Secondary Instability and Mode Jumping of Deep Thermoelastically Buckled Composite Laminates

An analytic method is presented to study the secondary instability (bifurcation) and mode jumping of thermomechanically deep buckled composite laminates. Unlike most ad hoc approaches, the governing partial differential equations (PDEs) and constitutive relations are rigorously derived from an asymptotically correct, geometrically nonlinear theory. A novel and 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. The variety of possible modal interactions is expressed in an explicit and concise form by transforming the coupled nonlinear governing equations into a system of nonlinear 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 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. Qualitatively different propagations of buckling pattern are observed before and after mode jumping. Free vibration along the stable primary postbuckling and the jumped equilibrium paths are also studied.