On Euler Buckling and Snap-Through

Abstract

Bistable structures have seen significant attention in recent years for their potential uses in switching and energy harvesting. The behavior of these structures, however, is very sensitive to boundary conditions and initial geometry making their calibration for various applications a difficult task. Additionally, obtaining the force-deformation behavior of these highly (geometrically) nonlinear structures often requires computationally expensive continuation methods. This paper presents a very simple closed-form method which estimates several important characteristics of classical snap-through curves of transversely loaded beams. The estimation is based on a relationship between classic Euler buckling of beams under axial load and the snap-through of post-buckled and curved beams and arches under transverse loading that has recently been investigated by the authors.