Static snapping load of a hinged extensible elastica

In this paper we discuss the static snapping load of a hinged buckled beam subject to a midpoint force. Three different models are compared; they are small-deformation theory, inextensible elastica, and extensible elastica. As expected, small-deformation theory fails to predict the static snapping load accurately in the large-deformation range. In the small-deformation range, on the other hand, inextensible elastica model predicts the static snapping load poorly. Finally, by allowing the elastica to be extensible, it is observed that one can predict the static snapping load accurately both in the small- and large-deformation ranges.