Unified refined beam theory applied to the spectral finite element method for analysis of laminated composites

Due to the limitation that the classical beam theories have in representing transversal shear stress fields, new theories, called high order, have been emerging. In this work, the principal high order theories are unified in single kinematics and applied to the Equivalent Single Layer Theory. The governing equations and the boundary conditions for laminated beams are consistent variational obtained. From the equilibrium equations, the high order spectral finite element model was developed using the polynomial functions of Hermite and Lagrange, with interpolants in the zeros of Lobatto's polynomials. Finally, to demonstrate the finite element model's outstanding efficiency, numerical results (static and dynamic) are shown and compared with the elasticity theory solution.