An equilibrium method for the global computation of critical configurations of elastic linkages

•An equilibrium method is developed for computing critical equilibrium states.•Non-linearly elastic linkages are studied considering large displacements.•Statically indeterminate structures and general loadings are dealt with.•A global, robust numerical procedure is utilised.•Snapping phenomena and structurally unstable equilibrium states are revealed.

In this paper we develop an equilibrium method for the derivation of critical equilibrium configurations of a non-linearly elastic, discrete rod model, which is supported in a statically indeterminate way, and subjected to general loading. We construct a global computation scheme for the critical equilibrium configurations and demonstrate the effectiveness of the method via a clamped-pinned rod fabricated from linearly elastic, or specially hardening/softening material, loaded by either a horizontal or a follower force. We show some correspondence between the equilibrium states of these two load cases, and different snapping processes are revealed.