Underconstrained structural systems

Abstract Underconstrained structural systems have fewer independent constraints than necessary to be geometrically invariant. Yet these systems can be statically indeterminate, with far-reaching implications for their kinematic mobility. In particular, such a system may possess a unique geometric configuration, in which it lacks finite mobility and allows a stable self-stress. The possibility of stable self-stress is shown to be a statical (as opposed to geometric) criterion for underconstrained systems with only infinitesimal kinematic mobility. Both local and global properties of underconstrained systems are investigated within the context of statical-kinematic interrelations. Among these, the relation between the equilibrium loads and configurations is of special interest as it underlies the concept of statically controlled geometry.