Dynamic snapping of a hinged extensible elastica under a step load

• Crank–Nicolson method is adopted to solve for the dynamic response.
• A weak sense of convergence based on energy conservation is proposed.
• The concept of energy barrier is used to define a conservative dynamic critical load.

In this paper we study the transient response of a hinged extensible elastica under a step load at the midpoint. Emphasis is placed on the effect of extensibility on the dynamic snapping phenomenon. A second-order Crank–Nicolson method associated with finite difference discretization is employed to solve for the dynamic response. A weak sense of convergence based on the conservation of total energy over time is proposed. It is possible that under the same loading condition the extensible and inextensible elasticas may predict different types of snapping, one symmetric and another unsymmetric. Generally speaking, the inextensible model tends to overestimate the dynamic snapping load. It is impractical to determine the exact dynamic snapping load via direct simulation. Instead, the concept of energy barrier is used to find a conservative dynamic critical load, below which the elastica is guaranteed to be safe from snapping.