Explicit analytic solutions for the accurate evaluation of the shear stresses in sandwich beams

The purpose of this study is to find analytic solutions for the accurate computation of the shear stresses in sandwich beams under flexure. Specifically, the Jourawski approach for treating the shear problem is applied to the structural beam model on the basis of the piecewise linear (i.e., zigzag) warping. This approach is shown to work very well for sandwiches in which one may neglect the normal deformation component along the core thickness. The focus is limited to sandwiches whose cross section is symmetric with respect to the neutral axis. For such a case, general expressions are obtained for the shear stresses in terms of the rotations of skins and core. By resorting to the description of the zigzag warping developed in the 1970s an explicit analytic expression is obtained 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.