A generalized nonlinear strong unified formulation for large deflection analysis of composite beam structures

Geometrically nonlinear analysis is an important procedure for accurate stress prediction of flexible beam structures that undergo large displacements and rotations. In the context of geometrically nonlinear analysis, the Unified Formulation (UF) has shown capability for efficient prediction of stresses in thin and thick composite beams using high-order layerwise beam kinematics based on finite element analysis. To further improve the efficiency of the UF-based model, we develop a geometrically nonlinear strong Unified Formulation (SUF) based on a high-order differential quadrature method for 3D large deflection analysis of composite beams. A detailed derivation of the 1D SUF combined with Serendipity Lagrange-based cross-sectional kinematics is provided. Numerical examples of cantilevered cross-ply and asymmetric composite laminates under transverse and compression loadings are presented to demonstrate the capacity of the proposed model to account for non-classical phenomena such as compression-bending and bend-twist couplings. To validate the performance of the SUF model, the results obtained for transverse and compression loadings are benchmarked against layerwise models (L-models) proposed in the literature and ABAQUS 3D finite element models. From the equilibrium path and through-thickness stress distributions obtained, it is demonstrated that SUF is able to predict the global and local behaviors of composite beams with much fewer degrees of freedom compared to L-models and ABAQUS models.