On explicit analytic solutions for the accurate evaluation of the shear stress in sandwich beams with a clamped end

Abstract

We focus on analytic solutions for the accurate computation of the shear stress in sandwich beams under flexure. To this purpose, we follow the strategy recently proposed by our group and apply the Jourawski method to the structural beam model based on the zigzag warping. We consider sandwiches whose cross-section is symmetric with respect to the neutral axis and whose skin shear deformation and core longitudinal stress are accounted for (that is, we do not limit our attention to thin skins nor to antiplane sandwiches). We obtain explicit analytic expressions for the cases of cantilever and propped-cantilever beams subject to uniform transverse load. The comparison with numerical solutions obtained through plane stress finite element simulations shows the excellent accuracy of the analytic solution, apart in a region close to the fully clamped cross-section, where the finite element solution itself is unreliable, while the new analytic solutions provide useful estimates.