Structural theory and finite element modelling of linear elastic sandwich beams subject to severe boundary conditions

We further develop and improve a structural theory recently proposed by our group, with the aim of determining the simplest kinematics which allows the accurate modelling of any plane sandwich beam in the linear elastic regime. The model builds on Yu-Krajcinovic zig-zag warping, in which each layer, of arbitrary thickness and modulus, is allowed to shear through an independent cross-section rotation. Moreover, the core kinematics is enriched by allowing for a quadratic variation along the core thickness of both the longitudinal and the transverse displacement components. By implementing the proposed theory in a structural finite element, we discuss the contribution to the modelling capability of each independent term entering the chosen core kinematics. Such kinematics, along with a Jourawski-like approach to evaluate the shear stress, leads to a model which can accurately describe the stress state for any relative stiffness between the sandwich layers, even in the case of "severe boundary conditions", including loading on a specific skin coupled with constraints realised, on certain cross-sections, on the opposite skin only. We demonstrate this claim by considering many benchmarks and by a thorough comparison with the results obtained from continuum plane stress Finite Element (FE) simulations. From such a comparison we also clearly establish the superior computational efficiency of the new structural finite element with respect to the continuum FE analyses.