Nonlinear composite beam finite elements with arbitrary cross-sectional displacement fields

This paper presents an approach to developing one-dimensional structural theories for quasi-static nonlinear analysis. This paper is developed within the beam Unified Formulation, which enables results with 3D-like accuracy. In the context of nonlinear analysis, however, it is particularly desirable to obtain accurate stress results and equilibrium curves using efficient models, as these analyses often involve complex and timeconsuming procedures. Thus, the purpose of this paper is to enable each displacement component to be represented by an independent expansion function, allowing the integration of both Taylor- and Lagrangebased models within a unified framework. Moreover, the method should facilitate the combination of the Equivalent Single Layer and Layer-Wise approaches within a single structural theory. The proposed structural model is implemented within a finite element framework using a modified version of the Unified formulation, enabling the analysis of complex structures. The governing equations are derived through the principle of virtual displacements and linearized using the Newton–Raphson method. Furthermore, the Crisfield arc-length method is adopted as the incremental solution scheme. The accuracy of the proposed models is assessed by comparing displacement and stress results for composite multilayered beams with data from the literature, focusing on large-deflection and post-buckling behaviours.