Interlaminar Stresses Analysis for laminated composite beams on Elastic foundation with Horizontal and Vertical springs

In this manuscript, in-plane normal and shear interlaminar stresses in composite Timoshenko beam under transverse loading placed on the elastic foundation are studied. The elastic behavior of interlaminar stresses at the interface of adjacent layers is modeled by radial and tangential springs of high stiffnesses. In the first, governing equations and boundary conditions are derived by the virtual work principle and then they are solved by generalized differential quadrature method. By calculating the displacements of the beam laminates, the interlaminar stresses, which are the reaction of radial and tangential springs between adjacent layers of the laminated beam, are obtained. Also, the other stresses of the beam are calculated and drawn by equilibrium equations. Comparison between the results of presented analysis for a beam the and the results of three dimensional elastic solution is shown that the presented method has good accurate to predict the in-plane stresses. The results showed that Winkler effects on interlaminar stresses are lower than Pasternak effects. Also, the elastic foundation caused decrease and increase for interlaminar shear stress and normal stress, respectively.