Multiple buckled states of rectangular plates

We consider the buckling of a simply supported plate subjected to a constant edge thrust λ. The aspect ratio l is such that the critical thrust (the first bifurcation point of the associated non-linear eigenvalue problem) is of multiplicity two. A study of the non-linear static problem indicates that there are nine possible equilibrium states. One of these corresponds to the unbuckled state while the remaining eight represent buckled states. A linear stability analysis and a calculation of the potential energy of each of the static solutions indicates that four of the solutions are stable and five are unstable.