Nonlinear buckling of imperfect systems with symmetric imperfections

The nonlinear stability of a 2-DOF imperfect elastic system with symmetric imperfections under a concentrated load is thoroughly discussed using an analytical approach. The perfect system loses its stability via an unstable symmetric bifurcation, which upon inclusion of imperfections is degenerated to a limit point. In this paper, it is shown that when the imperfections are symmetric, the system loses its stability through an unstable symmetric bifurcation point lying on the nonlinear prebuckling path. The corresponding critical (bifurcational) load is much lower than the limit point load related to symmetric buckling. The effect of initial imperfections on the critical bifurcational load (imperfection sensitivity) is also analytically discussed in detail. The paper is supplemented by various numerical results.