Static analysis of laminated beams via a unified formulation

A linear static analysis of composite beams is presented in this work. Simply supported, cross-ply laminated beams are examined. Beams with different values of length-to-thickness ratio subjected to bending loadings are considered. Carrera’s Unified Formulation is adopted to derive several hierarchical theories. The kinematic field is imposed above the cross-section via a N-order polynomials approximation of the displacements unknown variables. The governing equations and boundary conditions are variationally obtained through the Principle of Virtual Displacements. A closed form, Navier-type solution is adopted. Thanks to this formulation, quasi three-dimensional strain and stress fields can be obtained. Classical beam models, such as Euler–Bernoulli’s and Timoshenko’s, are obtained as particular cases. Results are validated in terms of accuracy and computational costs towards three-dimensional FE models implemented in the commercial code ANSYS. Numerical investigations show that good results are obtained as long as the appropriate expansion order is used.