Large-deflection and post-buckling analyses of laminated composite beams by Carrera Unified Formulation

The Carrera Unified Formulation (CUF) was recently extended to deal with the geometric nonlinear analysis of solid cross-section and thin-walled metallic beams (Pagani and Carrera, 2017). The promising results provided enough confidence for exploring the capabilities of that methodology when dealing with large displacements and post-buckling response of composite laminated beams, which is the subject of the present work. Accordingly, by employing CUF, governing nonlinear equations of low- to higher-order beam theories for laminated beams are expressed in this paper as degenerated cases of the three-dimensional elasticity equilibrium via an appropriate index notation. In detail, although the provided equations are valid for any one-dimensional structural theory in a unified sense, layer-wise kinematics are employed in this paper through the use of Lagrange polynomial expansions of the primary mechanical variables. The principle of virtual work and a finite element approximation are used to formulate the governing equations in a total Lagrangian manner, whereas a Newton-Raphson linearization scheme along with a path-following method based on the arc-length constraint is employed to solve the geometrically nonlinear problem. Several numerical assessments are proposed, including post-buckling of symmetric cross-ply beams and large displacement analysis of asymmetric laminates under flexural and compression loadings.