by Dusan Krajcinovic in the early Seventies. By following a variational approach, we obtain and discuss the (Euler-Lagrange) balance equations and the (natural) boundary conditions governing the model. In sandwich beams having a soft core, this model can describe relevant features of the stress state due to "severe boundary conditions", including, for instance, loading on a specific skin coupled with constraints realised, at certain cross-sections, on the opposite skin only. In this work we focus on the flexure accompanied with non-uniform shear. In particular, we consider the cases of cantilever and propped-cantilever beams subject to uniform load. We provide accurate shear stress estimates by post-processing, through a Jourawski-like approach, the longitudinal normal stress predicted by the beam model. We demonstrate the capability of the proposed model by comparison of its results, obtained by using the Rayleigh-Ritz method, with those of continuum plane stress Finite Element (FE) simulations. The predictions of the present beam model are shown to be useful at fully clamped cross-sections, where displacement-based FE results are unreliable.
Author Keywords: Sandwich structures; Warping; Total Potential Energy