Energy method solution for the postbuckling response of an axially loaded bilaterally constrained beam

• A novel model for the postbuckling of a bilaterally constrained elastica is proposed.
• Both force- and displacement-control axial loading formulations are presented.
• The model accurately predicts buckling mode transitions and the flattening behavior.
• The kinetic energy released through mode transitions is determined by dynamic analysis.

Bistable and multistable structures have shown great usefulness in many applications such as MEMS actuation and energy harvesting. Bistability of structures can be achieved through buckling. Confining a buckled beam between two lateral constraints allows it to buckle into higher modes as the axial load increases. This paper presents a theoretical study of the postbuckling response of a bilaterally constrained elastica subjected to gradually increased axial load. Equilibrium states are determined using an energy method. Under small deformation assumptions, the total potential energy is minimized under the defined constraints. The presented model allows for an accurate representation of the flatting behavior and the increase in the length of contact areas with the lateral constraints before the sudden snapping between equilibrium states. Mode transitions are manifested by jumps in the response curves. Previously developed models based on geometry and symmetries overestimate the required forces for higher equilibrium modes and do not match experimental observations. Results are validated with experimental force–displacement measurements under both force- and displacement-control. The kinetic energy released during buckling mode transitions is determined by a dynamic analysis.