Explicit analytic solutions for the accurate evaluation of the shear stresses in sandwich beams
Lorenzo Bardella and Daniele Tonelli
DICATA, University of Brescia, Via Branze 43, Brescia 25123, Italy
We focus on analytic solutions for the accurate computation of the shear stresses in sandwich beams under flexure. We propose to apply the Jourawsky idea for treating the shear problem to the structural beam model based on the piecewise linear (i.e., zig-zag) warping. We show that this approach works very well for sandwiches in which one may neglect the normal deformation component along the core thickness. We limit our attention to sandwiches whose cross-section is symmetric with respect to the neutral axis. For such a case we obtain general expressions for the shear stresses in terms of the rotations of skins and core. By resorting to the description of the zig-zag warping developed by Dusan Krajcinovic in the Seventies, we obtain an explicit analytic expression for the case of simply supported sandwich beams subject to uniform transversal loading. The comparison with finite element simulations shows the excellent accuracy and wide range of applicability of the proposed method.
Author Keywords: Sandwich structures; Shear deformation; Shear stress; Stress analysis; Finite element method