A novel theory for laminated composite beam

The analysis of laminate or sandwich structures has a large field of application, in particular in the aerospace industries. As consequence, a great number of theories have been developed due to the specific mechanisms of failure. However, to analyze highly localized effects (free-edges, cut-outs or concentrated loads), the most appropriate strategy is probably the adoption of a global-local solution where beam theory will play an essential role, providing global results to be used as boundary condition of the local domain. This paper presents a novel theory (with a unified approach for isotropic, laminated and sandwich beams and include a new vision about the shear correction factor) where the solution may be obtained from a superposition of a sequence of known equilibrium solutions (referred to as Fundamental States). It is not a standard method of Ritz since the basis functions for the approximations are invariant components of the stress and strain fields corresponding to the Fundamental States. Another point is that the problem is completely and accurately represented in terms of stress, strain and displacement moments which are internally consistent, and avoid, in general, the difficulty associated with the fact that the displacement fields are not differentiable through the thickness. A companion paper presents the application of this novel theory to the development of a FE model, for a k-layer prismatic beam, and its use in the analysis of a cantilever sandwich beam.