Postbuckling and mode jumping analysis of composite laminates using an asymptotically correct, geometrically non-linear theory

An analytic method is presented in this paper to study the postbuckling and mode jumping behavior of bi-axially compressed composite laminates. The governing partial differential equations (PDEs) are derived rigorously from an asymptotically correct, geometrically non-linear theory. A novel and relatively simpler solution approach is developed to solve the two coupled fourth-order PDEs, namely, the compatibility equation and the dynamic governing equation. The generalized Galerkin method is used to solve boundary value problems corresponding to antisymmetric angle-ply and cross-ply composite plates, respectively. The variety of possible modal interactions is expressed in an explicit and concise form by transforming the coupled non-linear governing equations into a system of non-linear ordinary differential equations (ODEs).The comparison between the present method and the finite element analysis (FEA) shows a pretty good match in their numerical results in the primary postbuckling region. While the FEA may lose its convergence when solution comes close to the secondary bifurcation point, the analytic approach has the capability of exploring deeply into the post-secondary buckling realm and capture the mode jumping phenomenon for various combinations of plate configurations and in-plane boundary conditions. Free vibration along the stable primary postbuckling and the jumped equilibrium paths are also studied.