Finite element analysis of post-buckling dynamics in plates. Part II: A non-stationary analysis

With the secondary bifurcation and the local post-secondary buckling behavior being analyzed in Part I, Part II of this study consists of developing an adaptive non-stationary load sweeping algorithm to investigate post-buckling dynamics and mode jumping phenomena of generally (mechanically and thermally) loaded thin plates in a global context. The nonstationary sweeping procedure has the merits of adapting large load steps to capture static characteristics of stable equilibrium paths both before and after mode jumping and reduce automatically the step size to ensure a dynamic transition between the two stable branches. Thus, it is computationally effective. Furthermore, by adopting the non-stationary sweeping scheme, this procedure can avoid spurious convergence of the transient response to an unstable equilibrium. Corresponding to different post-secondary bifurcation forms, which are determined using asymptotical finite element analysis developed in Part I, subsequent buckling patterns of various complexity occurring after mode jumping are obtained using the method developed in this article. Qualitative changes in post-buckled patterns are observed after the occurrence of the secondary bifurcation or the mode jumping. Free vibration analysis using the tangent stiffness matrix obtained from the converged static or dynamic solutions shows a vibration modal shifting phenomena occurs during the process of the load sweep. The spurious convergence phenomenon caused by the application of the traditional hybrid static–dynamic method is found and explained.