Bi-stable lateral buckled beam: Equilibrium configurations analysis based on perturbation method

Abstract

This paper lays stress on the equilibrium configurations analysis of a bi-stable unit composed of two cantilever beams with lateral post-buckling deformations. Two equilibrium configurations of the unit are described by deformations of the cantilever beam which is subjected to a shear force and has a boundary condition of zero-twist at the cantilever end. An analytical model based on the perturbation method was established for accurate post-buckling analysis of the beams. Experiments and numerical studies validate the analytical solutions on slender beams. Geometric parameters analysis on beam deformations demonstrates the application and limitation of the theoretical model. Finally, a multi-stable structure assembled by such bi-stable unit is illustrated, whose shapes are predicated by the analytical method. These results can be used to guide the design of shape reconfigurable structures with adjustable mechanical properties.