Fluid-Supported Elastic Sheet Under Compression: Multifold Solutions

The properties of a hinged floating elastic sheet of finite length under compression are considered. Numerical continuation is used to compute spatially localized buckled states with many spatially localized folds. Both symmetric and antisymmetric states are computed and the corresponding bifurcation diagrams determined. Weakly nonlinear analysis is used to analyze the transition from periodic wrinkles to singlefold and multifold states and to compute their energy. States with the same number of folds have energies that barely differ from each other and the energy gap decreases exponentially as localization increases. The stability of the different competing states is studied and the multifold solutions are all found to be unstable. However, the decay time into solutions with fewer folds can be so slow that multifolds may appear to be stable. © 2019 American Physical Society.