Analysis of laminated beams via Unified Formulation and Legendre polynomial expansions

A novel one-dimensional refined model for the analysis of laminated structures is presented in this paper. The Layer Wise approach in conjunction with the Carrera Unified Formulation (CUF) enables to create hierarchical refined models which are capable of detecting both local and global mechanical behaviors. In the framework of the CUF, the FEM matrices are obtained in the form of fundamental nuclei, which are independent of the theory adopted for the model and the FEM discretization along the beam axis. A hierarchical set of expansions above the cross-section is developed by adopting Legendre-class polynomials for the definition of the beam theory kinematics. In this way, the polynomial order of the expansion can be introduced as a free-parameter, enabling to vary the accuracy of the theory of structure in a straightforward manner. Compact cross-ply laminates with different number of layers, as well as more complex composite cases like box beams have been adopted to test the Hierarchical Legendre Expansions (HLE) adapted to the Layer Wise approach. The model has been verified through published literature and also through the use of the commercial software MSC Nastran.