Interrogating the Configuration Space of Postbuckled Beams

Abstract

This paper considers the global configuration space of postbuckled structures. Initially, a slender buckled beam is considered. The boundary conditions are pinned at one end and fully fixed at the other. The pin-end of the initially flat beam is moved toward the other end by a small amount. This causes the beam to buckle laterally (the beam is axially inextensional) with a characteristic shape. Since this is the outcome of a stable-symmetric pitchfork bifurcation, the buckled shape possesses a near mirror-image shape on the other side. Which of the two available equilibrium configurations is taken up depends on the usual, often small, symmetry-breaking effects commonly encountered in axially loaded systems. Given fixed conditions to maintain this initial buckled shape we then apply a moment at the pinned end. The relation between the applied moment and the change in shape is the primary focus of this study. The extent of the buckling (end shortening) is varied, with the magnitude of the moment, as a function of the angle, providing considerable information about the potential energy landscape in which the axially loaded system operates. The applied moment can be thought of as a probing mechanism whereby various equilibrium configurations are revealed, together with information regarding their stability and robustness. A similar approach is then used where the structure consists of two nominally identical beams attached at a right angle. In both cases, the opposite end from the actuation is clamped. An experimental study is conducted on 3D-printed specimens, and this is compared with a finite element analysis using ANSYS, and a large-deflection elastica analysis.