Controlling the snap-through behavior of an elastica strip by cuts

Abstract

This work examines the snap-through behavior of a clamped-clamped elastica made from initially flat, thin, cut sheets under increasing vertical concentrated load acting at midspan. A two-parameter, symmetric pattern is introduced to conduct a numerical parameter analysis across three different support distances. When the support distance is one-quarter of the total length of the sheet, the structure loses stability at a symmetry point bifurcation over a wide range of parameters. Additionally, there exists a small range of parameters where limit point bifurcation occurs. In this case, the cuts can induce symmetry in the stability loss. For larger support distances (half or three-quarters of the total length), limit point bifurcation occurs only for small cuts, and there is a range of cut parameters that leads to monotonic monostability, indicating that no stability loss occurs. These findings are supported by experimental data. Overall, our research demonstrates that carefully designed cut patterns can either control the mode of stability loss in elastica strips or suppress it entirely.