Accurate stress fields of post-buckled laminated composite beams accounting for various kinematics

Abstract

Highly flexible laminated composite structures, prone to suffering large-deflection and post-buckling, have been successfully employed in a number of scenarios. Therefore, accurate predictions of their stress distributions in the geometrically nonlinear analysis are of paramount importance for their design and failure evaluation. In this paper, for composite beams subjected to large-deflection and post-buckling, we investigate the effectiveness of different geometrically nonlinear strain approximations for the description of their nonlinear static response and for the determination of stress distributions. For this purpose, a unified formulation of geometrically nonlinear refined beam theory based on the Carrera Unified Formulation (CUF) and a total Lagrangian approach constitutes the basis of our analysis. Accordingly, various kinematics of one-dimensional structures are formulated via an appropriate index notation and an arbitrary cross-section expansion of the generalized variables, leading to lower- to higher-order beam models with only pure displacement variables for laminated composite beams. In view of the intrinsic scalable nature of CUF and by exploiting the principle of virtual work and a finite element approximation, nonlinear governing equations corresponding to various nonlinear strain assumptions can be straightforwardly and easily formulated in terms of fundamental nuclei, which are independent of the theory approximation order. Several numerical assessments are conducted, including large-deflection and post-buckling analyses of asymmetric and symmetric laminated beams under compression loadings. The numerical solutions are solved by using a Newton–Raphson linearization scheme along with a path-following method based on the arc-length constraint. Our numerical findings demonstrate the capabilities of the CUF model to calculate the large-deflection and post-buckling equilibrium curves as well as the stress distributions with high accuracy, which could be a basis to assess the validation ranges of various kinematics and different nonlinear strain approximations.