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.