Unified classification of stability of pin-jointed bar assemblies

Based on the energy criterion and geometrical nonlinearity theory, this paper broadens conventional concepts of structural stability to explain some non-generic stability phenomena of pin-jointed bar assemblies in a unified and coherent way. A novel classification for stability conditions of such kind of structures is put forward, using analysis of the constitution of the tangential stiffness matrix. Some classical issues, including geometrical stability and stability of mechanisms, are re-investigated under this new concept as part of the formal theoretical development. Effects of bars stiffness are introduced into the necessary and sufficient conditions of intrinsic stability (stability of structure devoid of internal forces). The stability conditions for mechanisms, whether they acquire stiffness from self-stressing or external loading, are also probed. The stability of infinitesimal mechanism is expounded through consideration of high-order variations of the potential energy. Some discussions are provided at the end to build up an integrated understanding of stability of pin-jointed bar assemblies.