Post-buckling analysis of composite beams: Simple and accurate closed-form expressions

The present study proposes simple, elegant, and accurate closed-form expressions for predicting the post-buckling behavior of composite beams with axially immovable ends using the Rayleigh–Ritz (R–R) method, where geometric nonlinearity arises from mid-plane stretching of the beam. The displacement fields used for the analysis are coupled using the axial equilibrium equation of the composite beam. An exhaustive set of beam boundary conditions are studied, namely, hinged–hinged, clamped–clamped, clamped–hinged, hinged–guided, and clamped–guided beams in order to prove the efficacy of the present formulation. Post-buckling analysis results are presented for laminated composite beam with symmetric and asymmetric layup schemes. Post-buckling analysis results obtained using the R–R method are compared with the results obtained from the finite element (FE) method for all layup schemes considered and comparison shows an excellent match for all the beam boundary conditions considered and thereby proves simplicity, accuracy, and robustness of present closed-form analytical expressions for predicting the buckling and post-buckling behavior of composite beams with symmetric and asymmetric layup orientations.