An analytical solution for multilayered beams subjected to ends loads

An alternative model for multilayered beams undergoing axial, shear and bending loads applied at the beam’s ends is developed. It is based on a layer-wise kinematics, which inherently fulfills the equilibrium equations at layer level and the interface continuity conditions. This kinematics is suitably expressed by introducing a set of generalized variables representative of the beam midline displacement field, which become the primary variables of the problem governing equations. As a consequence, the proposed beam model exhibits the computational characteristics of an equivalent single layer model and possesses the accuracy of layer-wise beam theories, as well. Closed form solutions for different beam support and load conditions are given. Validation results are presented for composite laminates and functionally graded beams are investigated to show the potentiality of the presented beam theory.