Analysis of laminated beams via Unified Formulation and Legendre polynomial expansions

Abstract

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 behaviours. 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.

Extension of MITC to higher‐order beam models and shear locking analysis for compact, thin‐walled, and composite structures

“…In this context, a cantilever beam consisting in a 2-layer asymmetric [0 • , 90 • ] cross-ply is considered in this section. This structural problem, represented in Figure 8, was already studied by Pagani et al 54 The geometrical dimensions are b = 0.2 m, h = 0.1 m, and L = 2 m. Both laminae have the same thickness, equal to h∕2, and the material properties, given in a dimensionless form, are E L ∕E T = 25, LT = TT = 0.25, G LT ∕G TT = 0.25, where the subscript L corresponds to the fiber direction and T refers to the normal direction. The beam is loaded at the free-tip with 4 point forces of the same magnitude, F z = 25 N, as shown in Figure 8.…”

“…Hierarchical Legendre expansions theories have been used for the analysis of laminated structures 54 and further extended to develop geometrically exact beam models through the blending mapping technique. 55…”

Micromechanics Modeling of Unit Cells Using CUF Beam Models and the Mechanics of Structure Genome

“…The choice of F τ defines the theory of structure employed in the model. In the present work, the Hierarchical Legendre Expansion is selected due to its remarkable capabilities in capturing component-wise solutions [17].…”

Computationally efficient, high-fidelity micromechanics framework using refined 1D models

“…The efficiency of the framework is derived from the ability of CUF models to provide accurate 3D displacement and stress fields at a reduced computational cost (approximately one order of magnitude of degrees of freedom less as compared to standard 3D brick elements) [24,25,27]. Over the last couple of decades, CUF models have been extensively used for wide range of structural simulations such as static analysis of laminated beams [28], dynamic response for aerospace structures [29], vibration characteristics of rotating structures [30], evaluation of failure indices in composite structures [26], buckling and post-buckling analysis of compact and composite structures [31,32]. Carrera et al reported an extended review of recent developments in refined theories for beam based on CUF with particular focus on diverse applications [33].…”