Analysis of multiple bifurcation behavior for periodic structures

The classification of simple singularities in the post-buckling analysis of truss structures is well-known for elastic stability. To focus on multiple singularities including a hilltop bifurcation point (h-BP) and its bifurcation paths, we reviewed the multiple bifurcation analysis of multi-folding microstructure (MFM) models with periodic symmetry. Because the Jacobian at the h-BP of the MFM involves multiple 0-eigenvalues, it is challenging to analyse the bifurcation paths from the h-BP accurately. In this study, we investigated the multiple folding mechanism by analysing the neighbourhood of the h-BP and the symmetric subgroups of the geometric system in the two-dimensional plane and three-dimensional core of the MFM. We demonstrated that through the classification of multiple h-BP and bifurcation paths, it is possible to determine the unknown bifurcation equilibrium paths following h-BP, based on the Jacobian stability and the mechanism of symmetric subgroups in group theory containing the relationships between the primary path and the known bifurcation path(s) in the MFM system with periodic symmetry.