Singular configurations of structural systems

A singular configuration of a structural system is characterized by rank deficiency of the equilibrium matrix and kinematic matrix (the rank is lower than both the number of degrees of freedom and the number of constraints) . Such configurations exist only in systems that are not geometrically invariant (underconstrained structural systems) . Most interesting among them are systems with infinitesimal mobility which attracted attention of many prominent researchers. This paper puts the entire issue in a different perspective by addressing a critical, yet so far unexplored, aspect of singular configurations—their realizability. It turns out that the only generic, physically realizable type of a singular configuration is a system with first-order infinitesimal mobility, and even this cannot be constructed without inducing prestress of finite magnitude. All other singular configurations (unprestressable first-order mechanisms; higher-order mechanisms; and singular configurations of finite mechanisms) are unrealizable. Moreover, short of exact or symbolic calculation, they are also noncomputable and are just formal analytical constructs.