Reliability of First-Order Shear Deformation models for sandwich beams

Lorenzo Bardella

DICATA, University of Brescia, Via Branze 43, Brescia 25123, Italy


We are interested in sandwich beams whose skins may be thick (as defined in the classical book of Allen) and whose core stiffness along the sandwich longitudinal axis may be large enough to influence the deflection (that is, we also account for non-antiplane sandwiches), whereas the core is such that it is allowed to disregard its deformability along its height (i.e., the direction of the applied load). For such sandwiches we are particularly interested in investigating the reliability of simple models, as the First-Order Shear Deformation models, for the accurate computation of the deflection in the linear elastic range. We therefore compare different theories on the basis of Finite Element simulations and focus on the case of a propped cantilever beam supporting a uniform load. In fact, this boundary value problem leads to slightly different conclusions than those previously drawn based on statically determinate cases such as the three-point bending. The analysis suggests that known models may be largely inaccurate in predicting the sandwich behaviour under bending and shear, depending on a peculiarity of the actual sandwich kinematics indirectly describing the interaction between skins and core, in turn due both to their material and geometrical properties and to the boundary conditions.

Author Keywords: sandwich beam; Total Potential Energy; Ritz method; Allen's superposition theory; Timoshenko beam theory; Jourawsky shear theory; de Saint-Venant principle; Finite Element method