Fluid-supported elastic sheet under compression: Multifold solutions

TL;DR

This paper investigates the buckling behavior of a floating elastic sheet under compression, revealing multiple localized fold solutions, their bifurcations, energies, and stability properties through numerical and analytical methods.

Contribution

It introduces a comprehensive analysis of localized fold states in a floating elastic sheet, combining numerical continuation and weakly nonlinear analysis to explore bifurcations and stability.

Findings

Multiple localized fold solutions identified

Energy differences between states decrease exponentially with localization

Stability analysis of competing buckled states conducted

Abstract

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 single fold 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 properties of the different competing states are established and provide a basis for the study of fold interactions.